Chapter 132 - LEARNING RESULTS: PARAMETERS FOR ESSENTIAL INSTRUCTION

Current through 2022-14, April 6, 2022

SUMMARY: The Maine Department of Education Regulation 132 - The Maine Learning Results: Parameters for Essential Instruction establishes parameters for essential teaching and learning in grades Pre-Kindergarten through Diploma across eight content areas and supports the goals outlined in the Guiding Principles. The Maine Learning Results: Parameters for Essential Instruction will inform the blueprint for item development of the large-scale State assessments aligned to the federal accountability standards found in Maine Department of Education Regulation 131 - The Federal, State, and Local Accountability Standards. High school, middle school, and elementary school programming in Maine's publicly supported schools must be aligned to the knowledge and skills described in the Maine Learning Results: Parameters for Essential Instruction.

The Maine Department of Education Regulation 132 - The Maine Learning Results: Parameters for Essential Instruction augments and expands upon the content standards for federal accountability (Maine Department of Education Regulation 131: The Maine Federal, State, and Local Accountability Standards) by describing details for essential teaching and learning for eight content areas. These learning goals identify the knowledge and skills required for college, career and citizenship in the 21st century.

THE GUIDING PRINCIPLES - The knowledge and skills described in the Maine Department of Education Regulation 132 support Maine students in achieving the goals established in Maine's Guiding Principles. The Guiding Principles state that each Maine student must leave school as:

A. A clear and effective communicator who:
1. Demonstrates organized and purposeful communication in English and at least one other language;
2. Uses evidence and logic appropriately in communication
3. Adjusts communication based on the audience; and
4. Uses a variety of modes of expression (spoken, written, and visual and performing including the use of technology to create and share the expressions);
B. A self-directed and lifelong learner who:
1. Recognizes the need for information and locates and evaluates resources;
2. Applies knowledge to set goals and make informed decisions;
3. Applies knowledge in new contexts;
4. Demonstrates initiative and independence;
5. Demonstrates flexibility including the ability to learn, unlearn, and relearn;
6. Demonstrates reliability and concern for quality; and 7. Uses interpersonal skills to learn and work with individuals from diverse backgrounds;
C. A creative and practical problem solver who: [1995, c. 649, §1 (new).]
1. Observes and evaluates situations to define problems;
2. Frames questions, makes predictions, and designs data/information collection and analysis strategies;
3. Identifies patterns, trends, and relationships that apply to solutions;
4. Generates a variety of solutions, builds a case for a best response and critically evaluates the effectiveness of the response;
5. Sees opportunities, finds resources, and seeks results;
6. Uses information and technology to solve problems; and 7. Perseveres in challenging situations;
D. A responsible and involved citizen who:
1. Participates positively in the community and designs creative solutions to meet human needs and wants;
2. Accepts responsibility for personal decisions and actions;
3. Demonstrates ethical behavior and the moral courage to sustain it;
4. Understands and respects diversity;
5. Displays global awareness and economic and civic literacy; and 6. Demonstrates awareness of personal and community health and wellness;
E. An integrative and informed thinker who:
1. Gains and applies knowledge across disciplines and learning contexts and to real life situations with and without technology;
2. Evaluates and synthesizes information from multiple sources;
3. Applies ideas across disciplines; and
4. Applies systems thinking to understand the interaction and influence of related parts on each other and on outcomes.

CAREER AND LIFE READY STANDARDS INTRODUCTION

Life and Career Ready standards in Maine include an emphasis on multiple pathways toward meaningful careers and focus on life skills and experiences that will allow students to pivot as economic needs change and personal interests evolve. They have been crafted to allow flexibility and variation in focus and implementation, while ensuring all students exhibit key skills required to successfully navigate the changing career landscape.

Maine's economic future depends on a well-prepared, resilient, adaptable and skilled workforce. To achieve this, schools must creatively offer relevant opportunities that include interactive experiences and allow for direct exposure between students and a variety of career options. Schools must partner with local communities to bridge the gap between traditional K-12 education and ongoing career development. Networking with local community partners can provide opportunities which may include internships/pre-apprenticeships, job shadows, work-based learning options, early college courses, service learning, volunteering, guest speakers, field trips, and first-time work experiences.

These standards are a dynamic approach that frame multiple pathways for our students as they progress through grades K-12 and begin their post high school journey. To meet the needs of all youth, institutions need to examine educational practices and strategies, understanding the need to prepare students to experience and explore a variety of roles within their communities and recognizing students will choose to enter the workforce in different ways.

Outline of Life and Career Ready

Standards Strand A: Self-Knowledge and Life Skills

Standard A.1 Self-Knowledge Standard A. 2 Life Skills Standard A. 3 Problem Solving

Strand B: Aspirations

Standard B.1 Exploring Opportunities

Strand C: Building Pathways for the Future

Standard C.1 Planning Standard C.2 Career Awareness and Adaptability

How to Represent the Life and Career Ready Standards and Performance Expectations

Grade or Grade Span -> 9-Diploma A.1 <- Standard and Performance Expectation

Strand

A. Self-Knowledge and Life Skills

Standard

A.1 Self-Knowledge

Students demonstrate an understanding of their own capabilities, characteristics, attitudes and how these attributes impact their future choices, including local, state, national, and global opportunities.

Childhood

Performance Expectations

Kindergarten

Grade 1

Grade 2

Students demonstrate and reflect on likes and dislikes.

Students demonstrate and reflect on likes and dislikes that impact future choices.

Students demonstrate and reflect on personal characteristics and attitudes that impact future choices.

Performance Expectations

Grade 3

Grade 4

Grade 5

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness.

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness with a local community focus.

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness with a state of Maine focus.

Early Adolescence

Performance Expectation

Grades 6-8

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and lead to career readiness, emphasizing national and global awareness.

Adolescence

Performance Expectation

Grades 9-Diploma

Students demonstrate and reflect on personal characteristics, attitudes, and interests that develop life skills and assist in making post high school career and life decisions.

Strand

A. Self-Knowledge and Life Skills

Standard

A.2 Life Skills

Students demonstrate positive interpersonal and life skills and understand how they are important to success in relationships, school, work, and community.

Childhood

Performance Expectations

Kindergarten

Grade 1

Grade 2

Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in the classroom.

a. Get along with others

b. Follow established expectations for observing and listening.

Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in the classroom.

a. Accept and give constructive feedback.

Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in the classroom.

a. Use effective communication to manage conflict.

Performance Expectations

Grade 3

Grade 4

Grade 5

Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in school.

a. Be a responsible member or leader of a team.

Students demonstrate and reflect on social skills that influence interpersonal relationships in positive ways in school and the local community.

a. Exhibit ethical behavior.

Students demonstrate and reflect on skills that influence interpersonal relationships in positive ways in school and the Maine community.

a. Use strategies to cope with interpersonal issues.

b. Use organizational skills and time management strategies.

Strand

A. Self-Knowledge and Life Skills

Standard

A.2 Life Skills

Students demonstrate positive interpersonal and life skills and understand how they are important to success in relationships, school, work, and community.

Early Adolescence

Performance Expectation

Grades 6-8

Students demonstrate and reflect on skills that influence interpersonal relationships in positive ways in school, work, and the regional and national community.

a. Work independently to solve problems.

b. Work as a productive member or leader of a team.

c. Demonstrate the ability to resolve conflicts and to negotiate acceptable solutions.

Adolescence

Performance Expectation

Grades 9-Diploma

Students demonstrate and reflect on skills that influence interpersonal relationships in positive ways in school, work, and the global community.

a. Use a variety of communication skills in a responsible manner.

b. Exhibit ethical behavior, including responsibility for self and others.

c. Understand and exhibit professionalism in changing situations and environments.

Strand

A. Self-Knowledge and Life Skills

Standard

A.3 Problem Solving

Students are engaged community members who identify problems and apply skills to resolve problems within local and global communities

Childhood

Performance Expectations

Kindergarten

Grade 1

Grade 2

Students use and analyze communication skills in their classroom.

Students use and analyze problem-solving skills in their classroom.

Students use and analyze communication and problem-solving skills in their school.

Performance Expectations

Grade 3

Grade 4

Grade 5

Students integrate and analyze communication, collaboration, and problem-solving skills in their school.

Students integrate and analyze communication, collaboration, and problem-solving skills in their local community.

Students apply skills to analyze and creatively solve problems that impact their schools and local communities.

Early Adolescence

Performance Expectation

Grades 6-8

Students evaluate and develop problem-solving skills and resolve problems within the community.

a. Evaluate skills and understand gaps in skill sets.

b. Develop creative solutions to meet local and global needs.

Adolescence

Performance Expectation

Grades 9-Diploma

Students evaluate and implement strategies to manage multiple roles and responsibilities as involved members of their local and global communities.

a. Evaluate responsibilities and potential impact as students, community members and employees.

b. Engage in issues impacting local and global communities.

Strand

B. Aspirations

Standard

B.1 Exploring Opportunities

Students understand their options and can navigate choices and experiences concerning interests and future opportunities.

Childhood

Performance Expectations

Kindergarten

Grade 1

Grade 2

Students engage in new experiences and ask questions to promote creativity and curiosity about their interests.

Students use resources, seeking help proactively and asking questions when needed, to promote creativity and curiosity about their interests.

Students recognize and analyze available resources, using strategies described by others to promote creativity and curiosity about their interests.

Performance Expectations

Grade 3

Grade 4

Grade 5

Students integrate communication, collaboration, and problem-solving skills to identify and reflect on interests.

Students analyze and apply learning strategies to discover emerging questions and pursue new interests.

Students use learning strategies and available resources to explore future opportunities.

Early Adolescence

Performance Expectation

Grades 6-8

Students use and analyze resources to purposely and creatively explore a variety of post high school options.

Adolescence

Grades 9-Diploma

Performance Expectation

Students articulate a variety of post high school options based on individualized, in-depth exploration.

Strand

C. Building Pathways for the Future

Standard

C.1 Planning

Students develop goals and implement career and life plans.

Childhood

Performance Expectations

Kindergarten

Grade 1

Grade 2

Students participate in the development of classroom guidelines.

Students reflect upon and adjust classroom guidelines with guidance.

Students develop an awareness of goals and goal-setting practices.

Performance Expectations

Grade 3

Grade 4

Grade 5

Students engage in the goal-setting process.

Students reflect upon and adjust individual academic goals.

Students use feedback and experiences to develop, implement, and adjust goals. a. Demonstrate ability to learn from mistakes.

Early Adolescence

Performance Expectation

Grades 6-8

Students develop, implement, and adjust goals as they relate to potential future paths.

a. Demonstrate awareness of available academic opportunities, course levels, alternate options, and timelines.

b. Draw on curiosity to seek out meaningful career exploration opportunities in interactive settings.

Adolescence

Performance Expectation

Grades - 9-Diploma

Students develop, take steps to implement, and reflect on individualized, post high school plans.

a. Analyze educational achievement and performance strategies as it relates to future choices, adapting plans as needed.

b. Seek out meaningful career exploration opportunities, both individually and in small-group interactive settings.

c. Understand the financial impact of post high school credentialing programs, using that awareness to inform plans.

Strand

C. Building Pathways for the Future

Standard

C.2 Career Awareness and Adaptability

Students integrate personal aptitudes and interests, changing employment trends, community and societal needs, and current economic conditions into ongoing career plans, adapting as necessary.

Childhood

Performance Expectations

Kindergarten

Grade 1

Grade 2

Students explore jobs/careers and how these roles contribute to the community.

Students explore jobs/careers of individual interest and how these roles contribute to the community.

Students connect classroom learning with workplace skills and roles in the community.

Performance Expectations

Grade 3

Grade 4

Grade 5

Students explore the concept of career clusters.

Students identify and reflect on skills and education related to various career clusters.

Students identify and reflect on skills and education requirements of occupations within and across career clusters of interest to them.

Early Adolescence

Performance Expectation

Grades 6-8

Students consider personal aptitudes, evolving personal interests and current employment trends, locally and globally, as they develop future plans.

a. Identify horizontal and vertical opportunities (within career cluster hierarchies) related to personal aptitudes and interests and the skills needed for potential career options.

b. Recognize that career planning to attain career goals is a lifelong process.

c. Use knowledge of career clusters to develop and adapt career plans.

Adolescence

Performance Expectation

Grades 9-Diploma

Students are aware of changing career and economic trends and can adapt their personal plan to meet situational needs, personal aptitudes and interests.

a. Reflect on personal growth and alternative perspectives.

b. Analyze and adjust approach, timeline, and plan as needed.

c. Explore credentialing requirements.

d. Plan strategically (informed by changing career and economic trends) and choose learning experiences/courses/classes that strengthen knowledge and skills needed for individual next steps after high school.

ENGLISH LANGUAGE ARTS STANDARDS INTRODUCTION

Literacy is a basic human right, achievable by all students. Today's learners need to know how to read, write, speak, and communicate effectively in order to survive in an ever-changing and challenging global society. English Language Arts/Literacy is the foundation for learning in all of the content areas. The literacy continuum develops across an individual's lifetime, but literacy does not reside solely in the individual person; it requires and creates relationships with others through communication and interaction. Literacy is a developmental process that empowers students to become lifelong, effective learners and communicators.

The Maine Learning Results English Language Arts/Language standards are organized into four strands: Language, Speaking and Listening, Reading, and Writing. Each strand represents a body of knowledge and skills that students need to become lifelong learners. These strands are further broken down into standards that identify enduring understandings and skills that transfer across contexts, content areas, and grade levels. As students progress through the curriculum, the standards are broken down into Performance Expectations that are grouped by grade level through grade 5 and then are banded 6-8 and 9-Diploma. The Performance Expectations define skills and establish measurable articulations of what the student understands and can do.

The standards reference "Various Text Types" rather than emphasizing any one particular genre. Teachers are encouraged to use a variety of text types, including literature and informational texts in multiple formats. The skills outlined by the standards are designed so that students can receive literacy instruction with each text they encounter across all disciplines.

Guiding Principles

The Guiding Principles steer education in Maine and are reflected and embedded throughout the English Language Arts/Literacy standards. Examples of how students can show evidence of those guiding principles in English Language Arts/Literacy may include (but are not limited to) the following suggestions:

A. Clear and effective communicator: Students participate in a range of evidence-based discussions and generate detailed writing that are both used to communicate ideas clearly with others.
B. A self-directed and lifelong learner: Students apply knowledge in new contexts and demonstrate flexibility including the ability to learn, unlearn and relearn.
C. A creative and practical problem solver: Students use inquiry and writing processes that require adaptation to feedback through the use of reflection, sometimes persevering through multiple attempts.
D. A responsible and involved citizen: Students demonstrate ethical behavior, particularly during the discussion of ideas, maintaining awareness of, and respect for, multiple and diverse perspectives.
E. An integrative and informed thinker: Students frequently read, evaluate, and synthesize information and ideas from multiple sources, incorporating it into both oral and written communication.

LANGUAGE

Throughout the developmental continuum in English Language Arts/Literacy and across all content areas, language is the core of understanding and comprehension. Context is key. Human understanding is founded in communication and language, and organic experiences are the most effective means of learning language skills. While the language standards are presented separately from reading, writing, speaking, and listening, they are best utilized and presented as embedded skills within the other strands. A balance must be found between direct instruction of standards, like vocabulary acquisition and spelling, and integrated instruction of standards, like vocabulary use and nuance.

These standards are not a checklist, but key components of reading, writing, speaking, and listening instruction, and they should be treated as such. Frequent, intentional reference to and instruction in these skills is essential to teaching students to be clear communicators in every medium and field.

Each language standard may contain multiple concepts, at different levels of complexity. In early adolescence and adolescence grade spans, these are best taught in order as listed, even across grade levels, to provide students with the foundational knowledge required for success as they progress, not just through school, but through life. Developing facility with the language standards is key to building comprehension and fluency with increasingly complex texts and communications.

Strand

LANGUAGE: CONVENTIONS OF STANDARD ENGLISH

Standard 1

Demonstrate command of the conventions of Standard English grammar and usage when writing or speaking.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Use frequently occurring nouns and verbs.

b. Form regular plural nouns orally by adding /s/ or /es/ (e.g., dog, dogs; wish, wishes).

c. Understand and use question words (interrogatives) (e.g., who, what, where, when, why, how).

d. Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with).

e. Produce and expand complete sentences in shared language activities.

a. Use common, proper, and possessive nouns.

b. Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop).

c. Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their; anyone, everything).

d. Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home).

e. Use frequently occurring adjectives.

f. Use frequently occurring conjunctions (e.g., and, but, or, so, because).

g. Use determiners (e.g., articles, demonstratives).

h. Use frequently occurring prepositions (e.g., during, beyond, toward).

i. Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts.

a. Use collective nouns (e.g., group).

b. Form and use frequently occurring irregular plural nouns (e.g., feet, children, teeth, mice, fish).

c. Use reflexive pronouns (e.g., myself, ourselves).

d. Form and use the past tense of frequently occurring irregular verbs (e.g., sat, hid, told).

e. Use adjectives and adverbs; choose between them depending on what is to be modified.

f. Produce, expand, and rearrange complete simple and compound sentences (e.g., The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy).

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences.

b. Form and use regular and irregular plural nouns.

c. Use abstract nouns (e.g., childhood).

d. Form and use regular and irregular verbs.

e. Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses.

f. Ensure subject-verb and pronoun-antecedent agreement.

g. Form and use comparative and superlative adjectives and adverbs, and choose

h. between them depending on what is to be modified.

i. Standards for Language 3

j. Use coordinating and subordinating conjunctions.

k. Produce simple, compound, and complex sentences.

a. Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).

b. Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses.

c. Use modal auxiliaries (e.g., can, may, must) to convey various conditions.

d. Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).

e. Form and use prepositional phrases.

f. Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons. *

g. Correctly use frequently confused words (e.g., to, too, two; there, their).

a. Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences.

b. Form and use the perfect (e.g., I had walked; I have walked; I will have walked) verb tenses.

c. Use verb tense to convey various times, sequences, states, and conditions.

d. Recognize and correct inappropriate shifts in verb tense.

e. Use correlative conjunctions (e.g., either/or, neither/nor).

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Ensure that pronouns are in the proper case (subjective, objective, possessive).

b. Use intensive pronouns (e.g., myself, ourselves).

c. Recognize and correct inappropriate shifts in pronoun number and person.

d. Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents).

e. Recognize variations from standard English in their own and others' writing and speaking and identify and use strategies to improve expression in conventional language.

f. Explain the function of phrases and clauses in general and their function in specific sentences.

g. Choose among simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas.

h. Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers

i. Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences.

j. Form and use verbs in the active and passive voice.

k. Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood.

l. Recognize and correct inappropriate shifts in verb voice and mood.

Grade Span

Adolescence

Grades 9-Diploma

a. Use parallel structure.

b. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.

c. Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contestable.

d. Resolve issues of complex or contested usage, consulting references as needed.

Strand

LANGUAGE: CONVENTIONS OF STANDARD ENGLISH

Standard 2

Demonstrate command of the conventions of Standard English capitalization, punctuation, and spelling when writing.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Capitalize the first word in a sentence and the pronoun I.

b. Recognize and name end punctuation.

c. Write a letter or letters for most consonant and short-vowel sounds (phonemes).

d. Spell simple words phonetically, drawing on knowledge of sound-letter relationships.

a. Capitalize dates and names of people.

b. Use end punctuation for sentences.

c. Use commas in dates and to separate single words in a series.

d. Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.

e. Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions.

a. Capitalize holidays, product names, and geographic names.

b. Use commas in greetings and closings of letters.

c. Use an apostrophe to form contractions and frequently occurring possessives.

d. Generalize learned spelling patterns when writing words (e.g., cage? badge; boy? boil).

e. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Capitalize appropriate words in titles.

b. Use commas in addresses.

c. Use commas and quotation marks in dialogue.

d. Form and use possessives.

e. Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness).

f. Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words.

g. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.

a. Use correct capitalization.

b. Use commas and quotation marks to mark direct speech and quotations from a text.

c. Use a comma before a coordinating conjunction in a compound sentence.

d. Spell grade-appropriate words correctly, consulting references as needed.

a. Use punctuation to separate items in a series.

b. Use a comma to separate an introductory element from the rest of the sentence.

c. Use a comma to set off the words yes and no (e.g., Yes, thank you), to set off a tag question from the rest of the sentence (e.g., It's true, isn't it?), and to indicate direct address (e.g., Is that you, Steve?).

d. Use underlining, quotation marks, or italics to indicate titles of works.

e. Spell grade-appropriate words correctly, consulting references as needed.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Spell correctly.

b. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements.

c. Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt).

d. Use punctuation (comma, ellipsis, dash) to indicate a pause or break.

e. Use an ellipsis to indicate an omission.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses.

b. Use a colon to introduce a list or quotation.

c. Observe hyphenation conventions.

d. Spell correctly.

Strand

LANGUAGE: KNOWLEDGE OF LANGUAGE

Standard 3

Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style in writing and speaking, and to comprehend more fully when reading or listening.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Use knowledge of language and its conventions when speaking or listening.

Use knowledge of language and its conventions when writing, speaking, reading, or listening.

Use knowledge of language and its conventions when writing, speaking, reading, or listening. a. Compare formal and informal uses of English.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Use knowledge of language and its conventions when writing, speaking, reading, or listening.

a. Choose words and phrases for effect.

b. Recognize and observe differences between the conventions of spoken and written standard English.

Use knowledge of language and its conventions when writing, speaking, reading, or listening.

a. Choose words and phrases to

convey ideas precisely.

b. Choose punctuation for effect.

c. Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).

Use knowledge of language and its conventions when writing, speaking, reading, or listening.

a. Expand, combine, and reduce sentences for meaning, reader/listener interest, and style.

b. Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Vary sentence patterns for meaning, reader/listener interest, and style.

b. Maintain consistency in style and tone.

c. Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.

d. Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact).

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Write and edit work so that it conforms to the guidelines in a style manual appropriate for the discipline and writing task.

b. Vary syntax for effect, consulting references for guidance as needed; apply an understanding of syntax to the study of complex texts when reading.

Strand

LANGUAGE: VOCABULARY ACQUISITION AND USE

Standard 4

Use context clues, analyze meaningful word parts, and consult general and specialized reference materials as appropriate to determine or clarify the meaning of unknown and multiple-meaning words and phrases from grade level content.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on kindergarten reading and content. a. Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck). b. Use the most frequently occurring inflections and affixes (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies.

a. Use sentence-level context as a clue to the meaning of a word or phrase.

b. Use frequently occurring affixes as a clue to the meaning of a word.

c. Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking).

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies.

a. Use sentence-level context as a clue to the meaning of a word or phrase.

b. Determine the meaning of the new word formed when a known prefix is added to a known word (e.g., happy/unhappy, tell/retell).

c. Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., addition, additional). d. Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g., birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark).

d. Use glossaries and beginning dictionaries, both print and digital, to determine or clarify the meaning of words and phrases.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.

a. Use sentence-level context as a clue to the meaning of a word or phrase.

b. Determine the meaning of the new word formed when a known affix is added to a known word

(e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat).

c. Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion).

d. Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.

a. Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.

b. Use common, grade-appropriate Greek and Latin affixes and roots

as clues to the meaning of a word (e.g., telegraph, photograph, autograph).

c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.

a. Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase.

b. Use common, grade-appropriate Greek and Latin affixes and roots

as clues to the meaning of a word (e.g., photograph, photosynthesis).

c. Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Use context (e.g., the overall meaning of a sentence or paragraph; a word's position or function in a sentence) as a clue to the meaning of a word or phrase.

b. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., audience, auditory, audible in 6th grade; belligerent, bellicose, rebel in 7th grade; precede, recede, secede in 8th grade).

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses) to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word's position or function in a sentence) as a clue to the meaning of a word or phrase.

b. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable).

c. Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses) to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its usage.

d. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).

Strand

LANGUAGE: VOCABULARY ACQUISITION AND USE

Standard 5

Demonstrate understanding of figurative language, word relationships, and nuances in word meanings sufficient for reading, writing, speaking, and listening.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

With guidance and support from adults, explore word relationships and nuances in word meanings.

a. Sort common objects into categories (e.g., shapes, foods) to gain a sense of the concepts the categories represent.

b. Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites (antonyms).

c. Identify real-life connections between words and their use (e.g., note places at school that are colorful).

d. Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings.

With guidance and support from adults, demonstrate an understanding of word relationships and nuances in word meanings.

a. Sort words into categories (e.g., colors, clothing) to gain a sense of the concepts the categories represent.

b. Define words by category and by one or more key attributes (e.g., a duck is a bird that swims; a tiger is a large cat with stripes).

c. Identify real-life connections between words and their use (e.g., note places at home that are cozy ).

d. Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings.

Demonstrate understanding of word relationships and nuances in word meanings.

a. Identify real-life connections between words and their use (e.g., describe foods that are spicy or juicy).

b. Distinguish shades of meaning among closely related verbs (e.g., toss, throw, hurl) and closely related adjectives (e.g., thin, slender, skinny, scrawny).

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Demonstrate understanding of word relationships and nuances in word meanings.

a. Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps).

b. Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful).

c. Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered).

a. Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

b. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.

c. Recognize and explain the meaning of common idioms, adages, and proverbs.

d. Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).

Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

a. Interpret figurative language, including similes and metaphors, in context.

b. Recognize and explain the meaning of common idioms, adages, and proverbs.

c. Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words.

ade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Interpret figures of speech (e.g. personification in 6th grade; allusions in 7th grade; verbal irony, puns in 8th grade) in context.

b. Use the relationship between particular words (e.g., cause/effect, part/whole, item/category in 6th grade; synonym/antonym, analogy in 7th grade) to better understand each of the words.

c. Distinguish among the connotations of words with similar denotations (e.g., stingy, scrimping, economical, unwasteful, thrifty in 6th grade; refined, respectful, polite, diplomatic, condescending in 7th grade; bullheaded, willful, firm, persistent, resolute in 8th grade).

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Interpret figures of speech (e.g., euphemism, oxymoron, hyperbole, paradox) in context and analyze their role in the text.

b. Analyze nuances in the meaning of words with similar denotations.

Strand

LANGUAGE: VOCABULARY ACQUISITION AND USE

Standard 6

Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Use words and phrases acquired through conversations, reading and being read to, and responding to texts.

Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., because).

Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g., When other kids are happy that makes me happy).

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition).

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

SPEAKING AND LISTENING

Speaking and listening are essential components in our schools, our homes, our communities, and our places of work. Direct, interpersonal communication is the cornerstone of human relationships, and nowhere is this more clearly articulated than in dialogue, discussion, presentation, and debate. Successful students must be able to communicate in multiple mediums, through conversations, interviews, digital presentations, and countless day-to-day interactions that build understanding of their world and the perspectives of their peers. Key to success in our modern world is interaction with diverse others and ever-changing groups, and creating and following community guidelines and rules, which is critical practice for civic responsibility later in life.

Speaking and listening standards do not stand alone; like all Language Arts skills, they are interconnected. Early speaking and listening skills in primary grades are foundational to close reading skills in later grades, and throughout school and life the ability to understand, analyze, and evaluate others' words helps everyone develop a richer and deeper awareness of human motivation and purpose.

Strand

SPEAKING AND LISTENING: COMPREHENSION AND COLLABORATION

Standard 1

Prepare for and participate in conversations across a range of topics, types, and forums, building on others' ideas and expressing their own.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Participate in collaborative conversations about kindergarten topics and texts with peers and adults in small and larger groups.

b. Follow agreed-upon rules for discussions (e.g., listening to others and taking turns speaking about the topics and texts under discussion).

c. Continue a conversation through multiple exchanges.

a. Participate in collaborative conversations about grade 1 topics and texts with peers and adults in small and larger groups.

b. Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion).

c. Build on others' talk in conversations by responding to the comments of others through multiple exchanges.

d. Ask questions to clear up any confusion about the topics and texts under discussion.

a. Participate in collaborative conversations about grade 2 topics and texts with peers and adults in small and larger groups.

b. Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).

c. Build on others' talk in conversations by linking their comments to the remarks of others.

d. Ask for clarification and further explanation as needed about the topics and texts under discussion.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Engage effectively in a range of collaborative discussions (one-on-one, in groups, student-led and teacher-led) on grade 3 topics and texts, building on others' ideas and expressing their own clearly.

b. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.

c. Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).

d. Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others.

e. Explain their own ideas and understanding in light of the discussion.

a. Engage effectively in a range of collaborative discussions (one-on-one, in groups, student-led, and teacher-led) on grade 4 topics and texts, building on others' ideas and expressing their own clearly.

b. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.

c. Follow agreed-upon rules for discussions and carry out assigned roles.

d. Pose and respond to specific questions to clarify or follow up on information and make comments that contribute to the discussion and link to the remarks of others.

e. Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.

a. Engage effectively in a range of collaborative discussions (one-on-one, in groups, student-led, and teacher-led) on grade 5 topics and texts, building on others' ideas and expressing their own clearly.

b. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.

c. Follow agreed-upon rules for discussions and carry out assigned roles.

d. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.

e. Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Engage effectively in a range of collaborative discussions (one-on-one, in groups, student-led, and teacher-led) on grade 6-8 topics, texts, and issues, building on others' ideas and expressing their own clearly.

b. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.

c. Follow rules for collegial discussions and decision-making, set and track progress toward specific goals and deadlines, and define individual roles as needed.

d. Pose questions that elicit elaboration, connect the ideas of several speakers, and respond to others' questions and comments with relevant evidence, observations, and ideas.

e. Review the key ideas expressed and demonstrate understanding of multiple perspectives through paraphrasing and reflection. Acknowledge new information expressed by others, and, when warranted, modify, qualify, or justify their own views in light of the evidence presented.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Participate effectively in a range of collaborative discussions (one-on-one, in groups, student-led, and teacher-led) on grades 9-Diploma topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively.

b. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.

c. Work with peers to promote civil, democratic discussions and decision-making, set clear goals and deadlines, and establish individual roles as needed.

d. Propel conversations by posing and responding to questions that probe reasoning and evidence.

e. Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task.

Strand

SPEAKING AND LISTENING: COMPREHENSION AND COLLABORATION

Standard 2

Integrate and evaluate information presented in diverse media and formats, including point of view, reasoning, and use of evidence and rhetoric.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details to seek help if something is not understood.

b. Ask and answer questions in order to seek help, gather information, or clarify something that is not understood.

a. Ask and answer questions about key details in a text read aloud or information presented orally or through other media.

b. Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood.

a. Recount or describe key ideas or details from a text read aloud or information presented orally or through other media.

b. Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats.

b. Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.

a. Paraphrase portions of a text read aloud or information presented in diverse media and formats.

b. Identify the reasons and evidence a speaker provides to support particular points.

a. Summarize a written text read aloud or information presented in diverse media and formats.

b. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Interpret information, analyze the main ideas and supporting details, and analyze the purpose of information presented in diverse formats.

b. Explain how the presentation contributes to or clarifies a topic under study, and evaluate the motives (e.g., social, commercial, political) behind its presentation. c. Delineate a speaker's argument and specific claims, evaluate the soundness of the reasoning and sufficiency of the evidence, and identify when irrelevant evidence is introduced.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Integrate multiple sources of information presented in diverse formats and media in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data.

b. Evaluate the speaker's technique, including use of evidence, reasoning, stylistic and rhetorical elements, or other features appropriate to the task.

Strand

SPEAKING AND LISTENING: PRESENTATION OF KNOWLEDGE AND IDEAS

Standard 3

Present information and supporting evidence appropriate to task, purpose, and audience so listeners can follow the line of reasoning and incorporate multimedia when appropriate.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Describe familiar people, places, things, and events and, with prompting and support, provide additional detail.

b. Add drawings or other visual displays to descriptions as desired to provide additional detail.

a. Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly.

b. Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings.

a. Describe people, places, things, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences.

b. Create audio/video recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speak clearly at an understandable pace.

b. Create audio/video recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details.

a. Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

b. Add audio/video recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes.

a. Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

b. Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Present claims and findings, emphasizing salient points in a sequenced, focused, coherent manner with relevant evidence, sound and valid reasoning, and well-chosen details.

b. Use appropriate eye contact, adequate volume, and clear pronunciation.

c. When appropriate, integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Present information, findings, and supporting evidence, conveying a clear and distinct perspective so that listeners can follow the line of reasoning.

b. Address alternative or opposing perspectives; the organization development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks.

c. Use appropriate eye contact, adequate volume, and clear pronunciation.

d. Make strategic use of multimedia (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence.

Strand

SPEAKING AND LISTENING: PRESENTATION OF KNOWLEDGE AND IDEAS

Standard 4

Adapt speech to a variety of contexts, audiences, and communicative tasks.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Speak audibly and express thoughts, feelings, and ideas clearly.

Produce complete sentences when appropriate to task and situation. (See grade 1 Language standards 1 and 3 for specific expectations.)

Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 2 Language standards 1 and 3 for specific expectations.)

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 for specific expectations.)

Differentiate between contexts that call for different registers (e.g. formal English for presenting ideas and informal discourse for small-group discussion). (See grade 4 Language standards 1 and 3 for specific expectations.)

Adapt speech to a variety of contexts and tasks, demonstrating command of language in the appropriate register. (See grade 5 Language standards 1 and 3 for specific expectations.)

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Adapt speech to a variety of contexts, demonstrating command of language in the appropriate register (See grades 6-8 Language standards 1 and 3 for specific expectations.)

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Adapt speech to a variety of contexts, demonstrating a command of language in the appropriate register. (See grades 9-Diploma Language standards 1 and 3 for specific expectations.)

READING

The goal of all reading instruction is to help students become competent consumers of a wide variety of texts in diverse forms so that they can achieve independence, find meaning, and use literacy for lifelong learning, empowerment, and enjoyment.

A text is anything that can be read, heard or viewed. Texts may include words, images, objects, sounds, and symbols that convey messages from developers to consumers. They broadly encompass multiple purposes, audience appeal, and a wide variety of human experiences that create meaning for the reader. A student's experience with texts may range from cursive, print and digital fonts. When choosing texts, teachers must consider the qualities of complexity and the diversity of texts each student should experience.

The reading standards are designed progressively, using specificity and scaffolding to engage all readers in pursuing skills and experiences that contribute to personal, communal, and global needs and interests. This design promotes essential reading skills, allowing students to understand and enjoy a wide range of texts from a variety of perspectives. Teachers must employ a balance of research-based instructional approaches and strategies designed to provide multiple opportunities for transfer of learning.

Strand

READING: FOUNDATIONAL SKILLS/ PRINT CONCEPTS

Standard 1

Demonstrate understanding of the organization and basic features of print.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Follow words from left to right, top to bottom, and page by page.

b. Recognize that spoken words are represented in written language by specific sequences of letters.

c. Understand that words are separated by spaces in print.

d. Recognize and name all upper-and lowercase letters of the alphabet.

Recognize the distinguishing features of a sentence (e.g., first word, capitalization, ending punctuation).

Recognize the distinguishing features of a paragraph (e.g. indent).

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to help students move toward proficiency.

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to help students move toward proficiency.

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to help students move toward proficiency.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to move students toward proficiency.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to move students toward proficiency.

Strand

READING: FOUNDATIONAL SKILLS/ PHONOLOGICAL AWARENESS

Standard 2

Demonstrate understanding of words, syllables, and sounds (phonemes).

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Recognize and produce rhyming words.

b. Count, pronounce, blend, and segment syllables in spoken words.

c. Blend and segment onsets and rimes of single-syllable spoken words.

d. Isolate and pronounce the initial, medial vowel, and final sounds (phonemes) in three-phoneme (consonant-vowel-consonant, or CVC) words. (This does not include CVCs ending with /l/, /r/, or /x/.)

e. Add or substitute individual sounds (phonemes) in simple, one-syllable words to make new words.

a. Distinguish long from short vowel sounds in spoken single-syllable words.

b. Produce single-syllable words by blending sounds (phonemes), including consonant blends.

c. Isolate and pronounce initial, medial vowel, and final sounds (phonemes) in spoken single-syllable words.

d. Segment spoken single-syllable words into their complete sequence of individual sounds (phonemes).

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to move students toward proficiency.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency.

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency.

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and access district resources to help students move toward proficiency.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to move students toward proficiency.

Grade Span

Adolescence

Grades 9-Diploma

Performance

Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to move students toward proficiency.

Strand

READING: FOUNDATIONAL SKILLS/ PHONICS AND WORD RECOGNITION

Standard 3

Know and apply grade-level phonics and word analysis skills in decoding words.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Demonstrate basic knowledge of one-to -one letter-sound correspondences by producing the primary or many of the most frequent sound for each consonant.

b. Associate the long and short sounds with common spellings (graphemes) for the five major vowels.

c. Read common high-frequency words by sight (e.g., the, of, to, you, she, my, is, are, do, does).

d. Distinguish between similarly spelled words by identifying the sounds of the letters that differ

a. Know the spelling-sound correspondences for common consonant digraphs.

b. Decode regularly spelled one-syllable words.

c. Know final -e and common vowel team conventions for representing long vowel sounds.

d. Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word.

e. Decode two-syllable words following basic patterns by breaking the words into syllables.

f. Read words with inflectional endings.

g. Recognize and read grade-appropriate irregularly spelled words.

a. Distinguish long and short vowels when reading regularly spelled one-syllable words.

b. Know spelling-sound correspondences for additional common vowel teams.

c. Decode regularly spelled two-syllable words with long vowels.

d. Decode words with common prefixes and suffixes.

e. Identify words with inconsistent but common spelling-sound correspondences.

f. Recognize and read grade-appropriate irregularly spelled words.

Grade

Childhood

Grade 3

Grade 4

Grade 5

a. Identify and know the meaning of the most common prefixes and derivational suffixes.

b. Decode words with common Latin suffixes.

c. Decode multisyllabic words.

d. Read grade-appropriate irregularly spelled words.

Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.

Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to help students move toward proficiency.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Some learners may enter your classroom without having mastered the skills identified in previous grade levels or grade spans. In cases when this occurs, teachers should

* assess where students are,

* determine what they need to learn to master the skills appropriate to their grade level or grade span, and

* access district resources to help students move toward proficiency.

Strand

READING/KEY IDEAS AND DETAILS

Standard 4

Read various texts closely to determine what each text explicitly says and to make logical inferences; cite specific textual evidence to support conclusions drawn from the texts.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Ask and answer questions with prompting and support about who, what, when, where, and how.

Ask and answer questions about who, what, when, where, and how.

Ask and answer questions about who, what, when, where, how and why.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.

Refer to details and examples in a text when explaining what the text says explicitly and when making inferences.

Accurately quote details and examples from the text when explaining what the text says explicitly and when making inferences.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Cite several pieces of textual evidence that most strongly support an analysis of what the text says explicitly as well as inferences drawn from the text.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Cite strong and thorough textual evidence to support analysis of various texts in ways that demonstrate what the text(s) says explicitly and implicitly, including attending to moments of textual inconsistency or ambiguity.

Strand

READING/KEY IDEAS AND DETAILS

Standard 5

Provide an accurate summary of various texts; determine the central idea(s) or theme(s) and analyze its development throughout each text.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Retell familiar texts with prompting and support, including details about who, what, when, where, and how.

b. Retell key details of texts with prompting and support, including the main topic.

a. Retell texts, including details about who, what, when, where, and how; demonstrate an understanding of the theme.

b. Retell key details of texts, including the main topic.

a. Retell texts, including details about who, what, when, where, how, and why; demonstrate understanding of the theme.

b. Identify the main topic of a multi-paragraph text and the central ideas of specific paragraphs.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Retell texts, including details about who, what, when, where, why and how; explain how the theme is supported.

b. Explain how the key details support the central idea of a text.

a. Summarize texts, including details about who, what, when, where, how and why; explain how the theme is supported.

b. Summarize texts, including how the key details support the central idea.

a. Summarize texts, including theme and character development.

b. Summarize texts, including how the key details support two or more central ideas.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Provide an accurate summary of various texts;

b. Determine theme(s) or central idea(s) and analyze how its development is conveyed over the course of the texts, including its relationship to specific supporting details.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Provide accurate summaries of various texts that make clear the relationships among the key details and ideas.

b. Determine the theme(s) or central idea(s) of various texts and analyze the development of the theme(s) or central idea(s) over the course of the texts, including how elements interact and build on one another, to provide a complex account or analysis.

Strand

READING: KEY IDEAS AND DETAILS

Standard 6

Analyze how and why individuals, events, and ideas develop and interact over the course of a text.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. With prompting and support, identify characters, settings, and major events in a story.

b. With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.

a. Describe characters, settings, and major events in a story, including details about who, what, when, where, and how.

b. Describe the connection between two individuals, events, ideas, or pieces of information in a text.

a. Describe how characters in a story respond to major events and challenges.

b. Describe the relationship between a series of events, ideas or concepts, using language that pertains to time, sequence, and cause/effect.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Describe in depth a character, setting, or event in a story, drawing on specific details in the text (e.g., a character's thoughts, words, or actions).

b. Explain the relationship between events, ideas or concepts, using language that pertains to time, sequence, and cause/effect, based on information from the text.

a. Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events, drawing on specific details in the text.

b. Explain the relationships or interactions between two or more individuals, events, ideas, or concepts, explicitly referring to specific information from the text.

a. Analyze how two or more characters, settings, or events in a story are related, drawing on specific details in the text (e.g., how characters interact).

b. Analyze relationships or interactions between individuals, events, ideas, or concepts throughout the text.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Analyze in detail how an author develops individuals/characters, events, ideas, elements and/or techniques to create interactions over the course of a text (or a series of texts).

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Analyze the impact of an author's choices and determine how specific individuals/characters, elements and/or techniques, events, or ideas interact and develop over the course of the text (or a series of texts).

Strand

READING: CRAFT AND STRUCTURE

Standard 7

Interpret words and phrases as they are used in various texts, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. With prompting and support, ask and answer questions about unknown words in a text.

b. With prompting and support, ask and answer questions about unknown words in a text.

a. Identify words and phrases in a text that suggest feelings or appeal to the senses.

b. Ask and answer questions to help determine or clarify the meaning of words and phrases in a text.

a. Describe how words and phrases supply rhythm and meaning in a text.

b. Use provided resources to determine meaning of words and phrases in a text.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Determine the meaning of words and phrases as they are used in a text, distinguishing literal from figurative language.

b. Use provided resources to determine meaning of domain-specific words and phrases.

a. Determine the meaning of words and phrases including figurative language as they are used in a text.

b. Draw on a variety of strategies to determine meaning of domain-specific words and phrases.

a. Determine the meanings of words and phrases including figurative language and connotations as they are used in a text.

b. Initiate strategies to determine meaning of domain-specific words and phrases.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Determine the meaning of figurative, connotative, and technical word meanings and phrases as they are used in various texts; analyze the impact of specific word choices and techniques on meaning and tone.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

Determine the meaning of figurative, connotative, and technical word meanings and phrases as they are used in various contexts and texts; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings and/or language that is particularly evocative.

Strand

READING: CRAFT AND STRUCTURE

Standard 8

Analyze the structure of various texts, including how the features and components relate to each other and the whole.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Identify texts that tell stories.

b. Identify texts that provide information.

a. Explain major differences between texts that tell stories and texts that give information, drawing on various text types.

b. Determine and use text features (e.g., headings, bold print, indexes, graphics, tables of contents, glossaries, links, icons) that help locate key facts or information in a text.

a. Describe the overall structure of a text, including describing how the beginning introduces the story and the ending concludes the action.

b. Explain how various text features (e.g., headings, bold print, indexes, graphics, tables of contents, glossaries, links, icons) are used to locate key facts or information in a text efficiently.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Refer to parts of a text (e.g. chapters, scenes, or stanzas) and explain how each successive part builds on earlier sections.

b. Use various text features (e.g., headings, bold print, indexes, graphics, tables of contents, glossaries, links, icons) to locate key facts or information in a text efficiently.

a. Explain how individual parts of a text (e.g., chapters, scenes, or stanzas) work together to provide meaning to the text as a whole.

b. Identify the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of a text and explain how the text features help support the overall structure.

a. Explain how the text's structure supports its meaning and the author's purpose of the text as a whole.

b. Compare and contrast the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts on the same topic.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

Analyze how the organization and structure of specific features and components in various texts develop ideas and/or meaning, contributing to the author's purpose for the text as a whole.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Analyze the organization and structure of specific features and components in various texts

b. Evaluate the effectiveness of text structures in conveying the overall meaning and/or purpose of the text as a whole.

Strand

READING: CRAFT AND STRUCTURE

Standard 9

Assess how perspective or purpose shapes the content and style of various texts.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. With prompting and support, name the author and illustrator of a story and define the role of each in telling the texts.

b. With prompting and support, name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text.

a. Identify who is telling the story at various points in a text.

b. Distinguish between information provided by pictures or other illustrations and information provided by the words in a text.

a. Acknowledge differences in the points of view of characters b. Identify the main purpose of a text, including what the author wants to answer, explain, or describe.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Distinguish the reader's personal point of view from that of the narrator or those of the characters.

b. Distinguish the reader's personal point of view from that of the author of a text.

a. Compare and contrast the point of view from which different texts are narrated, including the difference between first- and third-person narrations.

b. Compare and contrast primary and secondary sources of the same event or topic; describe the differences in perspective based on information in the texts.

a. Describe how a narrator's or speaker's point of view influences how events are described in various contexts.

b. Analyze multiple accounts and/or contexts of the same event or topic, noting important similarities and differences in the perspectives they represent based on information in the texts.

Grade Span

Early Adolescence

Grades 6-8

Analyze how and why authors from various contexts (e.g. diverse, intersectional, multicultural, religious) use perspective for intended purposes and/or audiences.

Grade Span

Adolescence

Grades 9-Diploma

Analyze and evaluate how authors from various contexts (e.g. diverse, intersectional, multicultural, religious) use perspective and purpose to shape the intended content, style, and effect of various texts.

Strand

READING: INTEGRATION OF KNOWLEDGE AND IDEAS

Standard 10

Evaluate the argument and specific claims in various texts.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

With prompting and support, identify the reasons an author or character gives to support points in a text.

Identify the reasons an author or character gives to support points in a text.

Describe how reasons support specific points an author or character makes in a text.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Explain how an author or character uses reasons and evidence to support a claim in a text.

Explain how an author or character uses reasons and evidence to support a claim in a text, identifying which reasons and evidence support the claim(s).

a. Trace the organization and development of a claim in a text.

b. Determine the effectiveness of an author's or character's claim.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Distinguish among fact, opinion, evidence, reasoning, and qualifying statements in a text.

b. Evaluate the effectiveness of how an author or character develops the argument.

c. Assess the validity and reasoning of the argument, considering if the argument is relevant and sufficient.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Evaluate the effectiveness of how authors use literary and/or rhetorical strategies to develop arguments in various texts.

b. Evaluate the premises, claims, and/or conclusions in various texts, verifying the information when possible and corroborating or challenging conclusions with other sources of information.

Strand

READING: INTEGRATION OF KNOWLEDGE AND IDEAS

Standard 11

Analyze and evaluate content presented in various texts (e.g. literary, historical, visual, artistic, quantitative, and technological).

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. With prompting and support, describe the relationship between illustrations and the text.

b. With prompting and support, compare and contrast the experiences of characters in two or more familiar texts.

c. With prompting and support, describe the relationship between the text and what person, place, thing, or idea the illustration depicts.

d. With prompting and support, compare and contrast two texts on the same topic.

a. Use illustrations and words in a text to describe its characters, setting, or events.

b. Compare and contrast the experiences of characters in various texts.

c. Use the illustrations and details in a text to describe its central idea.

d. Compare and contrast two texts on the same topic.

a. Use illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot.

b. Compare and contrast two or more versions of the same story presented in diverse forms

c. Explain how specific visuals contribute to and clarify the meaning of a text.

d. Compare and contrast the information presented by two texts on the same topic.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Explain how specific aspects of a text's illustrations contribute to the meaning of a text (e.g., create mood, emphasize aspects of a character or setting).

b. Compare and contrast themes, settings, characters, and plots of stories.

c. Use information gained from the text features and the words within to demonstrate an understanding of the whole text.

d. Compare and contrast the key details presented in two texts on the same topic

a. Compare and contrast between texts and other multimedia versions and how it influences the meaning and author's intent.

b. Compare and contrast similar themes, topics, and patterns of events in texts.

c. Interpret information presented in diverse forms and explain how the information contributes to an understanding of an idea or topic.

a. Analyze how diverse forms and their features contribute to the meaning, tone, and author's intent of a text.

b. Compare and contrast how two or more authors of the same text type interpret similar themes and topics.

c. Draw on information presented in various texts in order to answer a question or to solve a problem.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Analyze how two or more authors of various texts present information by emphasizing different interpretations of a theme and/or topic.

b. Evaluate the advantages and disadvantages of an author's choice for using a specific form and/or text type.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Evaluate and synthesize multiple sources of information and various texts (e.g., literary, visual, artistic, and quantitative) in order to achieve a specific purpose or to answer a question.

b. Analyze how various authors or texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

c. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of an idea or event, noting discrepancies among perspectives.

Strand

READING: FLUENCY

Standard 12

Read with sufficient accuracy and fluency to support comprehension

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Read emergent-reader texts with purpose and understanding.

a. Read various on-level text with purpose and understanding.

b. Read various on-level text with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

a. Read various on-level text with purpose and understanding.

b. Read various on-level text orally with accuracy, appropriate rate, and expression on successive readings.

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Read various on-level text with purpose and understanding.

b. Read various on-level text with accuracy, appropriate rate, and expression on successive readings

c. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

a. Read with sufficient accuracy and fluency to support comprehension.

b. Read various on-level text with purpose and understanding.

c. Read various on-level text with accuracy, appropriate rate, and expression on successive readings.

d. Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

a. Read with sufficient accuracy and fluency to support comprehension.

b. Read various on-level text with purpose and understanding.

c. Use context to confirm or self-correct word recognition.

Grade Span

Early Adolescence

Grades 6-8

Performance Expectations

a. Read with sufficient accuracy and fluency to support comprehension.

b. Read various on-level texts with purpose and understanding.

c. Use context to confirm or self-correct word recognition.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Read with sufficient accuracy and fluency to support comprehension.

b. Read various on-level texts with purpose and understanding.

c. Use context to confirm or self-correct word recognition.

WRITING

Writing is a lifelong, essential tool for communication. In order to prepare students for varied and evolving writing tasks, students should write routinely, in both long and short time frames, as a means of building writing stamina. Moreover, students should write in a breadth of modes and forms across all disciplines. This includes the foundational instruction of legible handwriting forms and skills such as printing, cursive, typing, as well as the use of technology to compose, where the use of formatting supports the task, audience, and purpose.

In order to manage the increasing complexity of what students read and write, educators provide guidance and support when developmentally appropriate, with the understanding that students need to develop autonomy and independence over time, particularly at the upper grade levels. To that end, the standards include a developmentally appropriate progression of performance expectations that includes all grade levels. The K-5 performance expectations reflect a foundational level of skill acquisition, while the 6-8 and 9-Diploma grade bands expect that writing grows in sophistication and complexity.

The strand of writing includes three standards, which have been arranged to reflect a traditional learning progression in the classroom, incorporating the use of technology when authentic to the task. Students begin with an exploration of a variety of texts/ideas, then use a process to refine, plan, and craft the communication of ideas, and finally compose with a style that reflects awareness of task, audience, and purpose. The standard and performance expectations for composing are consistent regardless of mode; therefore, the performance expectations for common modes (argument/opinion, informational/expository, and narrative) have been outlined in supporting documents.

Strand

WRITING: Inquiry to Build and Present Knowledge

Standard 1

Use an inquiry process to gather relevant, credible information/evidence from a variety of sources (e.g., print, digital, discussions, etc.) that build understanding of and lead to conclusions about a subject under investigation while avoiding plagiarism.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Investigate questions by participating in shared research and writing projects.

b. Gather information from provided sources and/or recall information from experiences in order to answer questions with guidance and support from adults.

a. Investigate questions by participating in shared research and writing projects.

b. Gather information from provided sources and/or recall information from experiences in order to answer questions with guidance and support from adults.

a. Investigate questions by participating in shared research and writing projects.

b. Gather information from provided sources and/or recall information from experiences in order to answer questions.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Investigate questions by participating in research that builds knowledge about a topic.

b. Gather information from a variety of sources and/or recall information from experiences in order to answer questions.

c. Take brief notes on sources and sort information into provided categories.

a. Investigate questions by participating in research that builds varied knowledge about a topic.

b. Gather relevant information from a variety of sources and/or recall information from experiences in order to answer questions.

c. Take notes on sources and sort information into provided categories.

d. Provide a list of sources.

a. Investigate and generate questions by participating in research that builds varied knowledge about a topic.

b. Gather relevant information from a variety of sources and/or recall information from experiences in order to answer questions.

c. Summarize or paraphrase notes on sources and sort information into provided categories.

d. Provide a list of sources.

Grade Span

Early Adolescence

Grade 6-8

Performance Expectations

a. Investigate self-generated questions by participating in inquiry that builds increasingly complex knowledge, refocusing inquiry as needed.

b. Assess the credibility and accuracy of a variety of sources in order to gather relevant information that leads to conclusions.

c. Take organized notes that purposefully quote, summarize, and/or paraphrase a variety of sources while avoiding plagiarism.

d. Follow a standard format for citation (in-text and a list of sources) that applies to task, audience, and purpose.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Investigate self-generated questions by participating in sustained inquiry that builds increasingly complex knowledge or that solves a problem, refocusing inquiry and/or incorporating effective advanced searches as needed.

b. Assess the credibility, accuracy, and usefulness of a variety of authoritative sources in order to synthesize relevant information that leads to logical, increasingly complex conclusions.

c. Take organized notes that purposefully quote, summarize, and/or paraphrase a variety of sources while avoiding plagiarism and overreliance on any one source.

d. Follow a standard format for citation (in-text and a list of sources) that applies to task, audience, and purpose.

Strand

WRITING: Process and Production

Standard 2

Develop, strengthen, and produce polished writing by using a collaborative process that includes the age-appropriate use of technology.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed.

b. With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including peer collaboration.

a. With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed.

b. With guidance and support from adults, use a variety of digital tools to produce and publish writing, including peer collaboration.

a. With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing.

b. With guidance and support from adults, use a variety of digital tools to produce and publish writing, including peer collaboration.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

b. With guidance and support from adults, use technology to produce writing, as well as to interact and collaborate with others.

c. Develop keyboarding skills.

a. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

b. With some guidance and support from adults, use technology to produce writing, as well as to interact and collaborate with others.

c. Demonstrate sufficient command of keyboarding skills to produce sustained writing of increasing length.

a. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, composing, revising, editing, rewriting, reflecting, and/or trying a new approach.

b. With some guidance and support from adults, use technology to produce writing, as well as to interact and collaborate with others.

c. Demonstrate sufficient command of keyboarding skills to produce sustained writing of increasing length.

Grade Span

Early Adolescence

Grade 6-8

Performance Expectations

a. With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, composing, revising, editing, rewriting, reflecting, and/or trying a new approach, focusing on how well purpose and audience have been addressed.

b. Use technology to produce writing, as well as to interact and collaborate with others.

c. Demonstrate and maintain command of keyboarding skills to produce sustained writing of increasing length.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Develop and strengthen writing as needed by planning, composing, revising, editing, rewriting, reflecting, and/or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.

b. Use technology and ongoing feedback, including new arguments and information, to produce increasingly dynamic writing products.

c. Demonstrate and maintain command of keyboarding skills to produce sustained writing of increasing length.

Strand

WRITING: Composing for Audience and Purpose

Standard 3

Routinely produce a variety of clear and coherent writing in which the development, organization, and style are appropriate to task, audience, and purpose.

Grade

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

a. Print many upper- and lowercase letters.

b. Use a combination of drawing and writing to communicate a topic.

a. Print all upper- and lowercase letters.

b. Use a combination of drawing and writing to communicate a topic with details.

Use a combination of drawing, and writing to communicate a topic with a beginning, middle (including details), and an end.

Grade

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

a. Use a combination of illustrations and writing to produce pieces with introductions and bodies including details and conclusions.

b. Develop the topic with relevant supporting details.

c. Use developmentally appropriate linking words and phrases.

d. Use precise vocabulary/word choice.

e. Provide a sense of closure that is related to the ideas presented.

a. Produce writing to communicate clearly and to organize increasingly complex pieces with introductions and bodies including details and conclusions.

b. Develop the topic with relevant supporting details.

c. Use developmentally appropriate linking words and phrases with increasing complexity.

d. Use precise vocabulary/word choice.

e. Provide a sense of closure that is related to the ideas presented.

a. Produce writing to communicate clearly and organize increasingly complex pieces with introductions and bodies including details and conclusions.

b. Develop the topic with relevant, logically ordered supporting details.

c. Use developmentally appropriate linking words and phrases with increasing complexity.

d. Use precise vocabulary/word choice.

e. Provide a sense of closure that is related to the ideas presented.

Grade Span

Early Adolescence

Grade 6-8

Performance Expectations

a. Compose clear and increasingly complex pieces with sections that are organized according to task, audience, and purpose.

b. Develop and support the topic with relevant techniques and logically ordered details.

c. Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas.

d. Effectively use increasingly complex and precise language to establish an appropriate voice and tone.

e. Provide a sense of closure that follows from, supports, and reflects the purpose of the piece.

Grade Span

Adolescence

Grades 9-Diploma

Performance Expectations

a. Compose clear and increasingly varied and complex pieces with purposefully designed sections that are organized to fully explore the depth and significance of ideas that are appropriate to task, audience, and purpose.

b. Develop and support the topic with a variety of relevant techniques and by purposefully embedding the most significant details.

c. Use appropriate and varied transitions, along with purposeful syntax, to create cohesion that clarifies relationships among increasingly complex ideas.

d. Effectively use increasingly sophisticated, precise language to establish a highly developed voice and tone.

e. Provide closure that enhances, supports, and reflects the purpose of the piece.

HEALTH EDUCATION AND PHYSICAL EDUCATION

The Health Education and Physical Education Standards and performance indicators represent the essential knowledge and skills students need to be healthy individuals. Every day, students make decisions affecting their health and well-being: what foods to eat; what company to keep; what risks to take; and what to do for physical activity. These decisions often lead to habits that stay with them throughout life. The Health Education and Physical Education Standards will guide instruction that will help students make better decisions about their health. Through achievement of the Health Education and Physical Education Standards, students learn that their decisions can affect their health and set a pattern for their lives. Students also learn to protect their health by acquiring good information, by seeking good advice and friendships, and by taking responsibility for their own wellness which contributes to a healthy, active, balanced approach to life.

Health education gives students the knowledge and skills to thrive physically, mentally, emotionally, and socially. It contributes to students' ability to successfully practice behaviors that protect and promote health, and avoid and reduce health risks. Health education helps students to determine personal values and group norms that support healthy behaviors. Through comprehensive health education, students learn basic health concepts and influences on health. They develop the skills required to adopt, practice, and maintain health-enhancing and safe behaviors. These skills include: analyzing the reliability and validity of media and health resources; communicating effectively using refusal and conflict management skills; setting goals; and making healthy decisions. Health education helps students to be better consumers of information, manage stress, and make healthy decisions in the face of conflicting messages. It assists them in living healthier lives.

Physical education provides students with the skills and knowledge needed to support participation i n a wide variety of physical activities that contribute to an active lifestyle. Physical education provides building blocks for skill development, skill analysis, physical fitness, stress reduction, decision-making, and positive social skills. Students learn to assess and set goals, evaluate their own physical fitness, and use the knowledge to maintain or improve their current fitness level. Students who participate in physical education on a regular basis learn the benefits of physical activity and its contribution to a healthy lifestyle.

OUTLINE OF HEALTH EDUCATION AND PHYSICAL EDUCATION STANDARDS AND PERFORMANCE INDICATOR LABELS

A. Health Concepts
1. Healthy Behaviors and Personal Health
2. Dimensions of Health
3. Diseases/Other Health Problems
4. Environment and Personal Health
5. Growth and Development
6. Basic Health Concepts
B. Health Information, Products, and Services
1. Validity of Resources
2. Locating Health Resources
C. Health Promotion and Risk Reduction
1. Healthy Practices and Behaviors
2. Avoiding/Reducing Health Risks
3. Self-Management
D. Influences on Health
1. Influences on Health Practices/Behaviors
2. Technology and Health
3. Compound Effect of Risky Behavior
E. Communication and Advocacy Skills
1. Interpersonal Communication Skills
2. Advocacy Skills
F. Decision-Making and Goal-Setting Skills
1. Decision-Making
2. Goal-Setting
3. Long-Term Health Plan
G. Movement/Motor Skills and Knowledge
1. Stability and Force
2. Movement Skills
3. Skill-Related Fitness Components
4. Skill Improvement
H. Physical Fitness Activities and Knowledge
1. Fitness Assessment
2. Health-Related Fitness Plan
3. Fitness Activity
4. Physical Activity Benefits
I. Personal and Social Skills and Knowledge
1. Cooperative Skills
2. Responsible Behavior
3. Safety Rules and Rules of Play
A. Health Concepts: Students comprehend concepts related to health promotion and disease prevention to enhance health.

A1 Healthy Behaviors and Personal Health

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students recognize that healthy behaviors impact personal health.

Students explain the relationship between healthy behaviors and personal health.

Students examine the relationship between behaviors and personal health.

a. Explain the importance of assuming responsibility for personal health.

b. Examine the relationship between healthy and unhealthy behaviors and personal health.

c. Identify the possible barriers to practicing healthy behaviors.

Students predict how behaviors can impact health status.

a. Analyze individual responsibility for enhancing health.

b. Predict how healthy behaviors can positively impact health status.

c. Describe barriers to practicing healthy behaviors.

d. Examine personal susceptibility to, and the potential severity of, injury or illness if engaging in unhealthy behaviors.

A2 Dimensions of Health

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students recognize that there are multiple dimensions of health.

Students identify examples of physical, mental, emotional, and social health during childhood.

Students explain the interrelationship of physical, mental/intellectual, emotional, and social health.

Students analyze the interrelationship of physical, mental/in tellectual, emotional, and social health.

A3 Diseases/Other Health Problems

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students describe the transmission and prevention of common childhood communicable diseases.

Students describe ways to detect and treat common childhood diseases and other health problems.

Students identify causes of common adolescent diseases and other health problems and describe ways to reduce, prevent, or treat them.

Students explain causes of common diseases, disorders, and other health problems and propose ways to reduce, prevent, or treat them.

A4 Environment and Personal Health

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students describe ways a safe and healthy school environment can promote personal health.

Students describe ways a safe and healthy school and community environment can promote personal health.

Students determine how environment and other factors impact personal health.

a. Analyze how environment impacts personal health.

b. Describe how family history can impact personal health.

c. Explain how appropriate health care can promote personal health.

Students determine the interrelationship between the environment and other factors and personal health.

a. Analyze how environment and personal health are interrelated.

b. Describe how genetics and family history can impact personal health.

c. Analyze the relationship between access to health care and health status.

A5 Growth and Development

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

No performance indicator.

Students identify the general characteristics of human growth and development.

Students describe specific characteristics of adolescent human growth and development.

Students describe the characteristics of human growth and development throughout the various stages of life.

A6 Basic Health Concepts

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify basic health terms related to family life; nutrition; personal health; safety and injury prevention; and tobacco, alcohol, and other drug use prevention.

Students define basic health concepts related to family life; nutrition; personal health; safety and injury prevention; and tobacco, alcohol, and other drug use prevention.

Students explain essential health concepts related to family life; nutrition; personal health; safety and injury prevention; and tobacco, alcohol, and other drug use prevention.

Students analyze complex health concepts related to family life; nutrition; personal health; safety and injury prevention; and tobacco, alcohol, and other drug use prevention.

B. Health Information, Products and Services: Students demonstrate the ability to access valid health information, services, and products to enhance health.

B1 Validity of Resources

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify trusted adults and professionals who can help promote health.

Students identify characteristics of valid health information, products, and services.

Students analyze the validity of health information, products, and services.

Students evaluate the validity and accessibility of health information, products, and services.

B2 Locating Health Resources

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify ways to locate school and community health helpers.

Students locate resources from home, school, and the community that provide valid health information.

Students locate valid and reliable health information, products, and services.

a. Explain situations requiring the use of valid and reliable health information, products, and services.

b. Locate valid and reliable health information.

c. Locate valid and reliable health products, and services.

Students access valid and reliable health information, products, and services.

a. Determine when professional health services may be required.

b. Access valid and reliable health information.

c. Access valid and reliable health products and services.

C. Health Promotion and Risk Reduction: Students demonstrate the ability to practice health-enhancing behaviors and avoid or reduce health risks.

C1 Healthy Practices and Behaviors

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate age-appropriate healthy practices to maintain or improve personal health.

a. Choose healthy foods.

b. Demonstrate personal hygiene skills, including hand-washing.

Students demonstrate age-appropriate healthy practices and/or behaviors to maintain or improve personal health.

a. Design healthy menus.

b. Demonstrate basic care of the human body.

Students demonstrate a healthy practice and/or behavior to maintain or improve their own health in each of the following areas: personal hygiene, healthy eating; physical activity; and tobacco, alcohol, and other drug use prevention.

Students demonstrate healthy practices and/or behaviors to maintain or improve the health of self and others in each of the following areas: healthy eating; physical activity; tobacco, alcohol, and other drug use prevention; and prevention of STDs, HIV and unintended pregnancy.

C2 Avoiding/Reducing Health Risks

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate behaviors to avoid or reduce personal health risks.

a. Demonstrate a variety of safety skills for different situations.

b. Differentiate between safe and harmful substances found at home and school.

c. Recognize basic signs, symbols, and warning labels for health and safety.

Students demonstrate a variety of behaviors to avoid or reduce personal health risks.

a. Demonstrate healthy and safe ways to recognize, deal with, or avoid threatening situations.

b. Develop injury prevention and safety strategies for personal health.

Students demonstrate behaviors to avoid or reduce health risks to self and others.

a. Demonstrate ways to recognize, avoid, or change situations that threaten the safety of self and others.

b. Develop injury prevention and response strategies including first aid for personal and family health.

Students demonstrate a variety of behaviors to avoid or reduce health risks to self and others.

a. Develop ways to recognize, avoid, or change situations that threaten the safety of self and others.

b. Develop injury prevention and response strategies including first aid for personal, family, and community health.

C3 Self-Management

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate coping strategies to use when feeling too excited, anxious, upset, angry, or out of control.

Students demonstrate strategies that can be used to manage stress, anger, or grief.

Students distinguish between healthy and unhealthy strategies for stress, anger, and grief management.

Students design, implement, and evaluate a plan for stress management.

D. Influences on Health: Students analyze the ability of family, peers, culture, media, technology, and other factors to enhance health.

D1 Influences on Health Practices/Behaviors

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify influences on personal health practices and behaviors.

a. Identify family influences on personal health practices and behaviors.

b. Identify what the school can do to support personal health practices and behaviors.

c. Describe how the media can influence health behaviors.

Students describe how a variety of factors influence personal health behaviors.

a. Describe how family, school, and community influence and support personal health practices and behaviors.

b. Describe how peers and culture can influence health practices and behaviors.

c. Explain how media influences thoughts, feelings, and health behaviors.

Students explain and analyze influences on adolescent health behaviors.

a. Examine how the family, school, and community influence the health behaviors of adolescents.

b. Describe how peers influence healthy and unhealthy behaviors.

c. Analyze how messages from media influence health behaviors.

d. Explain how the perceptions of norms influence healthy and unhealthy behaviors.

e. Explain how culture and personal values and beliefs influence individual health behaviors.

Students analyze and evaluate influences on health and health behaviors.

a. Analyze how family, school and community influence the health of individuals.

b. Analyze how peers influence healthy and unhealthy behaviors.

c. Evaluate the effect of the media on personal and family health.

d. Analyze how the perceptions of norms influence healthy and unhealthy behaviors.

e. Analyze how culture and personal values and beliefs influence individual health behaviors.

f. Investigate how public health policies and government regulations can influence health promotion and disease prevention.

D2 Technology and Health

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

No performance indicator.

Students describe ways technology can influence personal health.

Students analyze the influence of technology, including medical technology, on personal and family health.

Students evaluate the impact of technology, including medical technology, on personal, family, and community health.

D3 Compound Effect of Risk Behavior

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

No performance indicator.

No performance indicator.

Students describe how some health risk behaviors can influence the likelihood of engaging in unhealthy behaviors.

a. Describe how gateway drugs can lead to the use of other drugs.

b. Describe the influence of alcohol and other drug use on judgment and self-control.

Students analyze how some health risk behaviors can influence the likelihood of engaging in unhealthy behaviors.

a. Analyze the influence of alcohol use on individual and group behavior.

b. Analyze the influence of drug use on individual and group behavior.

E. Communication and Advocacy Skills: Students demonstrate the ability to use interpersonal communication and advocacy skills to enhance personal, family, and community health.

E1 Interpersonal Communication Skills

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate healthy ways to communicate.

a. Demonstrate healthy ways to express needs, wants, and feelings.

b. Distinguish between verbal and nonverbal communication.

c. Make requests to promote personal health.

d. Demonstrate listening skills to enhance health.

e. Demonstrate ways to respond to an unwanted, threatening, or dangerous situation including telling a trusted adult if threatened or harmed.

Students demonstrate effective verbal and nonverbal interpersonal communication skills to enhance health.

a. Demonstrate appropriate listening skills to enhance health.

b. Demonstrate effective verbal and non-verbal communication skills including assertiveness skills to enhance health.

c. Demonstrate how to ask for assistance to enhance personal health.

d. Demonstrate refusal skills to avoid or reduce health risks.

e. Demonstrate non-violent strategies to manage or resolve conflict.

Students apply effective verbal and nonverbal interpersonal communication skills to enhance health.

a. Demonstrate communication skills to build and maintain healthy relationships.

b. Demonstrate effective communication skills including asking for assistance to enhance the health of self and others.

c. Demonstrate refusal and negotiation skills to avoid or reduce health risks.

d. Demonstrate effective conflict management or conflict resolution strategies.

Students utilize skills for communicating effectively with family, peers, and others to enhance health.

a. Demonstrate effective communication skills including asking for and offering assistance to enhance the health of self and others.

b. Demonstrate refusal, negotiation, and collaboration skills to enhance health and avoid and reduce health risks.

c. Demonstrate strategies to prevent, manage, or resolve interpersonal conflicts without harming self or others.

E2 Advocacy Skills

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students encourage peers to make positive health choices.

Students encourage others to make positive health choices.

a. Express opinions about health issues.

b. Give accurate information about health issues.

Students describe ways to influence and support others in making positive health choices.

a. Develop a health-enhancing position on a topic and support it with information.

b. Develop health-enhancing messages using communication techniques that target a specific audience.

c. Demonstrate an ability to work cooperatively as an advocate for healthy individuals, families, and schools.

Students demonstrate ways to influence and support others in making positive health choices.

a. Utilize accurate peer and societal norms to formulate a health-enhancing message.

b. Adapt health messages and communication techniques for different audiences.

c. Demonstrate an ability to work cooperatively as an advocate for improving personal, family, and community health.

F. Decision-Making and Goal-Setting Skills: Students demonstrate the ability to make decisions and set goals to enhance health.

F1 Decision-Making

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify situations where a health-related decision is needed.

a. Differentiate between situations when health-related decisions can appropriately be made by the individual and when assistance is needed.

Students apply decision-making steps to enhance health.

a. Identify health-related situations that might require a thoughtful decision.

b. List healthy options to health-related issues or problems and predict the potential outcomes of each option when making a health-related decision.

c. Choose a healthy option when making a decision.

d. Describe the outcome of a health-related decision.

Students apply decision-making skills to enhance health.

a. Determine when health-related situations require the application of a thoughtful decision-making process.

b. Determine when individual or collaborative decision-making is appropriate.

c. Distinguish between healthy and unhealthy alternatives to health-related issues or problems and predict the potential short-term impact of alternative decisions for themselves and others.

d. Choose healthy alternatives over unhealthy alternatives when making a decision.

e. Analyze the outcomes of a health-related decision.

Students apply a decision-making process to enhance health.

a. Compare the value of thoughtful decision-making to quick decision-making in a health-related situation.

b. Justify when individual or collaborative decision-making is appropriate.

c. Generate alternative approaches to situations involving health-related decisions and predict the potential short-term and long -term impact for themselves and others for each alternative.

d. Defend the healthy choice when making a decision.

e. Evaluate the effectiveness of a health-related decision.

F2 Goal-Setting

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify a short-term personal health goal and take action toward achieving the goal.

Students utilize goal-setting skills to implement a short-term personal health goal.

a. Set a short-term personal health goal.

b. Identify resources to assist in achieving the health goal.

c. Track progress toward achieving the goal.

Students develop and apply strategies to attain a short-term personal health goal.

a. Assess personal health practices.

b. Develop a short-term goal to adopt, maintain, or improve a personal health practice.

c. Develop and apply strategies and monitor progress toward a personal health goal.

d. Describe how personal health goals can vary with changing abilities, priorities, and responsibilities.

Students develop and analyze a plan to attain a personal health goal.

a. Assess personal health practices and overall health status.

b. Develop a plan to attain a short-term personal health goal that addresses strengths, needs, and risks.

c. Implement strategies and analyze progress in achieving a personal health goal.

F3 Long-Term Health Plan

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

No performance indicator.

No performance indicator.

No performance indicator.

Students formulate a long-term personal health plan, incorporating decision-making and goal-setting strategies.

G. Movement/Motor Skills and Knowledge: Students demonstrate the fundamental and specialized movement skills and apply principles of movement for improved performance.

G1 Stability and Force

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate positions that create stability and force.

a. Show how base of support changes during static balances.

b. Demonstrate how body position can be adapted to pushing and pulling forces.

c. Demonstrate how to lift objects to prevent injuries.

Students demonstrate a variety of movements that apply stability and force.

a. Demonstrate movements that change the center of gravity and line of gravity during dynamic balances.

b. Show how increasing speed and mass can change the force on an object.

c. Demonstrate how body position can be changed to absorb force and decrease risk for injury.

Students change their motion and the motion of objects by applying the principles of stability and force during skill practice.

a. Demonstrate the principle of opposition.

b. Demonstrate how the point of contact changes the path of an object.

c. Demonstrate how the point of release changes the path of an object.

d. Demonstrate lifts and actions that decrease risk for injury.

Students change their motion and the motion of objects by applying the principles of stability and force to modify their performance in games/physical activities.

a. Demonstrate how spin and rebound affect the motion of an object.

b. Use the principle of opposition, point of contact, and point of release to change the path of an object during a game/physical activity.

c. Adjust movements to accommodate external forces that decrease risk for injury.

G2 Movement Skills

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate a variety of locomotor skills.

a. Demonstrate correct technique for a variety of locomotor skills.

b. Demonstrate a locomotor skill applying changes in direction, level, and/or pathway.

c. Demonstrate combinations of locomotor skills.

Students demonstrate a variety of locomotor skills and manipulative skills.

a. Demonstrate correct technique for a variety of manipulative skills.

b. Demonstrate locomotor skills and manipulative skills in combination using changes in direction, level, or pathway.

Students demonstrate motor skills and manipulative skills during drills or modified games/physical activities.

a. Demonstrate correct technique for motor skills and manipulative skills during drills or modified games/physical activities.

b. Combine manipulative skills with motor skills during drills or modified games/physical activities.

Students demonstrate a variety of specialized movement skills specific to a game/physical activity while participating in a game/physical activity.

G3 Skill-Related Fitness Components

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify the skill-related fitness components of balance and coordination.

Students identify the skill-related fitness components of balance, coordination, agility, and speed.

Students describe the following skill-related fitness components: balance, coordination, agility, speed, and power.

Students explain the relationship of skill-related fitness components to specialized movement skills.

G4 Skill Improvement

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

No performance indicator.

Although no performance indicator is stated, students are expected to have instructional experiences that help them to understand the importance of practice.

Students describe why practice is important to skill improvement.

Students explain how specific, positive, and correct feedback affect skill improvement.

Students design appropriate practice sessions, utilizing fundamental movement skills to improve performance.

H. Physical Fitness Activities and Knowledge: Students demonstrate and apply fitness concepts.

H1 Fitness Assessment

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

No performance indicator.

Students participate in multiple health-related fitness assessments (including a cardiovascular assessment) and reassess to observe changes over time.

Students participate in a health-related fitness assessment that addresses a variety of health-related fitness components to establish personal fitness goals.

Students participate in a health-related fitness assessment to establish personal fitness goals and reassess their fitness over time.

H2 Health-Related Fitness Plan

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify components of health-related fitness.

Students describe and give examples of the five health-related fitness components.

Students design a fitness program from established goals which addresses the five health-related fitness components and applies the frequency, intensity, time, and type (FITT) guidelines.

Students design and critique a personal fitness plan, from established goals, that applies the five health-related fitness components and the principles of training (specificity, overload, and progression).

H3 Fitness Activity

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students participate in physical activities to introduce the health-related fitness components of flexibility, cardiovascular endurance, muscular endurance, and muscular strength.

Students participate in physical activities that address each of the five health-related fitness components including flexibility, cardiovascular endurance, muscular endurance, muscular strength, and body composition.

Students participate in physical activities that address personal fitness goals for the health-related fitness components including flexibility, cardiovascular endurance, muscular endurance, muscular strength, and body composition.

Students select and participate in physical activities that address their personal fitness plans and apply the five health-related fitness components.

H4 Physical Activity Benefits

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify the physical benefits and bodily responses related to physical activities.

Students identify physical and mental benefits and bodily responses related to regular participation in physical activity.

Students describe physiological responses and physical, mental/intellectual, emotional, and social benefits related to regular participation in physical activity.

Students explain the interrelationship of physiological responses and physical, mental/intellectual, emotional, and social benefits related to regular participation in physical activity.

I. Personal and Social Skills and Knowledge: Students demonstrate and explain responsible personal behavior and responsible social behavior in physical activity settings.

I1 Cooperative Skills

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students demonstrate taking turns and sharing while participating in physical activities.

Students demonstrate cooperative skills while participating in physical activities.

a. Demonstrate active listening.

b. Get along with others.

c. Accept responsibility for personal behavior.

Students demonstrate cooperative and inclusive skills while participating in physical activities.

a. Work together as a team.

b. Respond appropriately to peer pressure.

c. Manage conflict.

d. Engage peers respectfully in activities.

Students demonstrate collaborative skills while participating in physical activities.

a. Accept constructive feedback.

b. Give constructive feedback.

c. Include peers respectfully in activities.

I2 Responsible Behavior

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students follow procedures for safe behaviors, including maintaining appropriate personal space, while participating in physical activities.

Students demonstrate safe behaviors and appropriate equipment use while participating in physical activities.

Students demonstrate responsible personal behaviors while participating in physical activities.

Students demonstrate responsible and ethical personal behavior while participating in physical activities.

I3 Safety Rules and Rules of Play

Performance Indicators & Descriptors

Pre-K-2

3-5

6-8

9-Diploma

Students identify safety rules and rule of play for games/physical activities.

Students describe safety rules and rules of play for games/physical activities.

Students describe game/physical activity rules and safety rules and their purposes.

a. Explain the purposes for modifying playing rules in specified situations.

b. Explain the safety rules and possible risks associated with specific games/physical activities.

Students predict how etiquette/rules improve games/activities.

a. Explain how etiquette/rules contribute to productive participation.

b. Predict how modifications to the environment can impact safety during games/physical activities.

Mathematics Standards Introduction

A strong mathematics education depends upon a clear understanding of its interrelated concepts, skills and practices to ensure students are on the pathway to success in their academic careers. The knowledge and skills students need to be prepared for mathematics in college, career, and life are woven throughout the K-12 mathematics performance expectations.

Outline of Mathematics Strands and Standards

These mathematical performance expectations are building blocks to standards. The standards are grouped into four strands:

Quantitative Reasoning (Blue): Counting and Cardinality, Number and Operations in Base Ten, Number and Operations Fractions, Ratio and Proportional Relations, The Number System, and Number and Quantity. Algebraic Reasoning (Green): Operations and Algebraic Thinking, Expressions and Equations, Functions, and Algebra Geometric Reasoning (Red): Geometry Statistical Reasoning (Purple): Measurement and Data, Statistics and Probability These mathematical performance expectations are broken into three grade spans: Childhood (K -5), Early Adolescence (6-8), and Adolescence (9-Diploma). The strands are color-coded, as indicated above, for continuity throughout the grade spans. Standards do not work in isolation, they are connected through and across strands.

How to Read the Standards

Strand Grade Span Standard Number

->QR.EA.3<-

Within the high school performance expectations, modeling is woven throughout the four strands and is denoted with a star (*). The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

The Guiding Principles & Standards for Mathematical Practice

The Guiding Principles influence education in Maine and should be reflected throughout Mathematics curriculum. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. Full descriptions of the Guiding Principles and Standards for Mathematical Practice can be found in the Supplemental Material. Examples of how students can show evidence of those Guiding Principles and Standards for Mathematical Practice may include:

Guiding Principles

A. A clear and effective communicator: Students will use written, oral, symbolic, and visual forms of expression to communicate mathematically.
B. A self-directed and lifelong learner: Students generate and persevere in solving questions while demonstrating a growth mindset.
C. A creative and practical problem solver: Students will pose and solve mathematical problems by using a variety of strategies that connect to real-world examples.
D. A responsible and involved citizen: Students make sense of the world around them through mathematics including economic literacy.
E. An integrative and informed thinker: Students connect mathematics to other learning by understanding the interrelationships of mathematical ideas and the role math plays in other disciplines and life.

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them: Students will plan strategies to use and persevere in solving math problems.
2. Reason abstractly and quantitatively: Students will think about numbers in many ways and make sense of numerical relationships as they solve problems.
3. Construct viable arguments and critique the reasoning of others: Students will explain their thinking and make sense of the thinking of others.
4. Model with mathematics: Students will use representations to show their thinking in a variety of ways.
5. Use appropriate tools strategically: Students will use math tools such as tables, diagrams, and technology to explore and deepen their understanding of concepts.
6. Attend to precision: Students will use precise mathematical language and check their work for accuracy.
7. Look for and make use of structure: Students will use their current mathematical understandings to identify patterns and structure to make sense of new learning.
8. Look for and express regularity in repeated reasoning: Students will look for patterns and rules to help create general methods and shortcuts that can be applied to similar mathematical problems.

Quantitative Reasoning

Quantitative reasoning is the application of basic mathematics skills to analyze and process real-world information. In the K-5 grades, students use numbers, including written numerals, to represent quantities and to solve quantitative problems. Students will work on counting and cardinality, number and operations in Base Ten and fractions. Students will develop strategies to extend their understanding of the base ten system and apply those strategies to solve real-world problems using all four operations. Students progress from working with whole numbers to fractions and decimals.

In grades 6-8 students use reasoning about multiplication and division to solve ratio and rate problems about quantities. They develop an understanding of proportionality to solve problems and graph relationships. Overall, students extend and develop their understanding of rational numbers and can compute in all operations. Students use these operations to solve real-world problems. Students use this understanding of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.

In the high school grades, the foundational concepts of operations with rational numbers and numerical properties built in the K-5 and 6-8 grade spans are applied to irrational numbers. Using a wider variety of units in modeling, (e.g. acceleration, currency conversions, and derived quantities such as person-hours and heating degree days), as well as the properties of rational and irrational numbers students are guided to the solution(s) to multi-step problems. Extending the properties of integer exponents to rational exponents deepens student understanding of how various but equivalent notations can facilitate their algebraic reasoning and problem-solving processes. Students are encouraged to expand these operations and properties into complex numbers, vectors, and matrices to further deepen their understanding of quantitative reasoning.

Strand

Quantitative Reasoning- Counting and Cardinality

Standard

QR.C.1 Know the number names and the count sequence.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

K.CC.A.1: Count to 100 by ones and by tens

K.CC.A.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1)

K.CC.A.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects)

Strand

Quantitative Reasoning- Counting and Cardinality

Standard

QR.C.2 Count to tell the number of objects.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality.

K.CC.B.4a: When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

K.CC.B.4b: Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

K.CC.B.4c: Understand that each successive number name refers to a quantity that is one larger. Recognize the one more pattern of counting using objects.

K.CC.B.5: Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

Strand

Quantitative Reasoning- Counting and Cardinality

Standard

QR.C.3 Compare numbers.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

K.CC.C.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Include groups with up to ten objects.

K.CC.C.7: Compare two numbers between 1 and 10 presented as written numerals.

Strand

Quantitative Reasoning - Numbers and Operations in Base Ten

Standard

QR.C.4 Extend the counting sequence.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

1.NBT.A.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Strand

Quantitative Reasoning - Numbers and Operations in Base Ten

Standard

QR.C.5 Understand place value.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

K.NBT.A.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8 and 10+8=18); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

1.NBT.B.2: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

1.NBT.B.2a: 10 can be thought of as a bundle of ten ones -called a "ten."

1.NBT.B.2b: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

1.NBT.B.2c: The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.B.3: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

2.NBT.A.1: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

2.NBT.A.1a: 100 can be thought of as a bundle of ten tens - called a "hundred."

2.NBT.A.1b: The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.A.2: Count within 1000; skip-count by 5s, 10s, and 100s. Identify patterns in skip counting at any number. (For example, 37, 47, 57 or 328, 428, 528, etc.)

2.NBT.A.3: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

2.NBT.A.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Strand

Quantitative Reasoning - Numbers and Operations in Base Ten

Standard

QR.C.6 Use place value understanding and properties of operations to add and subtract.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

1.NBT.C.4: Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

1.NBT.C.5: Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.C.6: Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

2.NBT.B.8: Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

2.NBT.B.6: Add up to four two -digit numbers using strategies based on place value and properties of operations.

2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.

Strand

Quantitative Reasoning - Numbers and Operations in Base Ten

Standard

QR.C.7 Use place value understanding and properties of operations to perform multi-digit arithmetic with whole numbers and decimals to hundredths.

Childhood

Grade 3

A range of algorithms may be used.

Grade 4

Grade 4 expectations in this strand are limited to whole numbers less than or equal to 1,000,000

Grade 5

Performance Expectations

3.NBT.A.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

3.NBT.A.3: Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two -digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.B.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, money and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Strand

Quantitative Reasoning - Numbers and Operations in Base Ten

Standard

QR.C.8 Understand the place value system.

Childhood

Grade 3 A range of algorithms may be used.

Grade 4 Grade 4 expectations in this strand are limited to whole numbers less than or equal to 1,000,000

Grade 5

Performance Expectations

3.NBT.A.1: Use place value understanding to round whole numbers to the nearest 10 or 100.

4.NBT.A.3: Use place value understanding to round multi-digit whole numbers to any place.

4.NBT.A.2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

5.NBT.A.4: Use place value understanding to round decimals to any place.

5.NBT.A.3: Read, write, and compare decimals to thousandths.

5.NBT.A.3a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

5.NBT.A.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.A.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.A.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Strand

Quantitative Reasoning - Numbers and Operations: Fractions

Standard

QR.C.9 Develop and extend the understanding of fractions as numbers, including equivalence and ordering.

Childhood

Grade 3 Grade 3 expectations in this strand are limited to fractions with denominators 2, 3, 4, 6, and 8.

Grade 4 Grade 4 expectations in this strand are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Grade 5

Performance Expectations

3.NF.A.1: Understand a unit fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.A.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.A.2a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

3.NF.A.2b: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.NF.A.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.A.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.A.3b: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

3.NF.A.3c: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

3.NF.A.3d: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n xb) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions, including fractions greater than 1.

4.NF.A.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Strand

Quantitative Reasoning - Numbers and Operations: Fractions

Standard

QR.C.10 Understand decimal notation for fractions, and compare decimal fractions.

Childhood

Grade 3

Grade 4 Grade 4 expectations in this strand are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.

Grade 5

Performance Expectations

4.NF.C.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

4.NF.C.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Strand

Quantitative Reasoning - Numbers and Operations: Fractions

Standard

QR.C.11 Use equivalent fractions as a strategy to add and subtract fractions.

Childhood

Grade 3

Grade 4 Grade 4 expectations in this strand are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.

Grade 5

Performance Expectations

4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.B.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.B.3b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model to build fractions from unit fractions. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

4.NF.B.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

4.NF.B.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Strand

Quantitative Reasoning - Numbers and Operations: Fractions

Standard

QR.C.12 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Childhood

Grade 3

Grade 4

Grade 5

Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

Performance Expectations

4.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

4.NF.B.4a: Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x(1/4), recording the conclusion by the equation 5/4 = 5 x(1/4).

4.NF.B.4b: Understand a multiple of a/b as a multiple of 1/b and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x(2/5) as 6 x(1/5), recognizing this product as 6/5. (In general, n x(a/b) = (n xa)/b.)

4.NF.B.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.B.4a: Interpret the product (a/b) xq as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x4 = 8/3, and create a story context for this equation. Do the same wi th (2/3) x(4/5) = 8/15. (In general, (a/b) x(c/d) = (ac)/(bd).

5.NF.B.4b: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.

5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.B.5: Interpret multiplication scaling (resizing), by:

5.NF.B.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

5.NF.B.5b: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.

5.NF.B.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

5.NF.B.7a: Interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x4 = 1/3.

5.NF.B.7b: Interpret division of a whole number by a unit fraction and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x(1/5) = 4.

5.NF.B.7c: Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins*

Strand

Quantitative Reasoning- Ratio and Proportional Relationships

Standard

QR.EA.1 Understand ratio and rate concepts and use ratio and rate reasoning to solve problems.

Early Adolescence

Grades 6-8

Performance Expectations

6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks of the chickadees in the pine tree was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

6.RP.A.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b [NOT EQUALS] 0 and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 5 lobsters, which is a rate of $15 per lobster." Expectations for unit rates in this grade are limited to non-complex fractions.

6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.A.3a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.A.3b: Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed*

6.RP.A.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

6.RP.A.3d: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Strand

Quantitative Reasoning- Ratio and Proportional Relationships

Standard

QR.EA.2 Analyze proportional relationships and use them to solve real-world and mathematical problems.

Early Adolescence

Grades 6-8

Performance Expectations

7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour

7.RP.A.2: Recognize and represent proportional relationships between quantities.

7.RP.A.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.A.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.A.2c: Represent proportional relationships by equations. For example, if the total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn

7.RP.A.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

7.RP.A.3: Use proportional relationships to solve multistep ratio, rate, and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Strand

Quantitative Reasoning- The Number System

Standard

QR.EA.3 Apply and extend previous understandings of operations with whole numbers to rational numbers.

Early Adolescence

Grades 6-8

Performance Expectations

6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and/or equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)

6.NS.B.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

7.NS.A.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.1a: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has a zero charge because its two constituents are oppositely charged.

7.NS.A.1b: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.A.1c: Understand subtraction of rational numbers as adding the additive inverse, p - q = p+ (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in real-world contexts.

7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.A.2a: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

7.NS.A.2b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.A.2c: Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.A.2d: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

Strand

Quantitative Reasoning- The Number System

Standard

QR.EA.4 Compute fluently with multi-digit whole numbers and find common factors and multiples.

Early Adolescence

Grades 6-8

Performance Expectations

6.NS.B.2: Fluently divide multi-digit numbers using the standard algorithm.

6.NS.B.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. (For example: Use prime factorization to find the greatest common factor); Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two relatively prime numbers. For example, express 36 + 8 as 4 (9 + 2).

Strand

Quantitative Reasoning - The Number System

Standard

QR.EA.5 Apply and extend previous understandings of numbers to the system of rational numbers.

Early Adolescence

Grades 6-8

Performance Expectations

6.NS.C.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative rational numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.C.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

6.NS.C.6b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

6.NS.C.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.C.7: Understand ordering and absolute value of rational numbers.

6.NS.C.7a: Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

6.NS.C.7b: Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3° C > -7° C to express the fact that -3° C is warmer than -7° C.

6.NS.C.7c: Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

6.NS.C.7d: Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

6.NS.C.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Strand

Quantitative Reasoning- The Number System

Standard

QR.EA.6 Know that there are numbers that are not rational, and approximate them by rational numbers.

Early Adolescence

Grades 6-8

Performance Expectations

8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansions terminate in 0s or eventually repeats and convert a decimal expansion into a rational number.

8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., TT 2). For example, by truncating the decimal expansion of [SQUARE ROOT RADICAL]2, show that [SQUARE ROOT RADICAL]2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Strand

Quantitative Reasoning - Number and Quantity: The Real Number System

Standard

QR.A.1 Extend the properties of exponents to rational exponents.

Adolescence

Grades 9-Diploma

Performance Expectations

HSN.RN.A.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

HSN.RN.A.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Strand

Quantitative Reasoning- Number and Quantity: The Real Number System

Standard

QR.A.2 Use properties of rational and irrational numbers.

Adolescence

Grades 9-Diploma

Performance Expectations

HSN.RN.B.3: Explain when and why the sum or product of two rational and/or irrational numbers is rational or irrational.

Strand

Quantitative Reasoning - Number and Quantity: Quantities

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol (*).

Standard

QR.A.3 Reason quantitatively and use units to solve problems. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSN.Q.A.1: Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Example: Marlena made a scale drawing of the sand volleyball court at her summer camp. The drawing of the volleyball court is 6 cm long by 3 cm wide. The actual volleyball court is 18 meters long. What scale did Marlena use for the drawing? *

HSN.Q.A.2: Define appropriate quantities for the purpose of descriptive modeling. Example: If a town in Aroostook county with a population of 1254 people is projected to double in size every 105 years, what will the population be 315 years from now? *

HSN.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Example: The label on a ½ - liter bottle of flavored water bottled in Maine indicates that one serving of 8 ounce contains 60 calories. The label also says that the full bottle contains 130 calories. Is this the actual amount or the estimated amount of calories in this bottle? How would you explain any discrepancy? *

Strand

Quantitative Reasoning - Number and Quantity: Complex Number System

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

QR.A.4 (+) Perform arithmetic operations with complex numbers.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSN.CN.A.1: Know there is a complex number i (which is a non-real number) such that i2 = -1, and every complex number has the form a + bi with a and b real.

(+) HSN.CN.A.2: Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

(+) HSN.CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Strand

Quantitative Reasoning - Number and Quantity: Complex Number System

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

QR.A.5 (+) Represent complex numbers and their operations on the complex plane.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSN.CN.B.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

(+) HSN.CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + [SQUARE ROOT RADICAL]3 i)3 = 8 because (-1 + [SQUARE ROOT RADICAL]3 i) has modulus 2 and argument 120°.

(+) HSN.CN.B.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Strand

Quantitative Reasoning - Number and Quantity: Complex Number System

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

QR.A.6 (+) Use complex numbers in polynomial identities and equations.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSN.CN.C.7: Solve quadratic equations with real coefficients that have complex solutions.

(+) HSN.CN.C.8: Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x -2i).

(+) HSN.CN.C.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Strand

Quantitative Reasoning - Number and Quantity: Vector and Matrix Quantities

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

QR.A.7 (+) Represent and model with vector quantities.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSN.VM.A.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

(+) HSN.VM.A.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

(+) HSN.VM.A.3: Solve problems involving velocity and other quantities that can be represented by vectors.

Strand

Quantitative Reasoning - Number and Quantity: Vector and Matrix Quantities

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

QR.A.8 (+) Perform operations on vectors.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSN.VM.B.4: Add and subtract vectors.

(+) HSN.VM.B4a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

(+) HSN.VM.B4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

(+) HSN.VM.B4c: Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

(+) HSN.VM.B.5: Multiply a vector by a scalar.

(+) HSN.VM.B5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).

(+) HSN.VM.B5b: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v [NOT EQUALS] 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).

Strand

Quantitative Reasoning - Number and Quantity: Vector and Matrix Quantities

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

QR.A.9 (+) Perform operations on matrices and use matrices in applications.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSN.VM.C.6: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

(+) HSN.VM.C.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

(+) HSN.VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.

(+) HSN.VM.C.9: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

(+) HSN.VM.C.10: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

(+) HSN.VM.C.11: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

(+) HSN.VM.C12: Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Algebraic Reasoning

Algebraic thinking is about generalizing arithmetic operations and determining unknown quantities by recognizing and analyzing patterns along with developing generalizations about these patterns. In this K-5 strand, students explore, analyze, represent, and generalize mathematical ideas and relationships. Students will develop an understanding of the fundamental properties of number and operations, understand the use of the equal sign to represent equivalence, and use quantitative reasoning to understand mathematical relationships.

Students in grades 6-8 progress in their understanding of variables in mathematical expressions and equations. They understand that expressions in different forms can be equivalent, use the properties of operations to rewrite expressions in equivalent forms, and describe relationships between quantities. Students begin to analyze and solve real-world and mathematical problems using equations and inequalities. They construct and interpret tables and graphs. Understanding builds from writing and solving simple equations to solving proportional situations. These skills lead to exploring slope and y-intercept and relationships between variables, and eventually include multiple equations to solve systems of linear equations. Students grow to understand that the concept of a function is a rule that assigns one output to each input, and they learn to translate among different representations of functions.

In grades 9-12, students will continue to develop their understanding of expressions, equations, functions and function notation. They will interpret the structure of algebraic expressions and be able to write expressions in equivalent forms to reveal information and to solve problems. Students will perform arithmetic operations on polynomials and rewrite rational functions. An understanding of the relationship between zeros and factors of polynomials will transition into using polynomial identities to solve problems. Students will create equations that describe relationships and solve equations as a process of reasoning (with appropriate justification). They will represent and solve equations, inequalities, and systems of equations using a variety of mathematically sound techniques.

Students will interpret functions that arise in applications in terms of context and analyze functions using different representations. They will build functions that model relationships between two quantities, and build new functions from existing functions through transformations, combinations, compositions, and examining the inverse. Students will construct and compare linear, quadratic, and exponential models and use those models to solve problems. They will interpret expressions for functions in terms of the situation they model. Students will be encouraged to extend their understanding of algebra and functions and apply similar processes of reasoning to polynomial, logarithmic and trigonometric functions and their graphs.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.1 Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Childhood

Kindergarten

(Drawings need not show detail but should show the mathematics in the problem. This applies wherever drawings are mentioned in the Standards.)

Grade 1

Grade 2

Performance Expectations

K.OA.A.1: Represent addition and subtraction with objects, fingers, mental images, drawings sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

K.OA.A.2: Solve addition and subtraction word problems, and add and subtract within 10, (e.g., by using objects or drawings to represent the problem).

K.OA.A.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

K.OA.A.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

K.OA.A.5: Fluently add and subtract within 5 including zero.

1.OA.A.1: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.A.2: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, (e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.)

2.OA.A.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.2 Understand and apply properties of operation and the relationship between addition and subtraction within 20.

Childhood

Kindergarten

Grade 1

Students need not use formal terms for these properties.

Grade 2

Performance Expectations

1.OA.B.3: Apply properties of operations as strategies to add. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) a + 0 = a (Additive identity property of 0)

1.OA.B.4: Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

1.OA.C.5: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.C.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 -8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

1.OA.D.7: Understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

1.OA.D.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

2.OA.B.2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.3 Work with equal groups of objects to gain foundations for multiplication.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

2.OA.C.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

2.OA.C.4: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.4 Understand properties of multiplication and the relationship between multiplication and division to represent and solve problems within 100.

Childhood

Grade 3

Students need not use formal terms for these properties.

Grade 4

Grade 5

Performance Expectations

3.OA.A.1: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 X 7.

3.OA.A.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

3.OA.A.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.A.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = _ ÷ 3, 6 x6 = ?

3.OA.B.5: Apply properties of operations as strategies to multiply. Examples: If 6 x4 = 24 is known, then 4 x6 = 24 is also known. (Commutative property of multiplication.) 3 x5 x2 can be found by 3 x5 = 15, then 15 x2 = 30, or by 5 x2 = 10, then 3 x10 = 30. (Associative property of multiplication.) Knowing that 8 x5 = 40 and 8 X 2 = 16, one can find 8 x7 as 8 x(5 + 2) = (8 x5) + (8 x2) = 40 + 16 = 56. (Distributive property.)

3.OA.B.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8by finding the number that makes 32 when multiplied by 8.

3.OA.C.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5= 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.5 Solve problems involving the four operations.

Childhood

Grade 3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in conventional order when there are no parentheses to specify a particular order (Order of Operations).

Grade 4

Grade 5

Performance Expectations

3.OA.D.8: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.6 Gain familiarity with factors and multiples.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

4.OA.B.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.7 Write and interpret numerical expressions.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2: Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Strand

Algebraic Reasoning - Operations and Algebraic Thinking

Standard

AR.C.8 Identify, explain, generate and analyze patterns.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

3.OA.D.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

4.OA.C.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

5.OA.B.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.1 Apply and extend previous understandings of arithmetic to algebraic expressions.

Early Adolescence

Grades 6-8

Performance Expectations

6.EE.A.1: Write and evaluate numerical expressions involving whole-number exponents.

6.EE.A.2: Write, read, and evaluate expressions in which letters represent numbers.

6.EE.A.2a: Write expressions that record operations with numbers and with letters representing numbers. For example, express the calculation "Subtract y from 5" as 5 - y.

6.EE.A.2b: Identify parts of an expression using mathematical terms (including but not limited to: sum, term, product, factor, quotient, coefficient, variable, constant); view one or more parts of an expression as a single entity. For example, describe the expression 2 (x + 7) as a product of two factors; view (x + 7) as both a single entity and a sum of two terms.

6.EE.A.2c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, using the order of operations. For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

6.EE.A.3: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to factor the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.A.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.2 Reason about and solve one-variable equations and inequalities.

Early Adolescence

Grades 6-8

Performance Expectations

6.EE.B.5: Understand solving an equation or i nequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

6.EE.B.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.B.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. For example, Sal is paid $0.50 per pound of blueberries that she rakes. If she rakes x pounds, and earns $17.25, write and solve an equation that determines how many pounds she raked.

6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.3 Represent and analyze quantitative relationships between dependent and independent variables.

Early Adolescence

Grades 6-8

Performance Expectations

6.EE.C.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.4 Use properties of operations to generate equivalent expressions.

Early Adolescence

Grades 6-8

Performance Expectations

7.EE.A.1: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x+1) and -3(x-5/3) = -3x +5

7.EE.A.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, A shirt is on sale for 20% off the regular price, p. The discount can be expressed as 0.2p. The new price for the shirt can be expressed as p - 0.2p or 0.8p.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.5 Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Early Adolescence

Grades 6-8

Performance Expectations

7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.EE.B.4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

7.EE.B.4b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.6 Work with radicals and integer exponents.

Early Adolescence

Grades 6-8

Performance Expectations

8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 X 3-5 = 3-3 = (1/3)3 = 1/27.

8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that v2 is irrational.

8.EE.A.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

8.EE.A.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.7 Understand the connections between proportional relationships, lines, and linear equations.

Early Adolescence

Grades 6-8

Performance Expectations

8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. For example, given the line y = 0.5x + 3 explain why the similar triangles have the same slope.

Click to view image

Strand

Algebraic Reasoning - Expressions and Equations

Standard

AR.EA.8 Analyze and solve linear equations and pairs of simultaneous linear equations.

Early Adolescence

Grades 6-8

Performance Expectations

8.EE.C.7: Solve linear equations in one variable.

8.EE.C.7a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

8.EE.C.7b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.

8.EE.C.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

8.EE.C.8b: Solve systems of two linear equations in two variables algebraically (i.e. by substitution or elimination) and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

8.EE.C.8c: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Strand

Algebraic Reasoning - Functions

Standard

AR.EA.9 Define, evaluate, and compare functions in order to model relationships between quantities.

Early Adolescence

Grades 6-8 Function notation is not required for Grade 8.

Performance Expectations

8.F.A.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.A.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.F.B.4: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Strand

Algebraic Reasoning - Algebra: Seeing Structure in Expressions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

AR.A.1 Interpret the structure of expressions.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context. *

SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients. *

SSE.A.1b: Interpret multi-part expressions by viewing one or more of their parts as a single entity. For example, view P(1+r)n as the product of P and a factor not depending on P and interpret the parts. *

HSA.SSE.A.2: Use the structure of an expression to identify ways to rewrite it. For example, see x4 - y4 as (x2)2 -(y2)2, allowing for it to be recognized as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

Strand

Algebraic Reasoning - Algebra: Seeing Structure in Expressions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

AR.A.2 Write expressions in equivalent forms to reveal information and to solve problems. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.SSE.B.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. *

HSA.SSE.B.3a: Rewrite a quadratic expression (such as by factoring) to reveal the zeros of the function it defines. *

HSA.SSE.B.3b: Rewrite a quadratic expression (such as by completing the square) to reveal the maximum or minimum value of the function it defines. *

HSA.SSE.B.3c: Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t ~ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. *

HSA.SSE.B.4: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, Watermilfoil in one Maine lake triples in the number of plants each week during the summer when boat propellers are not cleared when exiting the lake. If the lake has 20 plants at the beginning of the season, how many plants will exist at the end of the 12-week summer season? What is the general formula for Watermilfoil growth for this lake? *

Strand

Algebraic Reasoning - Algebra: Arithmetic with Polynomials & Rational Expressions

Standard

AR.A.3 Perform arithmetic operations on polynomials.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.APR.A.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.

HSA.APR.A.1a: Perform operations on polynomial expressions (addition, subtraction, multiplication, and division), and compare the system of polynomials to the system of integers.

HSA.APR.A.1b: Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive Property.

Strand

Algebraic Reasoning - Algebra: Arithmetic with Polynomials & Rational Expressions

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.4 Understand the relationship between zeros and factors of polynomials.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.APR.B.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). For example, consider the polynomial function P(x) = x4 - 2x3 + ax2 + 8x + 12, where a is an unknown real number. If (x-3) is a factor of this polynomial, what is the value of a*

(+) HSA.APR.B.3: Identify zeros of polynomials of degree three or higher when suitable factorizations (in factored form or easily factorable) are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Strand

Algebraic Reasoning - Algebra: Arithmetic with Polynomials & Rational Expressions

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.5 (+) Use polynomial identities to solve problems.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSA.APR.C.4: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

(+) HSA.APR.C.5: Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

Strand

Algebraic Reasoning - Algebra: Arithmetic with Polynomials & Rational Expressions

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.6 Rewrite rational expressions.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.APR.D.6: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

(+) HSA.APR.D.7: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Strand

Algebraic Reasoning -Algebra: Creating Equations and/or Inequalities

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

AR.A.7 Create equations and/or inequalities that describe numbers or relationships. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. *

HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *

HSA.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods such as lobsters, blueberries, and potatoes. *

HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. *

Strand

Algebraic Reasoning - Algebra: Reasoning with Equations & Inequalities

Standard

AR.A.8 Understand solving equations as a process of reasoning and explain the reasoning.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solution method.

HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing hextraneous solutions may arise.

Strand

Algebraic Reasoning - Algebra: Reasoning with Equations & Inequalities

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.9 Solve equations and inequalities in one variable.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HSA.REI.B.4: Solve quadratic equations in one variable.

HSA.REI.B.4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.

HSA.REI.B.4b: i) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

(+) HSA.REI.B.4b: ii) Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Strand

Algebraic Reasoning - Algebra: Reasoning with Equations & Inequalities

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.10 Solve systems of equations.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.REI.C.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

HSA.REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the point(s) of intersection between the line y = -3x and the circle x2 + y2 = 3.

(+) HSA.REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.

(+) HSA.REI.C.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).

Strand

Algebraic Reasoning - Algebra: Reasoning with Equations & Inequalities

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

AR.A.11 Represent and solve equations and inequalities graphically.

Adolescence

Grades 9-Diploma

Performance Expectations

HSA.REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation.

HSA.REI.D.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. *

HSA.REI.D.12: Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Strand

Algebraic Reasoning - Functions: Interpreting Functions

Standard

AR.A.12 Understand the concept of a function and use function notation.

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.IF.A.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

HSF.IF.A.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n = 1.

Strand

Algebraic Reasoning - Functions: Interpreting Functions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

AR.A.13 Interpret functions that arise in applications in terms of the context. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features may include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative and absolute maximums and minimums; symmetries; end behavior; and periodicity. *

HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. *

HSF.IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. *

Strand

Algebraic Reasoning - Functions: Interpreting Functions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.14 Analyze functions using different representations.

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.IF.C.7: Graph functions expressed symbolically and as well as show and describe key features of the graph, by hand in simple cases and using technology for more complicated cases. *

HSF.IF.C.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF.IF.C.7b: i) Graph square root and piecewise-defined functions, (including step functions and absolute value functions), as well as show and describe key features of the graph.

(+) HSF.IF.C.7b: ii) Graph cube root functions, as well as show and describe key features of the graph.

(+) HSF.IF.C.7c: Graph polynomial functions of degree three or higher, identifying zeros when suitable factorizations (in factored form or easily factorable) are available, and showing end behavior.

(+) HSF.IF.C.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

HSF.IF.C.7e: i) Graph exponential functions, showing intercepts and end behavior, and

(+) HSF.IF.C.7e: ii) Graph logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline, and amplitude.

HSF.IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF.IF.C.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, maximum and minimum values, and symmetry of the graph, and interpret these in terms of a context.

HSF.IF.C.8b: Use the properties of exponents to interpret expressions for exponential functions. For example, apply the properties to financial situations such as identifying appreciation and depreciation rate for the value of a house or car sometime after its initial purchase: Vn = P(1 + r)n.

HSF.IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Strand

Algebraic Reasoning - Functions: Building Functions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.15 Build a function that models a relationship between two quantities. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.BF.A.1: Write a function that describes a relationship between two quantities. *

HSF.BF.A.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

HSF.BF.A.1b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

(+) HSF.BF.A.1c: Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

HSF.BF.A.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. *

Strand

Algebraic Reasoning - Functions: Building Functions

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.16 Build new functions from existing functions.

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Okay as written.

HSF.BF.B.4: Find inverse functions.

HSF.BF.B.4a: Solve an equation of the form f(x) = c (where c represents the output value of the function) for a simple function f that has an inverse and write an expression for the inverse. For example, if f(x) =2 x3, then solving f(x) = c leads to x = (c/2)1/3, which is the general formula for finding an input from a specific output, c, for this function.

(+) HSF.BF.B.4b: Verify by composition that one function is the inverse of another.

(+) HSF.BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

(+) HSF.BF.B.4d: Produce an invertible function from a non-invertible function by restricting the domain. (+) HSF.BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Strand

Algebraic Reasoning - Functions: Linear, Quadratic, & Exponential Models

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.17 Construct and compare linear, quadratic, and exponential models and solve problems. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. *

HSF.LE.A.1a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

HSF.LE.A.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

HSF.LE.A.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

HSF.LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). *

HSF.LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. *

(+) HSF.LE.A.4: For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. *

Strand

Algebraic Reasoning - Functions: Linear, Quadratic, & Exponential Models

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

AR.A.18 Interpret expressions for function in terms of the situation they model. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context. *

Strand

Algebraic Reasoning - Functions: Trigonometric Functions

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.19 Extend the domain of trigonometric functions using the unit circle.

Adolescence

Grades 9-Diploma

Performance Expectations

HSF.TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

HSF.TF.A.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

(+) HSF.TF.A.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for p/3, p/4 and p/6, and use the unit circle to express the values of sine, cosine, and tangent for x, p + x, and 2p - x in terms of their values for x, where x is any real number.

(+) HSF.TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Strand

Algebraic Reasoning - Functions: Trigonometric Functions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.20 (+) Model periodic phenomena with trigonometric functions.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSF.TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. *

(+) HSF.TF.B.6: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

(+) HSF.TF.B.7: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. *

Strand

Algebraic Reasoning - Functions: Trigonometric Functions

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

AR.A.21 (+) Prove and apply trigonometric identities.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSF.TF.C.8: Prove the Pythagorean identity sin2([CIRCLED MINUS]) + cos2([CIRCLED MINUS]) = 1 and use it to find sin([CIRCLED MINUS]), cos([CIRCLED MINUS]), or tan([CIRCLED MINUS]) given sin([CIRCLED MINUS]), cos([CIRCLED MINUS]), or tan([CIRCLED MINUS]) and the quadrant of the angle.

(+) HSF.TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Geometric Reasoning

Geometric reasoning is the use of critical thinking, logical argument and spatial reasoning to solve problems and find new relationships. Students must first have a critical understanding of any underlying assumptions and relationships. This allows them to develop coherent knowledge and apply their reasoning skills. In this K-5 strand, students will develop an understanding of the attributes of two- and three-dimensional shapes and apply this knowledge to real-world problems. Students will also be introduced to the coordinate system.

Students in grades 6-8 work with two- and three-dimensional objects to reason about relationships among shapes. They learn to calculate area, surface area, volume, and circumference using multiple methods including decomposing shapes so that they can develop, justify, and use formulas including the Pythagorean Theorem and its converse. They use scale drawings and informal constructions to gain familiarity with the relationships between angles formed by intersecting lines and transformations.

During high school, students begin to formalize their geometry experiences from elementary and middle school, using more complex definitions and reasoning of proofs. Students make geometric constructions using a variety of technological tools and connect these explorations to reasoning and proofs. Attributes of parallel lines intersected by a transversal are further developed and extended into properties of triangles, quadrilaterals, and regular polygons as well as circles using informal and formal reasoning. Fundamental to the concepts of congruence, similarity, and symmetry are transformations which can preserve distance and angles.

The definitions of sine, cosine, and tangent for acute angles are founded on right triangles and similarity. The Pythagorean Theorem along with these ratios are fundamental in many real-world and theoretical situations. Correspondence between numerical coordinates and geometric points allows methods from algebra to be applied to geometry and vice versa. Concepts of two- and three-dimensional shapes are explored using algebraic formulas and modeling. Students are encouraged to extend their geometric reasoning through the exploration of trigonometric identities and properties of conic sections.

Strand

Geometric Reasoning - Geometry

Standard

GR.C.1 Identify, describe, analyze, compare, create, and compose shapes based on their attributes.

Childhood

Kindergarten

Grade 1

Students should apply the principle of transitivity of measurement to make indirect comparisons, but they need not use this technical term.

Grade 2

Sizes are compared directly or visually, not compared by measuring.

Performance Expectations

K.G.A.1: Describe objects in the environment using names of shapes and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

K.G.A.2: Correctly name shapes regardless of their orientations or overall size.

K.G.A.3: Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").

K.G.B.4: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length).

K.G.B.5: Model shapes in the world by building shapes fromcomponents (e.g., sticks and clay balls) and drawing shapes.

K.G.B.6: Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?"

1.G.A.1: Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

1.G.A.2: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

1.G.A.3: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

2.G.A.1: Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals (including squares, rectangles, rhombuses, and trapezoids) pentagons, hexagons, and cubes. Sizes are compared directly or visually, not compared by measuring.

2.G.A.2: Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

2.G.A.3: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Strand

Geometric Reasoning - Geometry

Standard

GR.C.2 Analyze, compare, create, and compose shapes based on their attributes.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

3.G.A.1: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

3.G.A.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

5.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties. (e.g., all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite sides parallel.)

Strand

Geometric Reasoning - Geometry

Standard

GR.C.3 Draw and identify lines and angles and classify shapes by properties of their lines and angles.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4.G.A.2: Classify two -dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category and identify right triangles.

4.G.A.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Strand

Geometric Reasoning - Geometry

Standard

GR.C.4 Graph points on the coordinate plane to solve real-world and mathematical problems.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line a nd a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.A.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

Strand

Geometric Reasoning - Geometry

Standard

GR.EA.1 Solve real-world and mathematical problems involving angle measure, area, surface area, and volume.

Early Adolescence

Grades 6-8

Performance Expectations

6.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h (where B stands for the area of the base) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

6.G.A.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

6.G.A.4: Represent three-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

7.G.B.4: Know that a circle is a two-dimensional shape created by connecting all the points equidistant from a fixed point called the center of the circle. Understand ancircumference and area of a circle. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.G.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and/or three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Strand

Geometric Reasoning - Geometry

Standard

GR.EA.2 Draw, construct, and describe geometrical figures and describe the relationships between them.

Early Adolescence

Grades 6-8

Performance Expectations

7.G.A.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.G.A.2: Draw (freehand, with ruler and protractor, and with technology) two-dimensional geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.A.3: Describe the shape of the cross-section two-dimensional face of the figures that results from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Strand

Geometric Reasoning - Geometry

Standard

GR.EA.3 Understand congruence and similarity using physical models, transparencies, or geometry software,

Early Adolescence

Grades 6-8

Performance Expectations

8.G.A.1: Verify experimentally the properties of rotations, reflections, and translations:

8.G.A.1a: Lines are taken to lines, and line segments to line segments of the same length.

8.G.A.1b: Angles are taken to angles of the same measure.

8.G.A.1c: Parallel lines are taken to parallel lines.

8.G.A.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.A.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.A.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.A.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Strand

Geometric Reasoning - Geometry

Standard

GR.EA.4 Understand and apply the Pythagorean Theorem.

Early Adolescence

Grades 6-8

Performance Expectations

8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse using pictures, diagrams, narratives or models.

8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Strand

Geometric Reasoning - Geometry: Congruence

Standard

GR.A.1 Experiment with transformations in the plane.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

HSG.CO.A.2: Represent transformations in the plane using, e.g., transparencies and/or geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

HSG.CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

HSG.CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

HSG.CO.A.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Strand

Geometric Reasoning - Geometry: Congruence

Standard

GR.A.2 Understand congruence in terms of rigid motions.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

HSG.CO.B.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

HSG.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Strand

Geometric Reasoning - Geometry: Congruence

Standard

GR.A.3 Prove geometric theorems and when appropriate, the converse of theorems.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.CO.C.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, and conversely prove lines are parallel; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

HSG.CO.C.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent, and conversely prove a triangle is isosceles; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

HSG.CO.C.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Strand

Geometric Reasoning - Geometry: Congruence

Standard

GR.A.4 Make geometric constructions.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

HSG.CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Strand

Geometric Reasoning - Geometry: Similarity, Right Triangles, & Trigonometry

Standard

GR.A.5 Understand similarity in terms of similarity transformations.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor:

HSG.SRT.A.1a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

HSG.SRT.A.1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

HSG.SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

HSG.SRT.A.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Strand

Geometric Reasoning - Geometry: Similarity, Right Triangles, & Trigonometry

Standard

GR.A.6 Prove theorems involving similarity using a variety of ways of writing proofs, showing validity of underlying reasoning.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.SRT.B.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

HSG.SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Strand

Geometric Reasoning - Geometry: Similarity, Right Triangles, & Trigonometry

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

GR.A.7 Define trigonometric ratios and solve problems involving right triangles.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

HSG.SRT.C.7: Explain and use the relationship between the sine and cosine of complementary angles.

HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. For example, find the current height of the tallest pine tree in Maine using the angle of elevation and the distance from the tree. *

Strand

Geometric Reasoning - Geometry: Similarity, Right Triangles, & Trigonometry

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

GR.A.8 (+) Apply trigonometry to general triangles.

Adolescence

Grades 9-Diploma

Performance Expectations

(+) HSG.SRT.D.9: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

(+) HSG.SRT.D.10: Prove the Laws of Sines and Cosines and use them to solve problems.

(+) HSG.SRT.D.11: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Strand

Geometric Reasoning - Geometry: Circle

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

GR.A.9 Understand and apply theorems about circles.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.C.A.1: Prove that all circles are similar.

HSG.C.A.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

HSG.C.A.3: Construct the inscribed and circumscribed circles of a triangle and prove properties of angles for a quadrilateral inscribed in a circle.

(+) HSG.C.A.4: Construct a tangent line from a point outside a given circle to the circle.

Strand

Geometric Reasoning - Geometry: Circle

Standard

GR.A.10 Find arc lengths and areas of sectors of circles.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.C.B.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Strand

Geometric Reasoning - Geometry: Expressing Geometric Properties with Equations

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

GR.A.11 Translate between the geometric description and the equation for a conic section.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

HSG.GPE.A.2: Derive the equation of a parabola given a focus and directrix.

(+) HSG.GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci and directrix, using the fact that the sum or difference of distances from the foci is constant.

Strand

Geometric Reasoning - Geometry: Expressing Geometric Properties with Equations

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

GR.A.12 Use coordinates to prove simple geometric theorems algebraically.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.GPE.B.4: Use coordinates to prove simple geometric theorems algebraically including the distance formula and its relationship to the Pythagorean Theorem. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, v3) lies on the circle centered at the origin and containing the point (0, 2).

HSG.GPE.B.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

HSG.GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

HSG.GPE.B.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *

Strand

Geometric Reasoning - Geometry: Geometric Measurements & Dimension

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard

GR.A.13 Explain volume formulas and use them to solve problems.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and/or informal limit arguments.

(+) HSG.GMD.A.2: Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

HSG.GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. *

Strand

Geometric Reasoning - Geometry: Geometric Measurements & Dimension

Standard

GR.A.14 Visualize relationships between two-dimensional and three-dimensional objects.

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.GMD.B.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two -dimensional objects.

Strand

Geometric Reasoning - Geometry: Modeling with Geometry

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard

GR.A.15 Apply geometric concepts in modeling situations. *

Adolescence

Grades 9-Diploma

Performance Expectations

HSG.MG.A.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). *

HSG.MG.A.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). *

HSG.MG.A.3: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). *

Statistical Reasoning

Statistical reasoning is the way people analyze data and make sense of information. It involves generalizations that connect one concept to another. In this K-5 strand, students will develop strategies to represent and interpret data, describe and compare measurable attributes, and understand concepts of measurement including perimeter, area, volume, time, and money.

Students in grades 6-8 continue to develop their ability to think statistically. Measures of central tendency (mean, median, and mode) as well as measures of variability (range, interquartile range, mean absolute deviation) are used to describe data. Previous work with single data distributions is expanded to compare two data distributions and address questions about differences between populations. Informal work with random sampling and learning about the importance of representative samples for drawing inferences is introduced. Students then expand their statistical understanding to include connections involving modeling with linear equations, as well as nonlinear expressions. Looking for patterns in a bivariate data system is emphasized.

In grades 9-12 students extend their statistical understanding of univariate and bi-variate data in a real-world context. This understanding is used to make decisions or predictions based on the data. Since data can be variable, statistics provide the tools for taking this variability into account. Data can be categorical or quantitative in nature. Appropriate methods for collecting, displaying, summarizing, and analyzing data are learned and employed. Algebraic and geometric reasoning are utilized to create linear regression models in order to interpret the relationship between two quantitative variables when appropriate.

The conditions under which data are collected and the use of randomization in the design of a study are necessary for drawing valid conclusions about the population under study. Since random processes can be described mathematically by using a probability model, the role of probability in making predictions or in making decisions becomes evident. Technology makes it possible to generate plots, find regression functions, compute correlation coefficients, and run simulations to better understand data. Statistical reasoning is a deeply rich and complex process which is essential to comprehend in order to stay informed in civic matters and personal decision-making.

Strand Statistical Reasoning - Measurement & Data
Standard SR.C.1 Describe and compare measurable attributes.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations K.MD.A.1: Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

K.MD.A.2: Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

K.MD.B.3: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)

1.MD.A.1: Order three objects by length; compare the lengths of two objects indirectly by using a third object.

1.MD.A.2: Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

2.MD.A.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

2.MD.A.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.A.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

2.MD.A.3: Estimate lengths using units of inches, feet, centimeters, and meters.

Strand Statistical Reasoning - Measurement & Data
Standard SR.C.2 Represent and interpret data.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations 1.MD.C.4: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

2.MD.D.9: Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Organize and record data on a line plot, where the horizontal scale is marked off in whole-number units.

2.MD.D.10: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Strand Statistical Reasoning - Measurement & Data
Standard SR.C.3 Relate addition and subtraction to length.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations 2.MD.B.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

2.MD.B.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and differences within 100 on a number line diagram.

Strand Statistical Reasoning - Measurement & Data
Standard SR.C.4 Work with time and money.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations 1.MD.B.3: Tell and write time in hours and half-hours using analog and digital clocks.

1.MD.D.5: Identify the coins and each corresponding value. (e.g. penny, nickel, dime, and quarter)

2.MD.C.7: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

2.MD.C.8: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Strand Statistical Reasoning - Measurement & Data
Standard SR.C.5 Solve problems involving measurement, conversion of measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Childhood
Grade 3 Excludes compound units such as cm3 and finding the geometric volume of a container

Excludes multiplicative comparison problems (problems involving notions of "times as much")

Grade 4 Grade 5
Performance Expectations 3.MD.A.1: Tell and write time to the nearest minute and measure time intervals in minutes using analog and digital clocks. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

3.MD.A.2: Measure and estimate liquid volumes and masses of objects using standard metric units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same metric units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

4.MD.A.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),.

4.MD.A.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Strand Statistical Reasoning - Measurement & Data
Standard SR.C.6 Represent and interpret data.
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations 3.MD.B.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

3.MD.B.4: Generate measurement data by measuring lengths of objects using rulers marked with halves and fourths of an inch. Record and show the data by making a line plot, where the horizontal scale is marked off in appropriate units- whole numbers, halves, or fourths.

4.MD.B.4: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 5.MD.B.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Strand Statistical Reasoning - Measurement & Data
Standard SR.C.7 Understand concepts of Geometric measurement: involving perimeter, area, and volume.
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations 3.MD.C.5: Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.C.5a: A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.

3.MD.C.5b: A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

3.MD.C.6: Measure areas by counting unit squares (square cm, square m, square in, square ft, and non- standard units

3.MD.C.7: Relate area to the operations

of multiplication and addition.

3.MD.C.7a: Find the area of a rectangle with whole-number side lengths by tiling it and show that the area is the same as would be found by multiplying the side lengths.

3.MD.C.7b: Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems and represent whole-number products as rectangular areas in mathematical reasoning.

3.MD.C.7c: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a X c. Use area models to represent the distributive property in mathematical reasoning.

3.MD.C.7d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

3.MD.D.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

5.MD.C.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

5.MD.C.3a: A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

5.MD.C.3b: A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

5.MD.C.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and non-standard units.

5.MD.C.5: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. When finding volumes of objects answers will be in cubic units.

5.MD.C.5a: Find the volume of a right rectangular prism with whole-number edge lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

5.MD.C.5b: Apply the formulas V = l x w x h and V = B x h (where B stands for the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

5.MD.C.5c: Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms b y adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Strand Statistical Reasoning - Measurement & Data
Standard SR.C.8 Geometric measurement: understand concept of angle and measure angles.
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations 4.MD.C.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

4.Md.C.5a: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

4.MD.C.5b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.C.7: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Strand Statistical Reasoning - Statistics & Probability
Standard SR.EA.1 Summarize distribution using measures of center, variability, and graphical displays.
Early Adolescence
Grades 6-8
Performance Expectations

6.SP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

6.SP.A.2: Understand that a set of data collected to answer a statistical question has a distribution which can be

described by its center (mean, median and/or mode), spread (range and/or interquartile range), and overall shape.

6.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5: Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5a: Reporting the number of observations.

6.SP.B.5b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

6.SP.B.5c: Calculating quantitative measures of center (median and/or mean) and variability (range and/or interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

6.SP.B.5d: Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Strand Statistical Reasoning - Statistics & Probability
Standard SR.EA.2 Use random sampling, visual representations, and measures of center and variability to draw inferences about one or more populations.
Early Adolescence
Grades 6-8
Performance Expectations 7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.A.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean length of a largemouth bass in a lake by randomly sampling largemouth bass from the lake; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

7.SP.B.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team and both distributions have similar variability (mean absolute deviation) of about 5 cm. The difference between the mean heights of the two teams (10 cm) is about twice the variability (5 cm mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

7.SP.B.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Strand Statistical Reasoning - Statistics & Probability
Standard SR.EA.3 Investigate chance processes and develop, use, and evaluate probability models.
Early Adolescence
Grades 6-8
Performance Expectations 7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.C.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

7.SP.C.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.C.7a: Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

7.SP.C.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.C.8a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

7.SP.C.8b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

7.SP.C.8c: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Strand Statistical Reasoning - Statistics & Probability
Standard SR.EA.4 Investigate patterns of association in bivariate data.
Early Adolescence
Grades 6-8
Performance Expectations 8.SP.A.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.A.2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.SP.A.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.A.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Strand

Statistical Reasoning - Statistics & Probability: Interpreting Categorical & Quantitative Data

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard SR.A.1 Summarize, represent, and interpret data on a single count or measurement variable. *
Adolescence
Grades 9-Diploma
Performance Expectations HHS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). *

HSS.ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. *

HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). *

HSS.ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. *

Strand

Statistical Reasoning - Statistics & Probability: Interpreting Categorical & Quantitative Data

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard SR.A.2 Summarize, represent, and interpret data on two categorical variables and two quantitative variables. *
Adolescence
Grades 9-Diploma
Performance Expectations HSS.ID.B.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. *

HSS.ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are

related. *

HSS.ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. *

HSS.ID.B.6b: Informally assess the fit of a function by plotting and analyzing residuals. *

HSS.ID.B.6c: Fit a linear function for a scatter plot that suggests a linear association. *

Strand

Statistical Reasoning - Statistics & Probability: Interpreting Categorical & Quantitative Data

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard SR.A.3 Interpret linear models. *
Adolescence
Grades 9-Diploma
Performance Expectations HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. *

HSS.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit. *

HSS.ID.C.9: Distinguish between correlation and causation. *

Strand

Statistical Reasoning - Statistics & Probability: Making Inferences & Justifying Conclusions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard SR.A.4 Understand and evaluate random processes underlying statistical experiments. *
Adolescence
Grades 9-Diploma
Performance Expectations HSS.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. *

HSS.IC.A.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? *

Strand

Statistical Reasoning - Statistics & Probability: Making Inferences & Justifying Conclusions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard SR.A.5 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. *
Adolescence
Grades 9-Diploma
Performance Expectations HSS.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. *

HSS.IC.B.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. *

HSS.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. *

HSS.IC.B.6: Evaluate reports based on data. For example, use an article in the local news and interpret the validity of the information presented. Consider animal wildlife reports, medical studies, and/or manufacturer claims. *

Strand

Statistical Reasoning - Statistics & Probability: Conditional Probability & the Rules of Probability

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

Standard SR.A.6 Understand independence and conditional probability and use them to interpret data. *
Adolescence
Grades 9-Diploma
Performance Expectations HSS.CP.A.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). *

HSS.CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. *

HSS.CP.A.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. *

HSS.CP.A.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. *

HSS.CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. *

Strand

Statistical Reasoning - Statistics & Probability: Conditional Probability & the Rules of Probability

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard SR.A.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. *
Adolescence
Grades 9-Diploma
Performance Expectations HSS.CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. *

HSS.CP.B.7: Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. *

(+) HSS.CP.B.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. *

(+) HSS.CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems. *

Strand

Statistical Reasoning - Statistics & Probability: Using Probability to Make Decisions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard SR.A.8 (+) Calculate expected values and use them to solve problems. *
Adolescence
Grades 9-Diploma
Performance Expectations (+) HSS.MD.A.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. *

(+) HSS.MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. *

(+) HSS.MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. *

(+) HSS.MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? *

Strand

Statistical Reasoning - Statistics & Probability: Using Probability to Make Decisions

Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appears throughout the high school standards indicated by a star symbol ( * ).

The high school standards also contain some performance expectations which are denoted by a plus (+). These performance expectations are intended to be extensions of learning. All students should be given opportunities to explore this content, but mastery is not expected.

Standard SR.A.9 (+) Use probability to evaluate outcomes of decisions. *
Adolescence
Grades 9-Diploma
Performance Expectations (+) HSS.MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. *

(+) HSS.MD.B.5a: Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. *

(+) HSS.MD.B.5b: Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. *

(+) HSS.MD.B.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *

(+) HSS.MD.B.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game and replacing the goalie with an extra skater). *

Definitions:

Strand: A body of knowledge in a content area identified by a simple title.

Standard: Enduring understandings and skills that students can apply and transfer to contexts that are new to the student.

Performance Expectation: Building blocks to the standard and measurable articulations of what the student understands and can do.

Science & Engineering Standards

Science and engineering provide people with knowledge and tools to understand and address many of the challenges of a rapidly changing world, thus enabling them to be creative and practical problem solvers (Maine Guiding Principle C). Science is a way of knowing about the world that enables people to both engage in the construction of new knowledge and to use information to achieve desired ends (NIH). Engineering enables people to systematically solve problems using scientific knowledge, to design and test solutions and evaluate them using agreed-upon and measurable criteria.

Science and Engineering Literacy

In the last few decades, much has been written about the critical role of science literacy in an equitable and just society. For example, the Board on Science Education within the National Academies of Science argue that

"Science literacy is desirable not only for individuals, but also for the health and well-being of communities and society. More than just basic knowledge of science facts, contemporary definitions of science literacy have expanded to include understandings of scientific processes and practices, familiarity with how science and scientists work, a capacity to weigh and evaluate the products of science, and an ability to engage in civic decisions about the value of science."

Here we recognize that, in addition to understanding and evaluating science knowledge and critiquing the development of that knowledge, learners must also develop literacy related to science and engineering practices and design. In other words, they should know about and be able to critique the processes by which engineers develop and test products in response to consumer, industrial, and/or civic needs. The Maine Science and Engineering Standards provide a framework for supporting K-12 students' development as self-directed lifelong learners (Maine Guiding Principle B) who are able to apply knowledge from the domains of science and engineering to set goals and make decisions.

Understanding Controversy in Science

Individuals have ready access to abundant information in our modern global society. Consequently, they will encounter myriad arguments related to various scientific topics. Moreover, arguments will change over time, as new evidence becomes available and as people draw on scientific evidence to formulate arguments in shifting social contexts. It is therefore imperative that individuals understand that controversy within the scientific community is normal and has been historically productive. "True scientific controversy involves competing scientific ideas that are evaluated according to the standards of science - i.e., fitting the evidence, generating accurate expectations, offering satisfying explanations, inspiring research, etc...few theories fit our observations of the world perfectly. There is usually some anomalous observation that doesn't seem to fit with our current understanding. Scientists assume that by working at such anomalies, they'll either disentangle them to see how they fit with the current theory or contribute to a new theory" ("Even Theories Change." Understanding Science. University of California Museum of Paleontology. 23 July 2018 <http://www.understandingscience.org/article/alvarez_01>). One well documented example of productive controversy is the development of modern theories that explain and predict phenomena in the physical world. Newton originally posited a theory of mechanics that adequately explained phenomena as varied as projectile motion and planetary orbit. Centuries later, Einstein developed the theory of special relativity to account for additional phenomena related to electricity and magnetism. The need to account for and predict the effects of gravity spurred scientists to offer the theory of general relativity. Thus, "theory change is a community process of feedback, experiment, observation, and communication. It usually involves interpreting existing data in new ways and incorporating those views with new results" ("Even Theories Change." Understanding Science. University of California Museum of Paleontology. 23 July 2018 <http://www.understandingscience.org/article/alvarez_01>).

Becoming Critical and Engaged Consumers of Science and Engineering

As learners encounter diverse perspectives related to scientific issues, it is crucial that they become integrative and informed thinkers (Maine Guiding Principle E) able to discern reliable and valid information. Such information is generated through accepted scientific and engineering practices (e.g., analyzing and interpreting data, engaging in argument from evidence, etc.). Armed with knowledge and these skills, learners will be able to function as responsible and involved citizens (Maine Guiding Principle D) who utilize clear and effective communication strategies (Maine Guiding Principle A) to participate productively in decision making that impacts the broader community.

References:

National Research Council. 2012. A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. Washington, DC: The National Academies Press.

From NAEP (https://nces.ed.gov/nationsreportcard/tel/)

NGSS Lead States. (2013). Next Generation Science Standards: For states, by states. Washington, DC: The National Academies Press.

https://www.ncbi.nlm.nih.gov/books/NBK396081/

Committee on Science Literacy and Public Perception of Science; Board on Science Education; Division of Behavioral and Social Sciences and Education; National Academies of Sciences, Engineering, and Medicine; Snow CE, Dibner KA, editors. Washington (DC): National Academies Press (US); 2016 Oct 14.

OUTLINE OF SCIENCE AND ENGINEERING STRANDS AND STANDARDS

Physical Sciences PS1 Matter and Its Interactions PS2 Motion and Stability: Forces and Interactions PS3 Energy PS4 Waves and Their Applications in Technologies Life Sciences LS1 From Molecules to Organisms: Structures and Processes LS2 Ecosystems: Interactions, Energy, and Dynamics LS3 Heredity: Inheritance and Variation of Traits LS4 Biological Evolution: Unity and Diversity Earth and Space Sciences ESS1 Earth's Place in the Universe ESS2 Earth's Systems ESS3 Earth and Human Activity Engineering, Technology, and Applications of Science ETS1 Engineering Design

OUTLINE OF SCIENCE AND ENGINEERING STRANDS AND STANDARDS

Physical Sciences

PS1 Matter and Its Interactions

PS2 Motion and Stability: Forces and Interactions

PS3 Energy

PS4 Waves and Their Applications in Technologies

Life Sciences

LS1 From Molecules to Organisms: Structures and Processes

LS2 Ecosystems: Interactions, Energy, and Dynamics

LS3 Heredity: Inheritance and Variation of Traits

LS4 Biological Evolution: Unity and Diversity

Earth and Space Sciences

ESS1 Earth's Place in the Universe

ESS2 Earth's Systems

ESS3 Earth and Human Activity

Engineering, Technology, and Applications of Science

ETS1 Engineering Design

HOW TO READ THE STANDARDS

COLOR SCHEME

Strand

Grade Level Standard

Performance Expectation

-> 2- LS 3-1 <-

Science & Engineering Practices (blue)

Disciplinary Core Ideas (orange)

Crosscutting Concepts (green)

Strand Physical Science (PS)
Standard PS1: Matter and Its Interactions
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

2-PS1-1 Plan and conduct an investigation to describe and classify different kinds of materials by their observable properties.

Further explanation: Observations could include color, texture, hardness, and flexibility. Patterns could include the similar properties that different materials share. Planning and Carrying out Investigations, Structure and Properties of Matter, Patterns

2-PS1-2 Analyze data obtained from testing different materials to determine which materials have the properties that are best suited for an intended purpose.

Further explanation: Examples of properties could include strength, flexibility, hardness, texture, and absorbency. Potential Maine connections include snow tires vs. regular tires and mittens made of varying materials (e.g. wool, cotton, Gortex, etc.) Analyzing and Interpreting Data, Structure and Properties of Matter, Cause and Effect

2-PS1-3 Make observations to construct an evidence-based account of how an object made of a small set of pieces can be disassembled and made into a new object.

Further explanation: Examples of pieces could include blocks, building bricks, or other assorted small objects. Constructing Explanations and Designing Solutions, Structure and Properties of Matter, Energy and Matter

2-PS1-4 Construct an argument with evidence that some changes caused by heating or cooling can be reversed and some cannot.

Further explanation: Examples of reversible changes could include materials such as water and butter at different temperatures. Potential Maine examples include snow and ice having reversible properties (e.g. water freezes and thaws which allows for ice fishing and skating in colder months). Examples of irreversible changes could include cooking an egg, freezing a plant leaf, heating paper and burning wood in a campfire or woodstove.

Engaging in Argument from Evidence, Chemical Reactions, Cause and Effect

Strand Physical Science (PS)
Standard PS1: Matter and Its Interactions
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

5-PS1-1 Develop a model to describe that matter is made of particles too small to be seen.

Further Explanation: Examples of evidence could include adding air to expand a basketball, compressing air in a syringe, dissolving sugar in water, and evaporating salt water. Investigate the science behind creating Maine maple sugar. Developing and Using Models, Structure and Properties of Matter, Scale, Proportion, and Quantity

5-PS1-2 Measure and graph quantities to provide evidence that regardless of the type of change that occurs when heating, cooling, or mixing substances, the total weight of matter is conserved.

Further Explanation: Examples of reactions or changes could include phase changes, dissolving, and mixing that form new substances. Investigate the conservation of mass when making fake snow and how the crystals form.

Using Mathematics and Computational Thinking, Structure and Properties of Matter, Chemical Reactions, Cause and Effect

5-PS1-3 Make observations and measurements to identify materials based on their properties.

Further Explanation: Examples of materials to be identified could include baking soda and other powders, metals, minerals, and liquids. Examples of properties could include color, hardness, reflectivity, electrical conductivity, thermal conductivity, response to magnetic forces, and solubility; density is not intended as an identifiable property. Possibly examine Maine minerals.

Planning and Carrying out Investigations, Structure and Properties of Matter, Scale, Proportion and Quantity

5-PS1-4 Conduct an investigation to determine whether the mixing of two or more substances results in new substances.

Planning and Carrying out Investigations, Chemical Reactions, Cause and Effect

Strand Physical Science (PS)
Standard PS1: Matter and Its Interactions
Early Adolescence
Grades 6-8
Performance Expectations MS-PS1-1 Develop models to describe the atomic composition of simple molecules and extended structures.

Further explanation: Emphasis is on developing models of molecules that vary in complexity. Examples of simple molecules could include ammonia and methanol. Examples of extended structures could include sodium chloride or diamonds. Examples of molecular-level models could include drawings, three-dimensional ball and stick structures, or computer representations showing different molecules with different types of atoms. Developing and using models; Obtaining, evaluating, and communicating information; structure and properties of matter; scale, proportion, and quantity

MS-PS1-2 Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred.

Further explanation: Examples of reactions could include burning sugar or steel wool, fat reacting with sodium hydroxide, and mixing zinc with hydrogen chloride. Examine electrical conductivity differences between fresh water and sea water.

Obtaining, evaluating, and communicating information; Analyzing and interpreting data; structure and properties of matter; chemical reactions; patterns

MS-PS1-3 Gather and make sense of information to describe that synthetic materials come from natural resources and impact society.

Further explanation: Emphasis is on natural resources that undergo a chemical process to form synthetic material. Examples of new materials could include new medicines, foods, and alternative fuels (alternative plastics derived from potatoes and jet fuel made from trees). Other possible areas of study might include plastics from organics, advanced composites and wood products under development at UMO. Obtaining, evaluating, and communicating information; chemical reactions; structure and properties of matter; structure and function

MS-PS1-4 Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed.

Further explanation: Emphasis is on qualitative molecular-level models of solids, liquids, and gases to show that adding or removing thermal energy increases or decreases kinetic energy of the particles until a change of state occurs. Examples of models could include drawings and diagrams. Examples of particles could include molecules or inert atoms. Examples of pure substances could include water, carbon dioxide, and helium. Developing and using models; structure and properties of matter; definitions of energy; cause and effect

MS-PS1-5 Develop and use a model to describe how the total number of atoms does not change in a chemical reaction and thus mass is conserved.

Further explanation: Emphasis is on the law of conservation of matter and on physical models or drawings,

including digital forms that represent atoms.

Developing and using models; chemical reactions; energy and matter

MS-PS1-6 Undertake a design project to construct, test, and modify a device that either releases or absorbs thermal energy by chemical processes.

Further explanation: Emphasis is on design, controlling the transfer of energy to the environment, and modification of a device using factors such as type and concentration of a substance. Examples of designs could involve chemical reactions such as dissolving ammonium chloride or calcium chloride for road treatments in Maine winters.

Constructing explanations and designing solutions; chemical reactions; developing possible solutions; optimizing the design solution; structure and function

Strand Physical Science (PS)
Standard PS1: Matter and Its Interactions
Adolescence
Grades 9-Diploma
Performance Expectations

HS-PS1-1 Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms.

Further explanation: Examples of properties that could be predicted from patterns could include reactivity of metals, types of bonds formed, numbers of bonds formed, and reactions with oxygen. Examples include the properties and bonding of water and the rusting of metals as found in guardrails, ship parts, etc. Consider the metal compounds found in fireworks. Developing and Using Models, structure and properties of matter, types of interactions, patterns

HS-PS1-2 Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties.

Further explanation: Examples of chemical reactions could include the reaction of sodium and chlorine, carbon and oxygen, or carbon and hydrogen. Examples could include ocean salt formation, combustion (as found in the burning of fuels in Maine homes, cars and the trucking industry) or the detection of carbon monoxide in a home (complete vs incomplete combustion).

Constructing Explanations and Designing Solutions, structure and properties of matter, chemical reaction, patterns

HS-PS1-3 Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles.

Further explanation: Emphasis is on understanding the strengths of forces between particles, not on naming specific intermolecular forces (such as dipole-dipole). Examples of particles could include ions, atoms, molecules, and networked materials (such as graphite). Examples of bulk properties of substances could include the melting point and boiling point, vapor pressure, and surface tension. Examples could consider why we salt roads in the winter, differences in melting points of water vs saltwater, the production of maple syrup or the strength of Maine minerals. Planning and Carrying out Investigations, structure and properties of matter, types of interactions, patterns

HS-PS1-4 Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends on the changes in total bond energy.

Further explanation: Emphasis is on the idea that a chemical reaction is a system that affects the energy change. Examples of models could include molecular-level drawings and diagrams of reactions, graphs showing the relative energies of reactants and products, and representations showing energy is conserved. Developing and Using Models, structure and properties of matter, Energy and Matter

HS-PS1-5 Apply scientific principles and evidence to provide an explanation about the effects of changing the temperature or concentration of the reacting particles on the rate at which a reaction occurs.

Further explanation: Emphasis is on student reasoning that focuses on the number and energy of collisions between molecules. Examples could include the varied rates of oxidation of metals in winter vs in summer or the rate of dissolution of calcium shells in the ocean due to an increase in carbon dioxide an increase in temperature from climate change. Constructing Explanations and Designing Solutions, Chemical Reactions, patterns

HS-PS1-6 Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium.

Further explanation: Emphasis is on the application of Le Chatelier's Principle and on refining designs of chemical reaction systems, including descriptions of the connection between changes made at the macroscopic level and what happens at the molecular level. Examples of designs could include different ways to increase product formation including adding reactants or removing products. Other examples to consider include the Kraft paper making process, soap making or rock candy formation.

Constructing Explanations and Designing Solutions, structure and properties of matter, Chemical Reactions, Types of Interactions, Optimizing Design Solution patterns, cause and effect, scale, proportion, and quantity

HS-PS1-7 Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.

Further explanation: Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students' use of mathematical thinking and not on memorization and rote application of problem-solving techniques. Examples could include the proportion of ingredients combined in baked goods or the combustion of fuels. Using Mathematics and Computational Thinking, Chemical Reactions, Energy and Matter

HS-PS1-8 Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay.

Further explanation: Emphasis is on simple qualitative models, such as pictures or diagrams and on the scale of energy released in nuclear processes relative to other kinds of transformations. Examples could include radon gas in basements, thorium in white gas mantles or, historically, Wiscasset's Maine Yankee nuclear power plant and Fukushima in Japan.

Developing and engineering practices, Nuclear Processes, patterns, cause and effect, scale, proportion, and quantity

Strand Physical Science (PS)
Standard PS2: Motion and Stability: Forces and Interactions
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

K-PS2-1 Plan and conduct an investigation to compare the effects of different strengths or different directions of pushes and pulls on the motion of an object.

Further explanation: Examples of pushes or pulls could include a string attached to an object being pulled, a person pushing an object, a person stopping a rolling ball, and two objects colliding and pushing on each other.

Planning and Carrying out Investigations, Forces and Motion, Types of Interactions, Relationship between Energy and Forces, Cause and Effect

K-PS2-2 Analyze data to determine if a design solution works as intended to change the speed or direction of an object with a push or a pull.

Further explanation: Examples of problems requiring a solution could include having a marble or other object move a certain distance, follow a particular path, and knock down other objects. Examples of solutions could include tools such as a ramp to increase the speed of the object and a structure that would cause an object such as a marble or ball to turn.

Analyzing and Interpreting Data, Forces and Motion, Defining Engineering Problems, Cause and Effect

Strand Physical Science (PS)
Standard PS2: Motion and Stability: Forces and Interactions
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-PS2-1 Plan and conduct an investigation to provide evidence of the effects of balanced and unbalanced forces on the motion of an object.

Further Explanation: Examples could include an unbalanced force on one side of a ball can make it start moving and balanced forces pushing on a box from both sides will not produce any motion at all. Other examples can be found in a variety of Maine sports from ice skating, curling, skiing to sledding.

Planning and Carrying Out Investigations, Forces and Motion, Types of Interactions, Cause and Effect

3-PS2-2 Make observations and/or measurements of an object's motion to provide evidence that a pattern can be used to predict future motion.

Further Explanation: Examples of motion with a predictable pattern could include a child swinging in a swing, a ball rolling back and forth in a bowl, and two children on a see-saw. Other examples include dropping down in a skate park, snowboarding pipes and telemark skiing (slowing down, turns, etc.). Planning and Carrying out Investigations,Forces and Motion, Patterns

3-PS2-3 Ask questions to determine cause and effect relationships of electrical or magnetic interactions between two objects not in contact with each other.

Further Explanation: Examples of an electric force could include the force on hair from an electrically charged balloon and the electrical forces between a charged rod and pieces of paper; examples of a magnetic force could include the force between two permanent magnets, the force between an electromagnet and steel paperclips, and the force exerted by one magnet versus the force exerted by two magnets. Examples of cause and effect relationships could include how the distance between objects affects strength of the force and how the orientation of magnets affects the direction of the magnetic force.

Asking Questions and Defining Problems, Types of Interactions, Cause and Effect

3-PS2-4 Define a simple design problem that can be solved by applying scientific ideas about magnets.

Further Explanation: Examples of problems could include constructing a latch to keep a door shut and creating a device to keep two moving objects from touching each other. Other examples include a magnetic latch for a container or device (Apple and magnetic plug for charger).

Asking Questions and Defining Problems, Types of Interactions

5-PS2-1 Support an argument that the gravitational force exerted by Earth on objects is directed down.

Further Explanation: "Down" is a local description of the direction that points toward the center of the spherical Earth. Engaging in Argument from Evidence, Types of Interactions, Cause and Effect

Strand Physical Science (PS)
Standard PS2: Motion and Stability: Forces and Interactions
Early Adolescence
Grades 6-8
Performance Expectations

MS-PS2-1 Apply Newton's Third Law to design a solution to a problem involving the motion of two colliding objects.

Further explanation: Examples of practical problems could include the impact of collisions between two cars, between a car and stationary objects, and between a meteor and a space vehicle.

Constructing explanations and designing solutions; forces and motion; system and system models;

MS-PS2-2 Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.

Further explanation: Emphasis is on balanced (Newton's First Law) and unbalanced forces in a system, qualitative comparisons of forces, mass and changes in motion (Newton's Second Law), frame of reference, and specification of units. Plan and carry out investigations; forces and motion; stability and change;

MS-PS2-3 Ask questions about data to determine the factors that affect the strength of electrical and magnetic forces.

Further e xplanation: Examples of devices that use electrical and magnetic forces could include electromagnets, electric motors, or generators. Examples of data could include the effect of the number of turns of wire on the strength of an electromagnet, or the effect of increasing the number or strength of magnets on the speed of an electric motor. Possible explorations include the effects of living near high tension power lines, the similarities found in hydroelectric generators and wind turbines or the growing electric car market in Maine. Asking questions and defining problems; types of interactions; cause and effect;

MS-PS2-4 Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects.

Further explanation: Examples of evidence for arguments could include data generated from simulations or digital tools and charts displaying mass, strength of interaction, distance from the Sun, and orbital periods of objects within the solar system. Examples include the gravitational effects of the moon on Maine tides.

Engaging in argument from evidence; types of interactions; system and system models;

MS-PS2-5 Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact.

Further explanation: Examples of this phenomenon could include the interactions of magnets, electrically-charged strips of tape, electrically-charged pith balls, and maglev trains. Examples of investigations could include first-hand experiences or simulations. Plan and carry out investigations; types of interactions; cause and effect;

Strand Physical Science (PS)
Standard PS2: Motion and Stability: Forces and Interactions
Adolescence
Grades 9-Diploma
Performance Expectations

HS-PS2-1 Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.

Further explanation: Examples of data could include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object rolling down a ramp, or moving object being pulled by a constant force. Examples could include the acceleration of a snowmobile in different gears (same mass with different forces creating different accele rations) or the comparison of gas mileage between a truck vs a truck hauling a boat (same acceleration with different masses). Analyzing and Interpreting Data, Types of Interactions, Forces and Motion, Cause and Effect

HS-PS2-2 Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.

Further explanation: Emphasis is on the quantitative conservation of momentum in interactions and the qualitative meaning of this principle. Examples could include jumping off a boat or canoe and the total momenta of all the various pieces exploding from fireworks. Using Mathematics and Computational Thinking, Forces and Motion, Systems and System Models

HS-PS2-3 Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.

Further explanation: Examples of evaluation and refinement could include determining the success of a device at protecting an object from damage and modifying the design to improve it. Examples of a device could include a football helmet or a parachute. Examples could also include the barriers on the sides of NASCAR tracks, truck safety hills on the sides of highways, bike helmets or car bumpers.

Constructing Explanations and Designing Solutions, structure and properties of matter, Forces and Motion, Defining and Delimiting Engineering Problems, Optimizing the Design Solution, types of interactions, Cause and Effects

HS-PS2-4 Use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to describe and predict the gravitational and electrostatic forces between objects.

Further explanation: Emphasis is on both quantitative and conceptual descriptions of gravitational and electrical

Using Mathematics and Computational Thinking, Types of Interactions, Patterns

HS-PS2-5 Plan and conduct an investigation to provide evidence that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current.

Further explanation: Examples could include wind turbines or generators along with any DC motorized toy. Planning and Carrying out an Investigation, Types of Interactions, Definitions of Energy, Cause and Effect

HS-PS2-6 Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials.

Further explanation: Emphasis is on the attractive and repulsive forces that determine the functioning of the material. Examples could include why electrically conductive materials are often made of metal, flexible but durable materials are made up of long chained molecules, and pharmaceuticals are designed to interact with specific receptors. Examples could also include composite material substitutes for wood and the structure of solar cells along with how they work.

Obtaining, Evaluating, and Communicating Information, Structure and Property of Matter, Types of Interactions, Structure and Function

Strand Physical Science (PS)
Standard PS3: Energy
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

K-PS3-1 Make observations to determine the effect of sunlight on Earth's surface.

Further explanation: Examples of Earth's surface could include sand, soil, rocks, and water. Potential Maine connections could also include beach sand in the sun vs. beach sand in the shade. Planning and Carrying out Investigations, Conservation of Energy and Energy Transfer, Cause and Effect

K-PS3-2 Use tools and materials to design and build a structure that will reduce the warming effect of sunlight on an area.

Further explanation: Examples of structures could include umbrellas, canopies, and tents that minimize the warming effect of the sun. Constructing Explanations and Designing Solutions, Conservation of Energy and Energy Transfer, Cause and Effect

Strand Physical Science (PS)
Standard PS3: Energy
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

4-PS3-1 Use evidence to construct an explanation relating the speed of an object to the energy of that object.

Further Explanation: Examples include coasting on a bike down a hill or how bumping into someone or something when walking or running changes speed. Other examples include dropping into a skateboard bowl or off of a ramp. Constructing Explanations and Designing Solutions, Definitions of Energy, Cause and Effect

4-PS3-2 Make observations to provide evidence that energy can be transferred from place to place by sound, light, heat, and electric currents.

Planning and Carrying out Investigations, Definitions of Energy, Conservation of Energy and Energy Transfer, Cause and Effect

4-PS3-3 Ask questions and predict outcomes about the changes in energy that occur when objects collide.

Further Explanation: Emphasis is on the changes in the energy due to the changes in speed, not on the forces, as objects interact. These changes can be observed in playing pool or marbles.

Asking Questions and Defining Problems, Definitions of Energy, Conservation of Energy and Energy Transfer, Relationship between Energy and Forces, Cause and Effect

4-PS3-4 Apply scientific ideas to design, test, and refine a device that converts energy from one form to another.

Further Explanation: Examples of devices could include electric circuits that convert electrical energy into motion energy of a vehicle, light, or sound and a passive solar heater that converts light into heat. Such devices can be used to make s'mores or to turn on a small light when camping in the Maine woods. Examples of constraints could include the materials, cost, or time to design the device. Constructing Explanations and Designing Solutions, Natural Hazards, Conservation of Energy and Energy Transfer, Energy in Chemical Processes, Defining Engineering Problems, Cause and Effect

5-PS3-1 Use models to describe that energy in animals' food (used for body repair, growth, and motion, and to maintain body warmth) was once energy from the sun.

Further Explanation: Examples of models could include diagrams, and flow charts.

Developing and Using Models, Energy in Chemical Processes and Everyday Life, Organization for Matter and Energy Flow in Organisms, Energy and Matter

Strand Physical Science (PS)
Standard PS3: Energy
Early Adolescence
Grades 6-8
Performance Expectations

MS-PS3-1 Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.

Further explanation: Emphasis is on descriptive relationships between kinetic energy and mass separately from kinetic energy and speed. Examples could include riding a bicycle at different speeds, rolling different sizes of rocks downhill, and getting hit by a whiffle ball versus a tennis ball. Consider different sized skiers or different vehicles from pulp trucks to personal cars. Analyzing and interpreting data; definitions of energy; scale, proportion, and quantity

MS-PS3-2 Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system.

Further explanation: Emphasis is on relative amounts of potential energy, not on calculations of potential energy. Examples of objects within systems interacting at varying distances could include the Earth and either a roller coaster cart at varying positions on a hill or objects at varying heights on shelves, changing the direction/orientation of a magnet, and a balloon with static electrical charge being brought closer to a classmate's hair. Examples of models could include representations, diagrams, pictures, and written descriptions of systems.

Developing and using models; definitions of energy; relationship between energy and forces; system and system models

MS-PS3-3 Apply scientific principles to design, construct, and test a device that either minimizes or maximizes thermal energy transfer.

Further explanation: Examples of devices could include an insulated box, a solar cooker, and a Styrofoam cup. Possible explorations could include insulating outerwear and clothing for winter sports or emergency shelters designed for Maine winters.

Constructing explanations and designing solutions; definitions of energy; conservation of energy and energy transfer; defining and delimiting an engineering problem; developing possible solutions; energy and matter

MS-PS3-4 Plan an investigation to determine the relationships among the energy transferred, the type of matter, the mass, and the change in the average kinetic energy of the particles as measured by the temperature of the sample.

Further explanation: Examples of experiments could include comparing final water temperatures after different masses of ice melted in the same volume of water with the same initial temperature, the temperature change of samples of different materials with the same mass as they cool or heat in the environment, or the same material with different masses when a specific amount of energy is added.

Planning and carrying out investigations, Definitions of energy; conservation of energy and energy transfer; scale, proportion, and quantity

MS-PS3-5 Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object.

Further explanation: Examples of empirical evidence used in arguments could include an inventory or other representation of the energy before and after the transfer in the form of temperature changes or motion of an object.

Engaging in argument from evidence; conservation of energy and energy transfer; energy and matter

Strand Physical Science (PS)
Standard PS3: Energy
Adolescence
Grades 9-Diploma
Performance Expectations

HS-PS3-1 Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

Further explanation: Emphasis is on explaining the meaning of mathematical expressions used in the model. Examples could include wind turbines, hydroelectric or tidal power. Further examples could be found in FunTown USA roller coasters or any sport (e.g. why a hockey puck changes motion, a baseball being hit, etc.). Using Mathematics and Computational Thinking, Definitions of Energy, Conservation of Energy and Energy Transfer, Systems and System Models

HS-PS3-2 Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects).

Further explanation: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electrically-charged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations. Developing and Using Models, Definitions of Energy, Energy and Matter

HS-PS3-3 Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.

Further explanation: Emphasis is on both qualitative and quantitative evaluations of devices. Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators. Examples of constraints could include use of renewable energy forms and efficiency. Consider the Wind Blade Challenge or use of a solar oven when camping.

Constructing Explanations and Designing Solutions, Definitions of Energy, Defining and Delimiting Engineering Problems, Energy and Matter

HS-PS3-4 Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics).

Further explanation: Emphasis is on analyzing data from student investigations and using mathematical thinking to describe the energy changes both quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water. Other examples can be found in heat pumps for radiant heat systems, insulation (to prevent heat transfer) or the use of hot rocks to warm a tent when camping.

Planning and Carrying out an Investigation, Conservation of Energy and Energy Transfer, Energy in Chemical Processes, Systems and System Models

HS-PS3-5 Develop and use a model of two objects interacting through electrical or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction.

Further explanation: Examples of models could include drawings, diagrams, and texts, such as drawings of

what happens when two charges of opposite polarity are near each other.

Developing and Using Models, Relationship between Energy and Forces, Cause and Effect

Strand Physical Science (PS)
Standard PS4: Waves and Their Applications in Technologies for Information Transfer
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

1-PS4-1 Plan and conduct investigations to provide evidence that vibrating materials can make sound and that sound can make materials vibrate.

Further explanation: Examples of vibrating materials that make sound could include tuning forks and plucking a stretched string. Examples of how sound can make matter vibrate could include holding a piece of paper near a speaker making sound and holding an object near a vibrating tuning fork. Planning and Carrying Out Investigations, Wave Properties, Cause and Effect

1-PS4-2 Make observations to construct an evidence-based account that objects can be seen only when illuminated.

Further explanation: Examples of observations could include those made in a completely dark room, a pinhole box, and a video of a cave explorer (in Acadia National Park) with a flashlight. Illumination could be from an external light source or by an object giving off its own light.

Constructing Explanations and Designing Solutions, Electromagnetic Radiation, Cause and Effect

1-PS4-3 Plan and conduct an investigation to determine the effect of placing objects made with different materials in the path of a beam of light.

Further explanation: Examples of materials could include those that are transparent (such as clear plastic), translucent (such as wax paper), opaque (such as cardboard), and reflective (such as a mirror). Planning and Carrying out Investigations, Electromagnetic Radiation, Cause and Effect

1-PS4-4 Use tools and materials to design and build a device that uses light or sound to solve the problem of communicating over a distance.

Further explanation: Examples of devices could include a light source to send signals, paper cup and string "telephones," and a pattern of drum beats. Constructing Explanations and Designing Solutions, Information Technologies and Instrumentation

Strand Physical Science (PS)
Standard PS4: Waves and Their Applications in Technologies for Information Transfer
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

4-PS4-1 Develop a model of waves to describe patterns in terms of amplitude and wavelength and that waves can cause objects to move.

Further Explanation: Examples of models could include diagrams, analogies, and physical models using wire to illustrate wavelength and amplitude of waves. Use an oscilloscope app to illustrate the patterns in an animal call or musical instrument and engineer a pattern to mimic the call. Developing and Using Models, Wave Properties, Patterns

4-PS4-2 Develop a model to describe that light reflecting from objects and entering the eye allows objects to be seen.

Further Explanation: Examples of Maine animal eyes at night such as coyotes, deer and foxes reflecting light from their retinas. Developing and Using Models, Electromagnetic Radiation, Patterns

4-PS4-3 Generate and compare multiple solutions that use patterns to transfer information.

Further Explanation: Examples of solutions could include drums sending coded information through sound waves, using a grid of 1's and 0's representing black and white to send information about a picture, and using Morse code to send text or introduce basic computer code.

Constructing Explanations and Designing Solutions, Information Technologies and Instrumentation, Optimizing the Design Solution, Patterns

Strand Physical Science (PS)
Standard PS4: Waves and Their Applications in Technologies for Information Transfer
Adolescence
Grades 9-Diploma
Performance Expectations

HS-PS4-1 Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

Further explanation: Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth. Examples include rainbows and how to aim when spearfishing. Using Mathematics and Computational Thinking, Wave Properties, Cause and Effect

HS-PS4-2 Evaluate questions about the advantages of using a digital transmission and storage of information.

Further explanation: Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft. Asking Questions and Defining Problems, Wave Properties, Stability and Change

HS-PS4-3 Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other.

Further explanation: Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect. Engaging in Argument from Evidence, Wave Properties, Systems and System Models

HS-PS4-4 Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter.

Further explanation: Emphasis is on the idea that photons associated with different frequencies of light have different energies, and the damage to living tissue from electromagnetic radiation depends on the energy of the radiation. Examples of published materials could include trade books, magazines, web resources, videos, and other passages that may reflect bias. Arguments around evidence could be made for dangers of cell phone usage or living near high voltage power lines. Obtaining, Evaluating, and Communicating Information, Electromagnetic Radiation, Cause and Effect

HS-PS4-5 Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy.

Further explanation: Examples could include solar cells capturing light and converting it to electricity; medical imaging; and communications technology.

Obtaining, Evaluating, and Communicating Information, Wave Properties, Electromagnetic Radiation, Information Technologies and Instrumentation, Cause and Effect

Strand Life Sciences (LS)
Standard LS1: From Molecules to Organisms: Structures and Processes
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

K-LS1-1 Use observations to describe patterns of what plants and animals (including humans) need to survive.

Further explanation: Examples of patterns could include that animals need to take in food but plants do not, the different kinds of food needed by different types of animals, the requirement of plants to have light, and that all living things need water. Examples could include the pattern a bear makes when preparing to hibernate for winter, the seasonal patterns of trees losing and/or keeping their leaves.

Analyzing and Interpreting Data, Organization for Matter and Energy Flow in Organisms, Patterns

1-LS1-1 Use materials to design a solution to a human problem by mimicking how plants and/or animals use their external parts to help them survive, grow, and meet their needs.

Further explanation: Examples of human problems that can be solved by mimicking plant or animal solutions could include designing clothing or equipment to protect bicyclists by mimicking turtle shells, acorn shells, and animal scales; stabilizing structures by mimicking animal tails and roots on plants; keeping out intruders by mimicking thorns on branches and animal quills; waterproofing boots, jackets, gloves thereby mimicking animal feathers and, detecting intruders by mimicking eyes and ears. Constructing Explanations and Designing Solutions, Structure and Function, Information Processing, Structure and Function

1-LS1-2 Read texts and use media to determine patterns in behavior of parents and offspring that help offspring survive.

Further explanation: Examples of patterns of behaviors could include the signals that offspring make (such as crying, cheeping, and other vocalizations) and the responses of the parents (such as feeding, comforting, and protecting the offspring). Potential Maine connections include Maine animal sounds to signal their offspring (e.g. loons, moose, deer, coyotes, etc.) and how animals, especially birds, bring back food for their young. Obtaining, Evaluating, and Communicating Information, Growth and Development of Organisms, Patterns

Strand Life Sciences (LS)
Standard LS1: From Molecules to Organisms: Structures and Processes
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-LS1-1 Develop models to describe that organisms have unique and diverse life cycles but all have in common birth, growth, reproduction, and death.

Further Explanation: Changes organisms go through during their life form a pattern. Potential Maine connections include frogs in vernal pools, Atlantic salmon life cycle and gestation vs. metamorphosis. Developing and Using Models, Growth and Development of Organisms, Patterns

4-LS1-1 Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction.

Further Explanation: Examples of structures could include thorns, stems, roots, colored petals, heart, stomach, lung, brain, and skin found in Maine plants and animals. Engaging in Argument from Evidence, Structure and Function, Systems and System Models

4-LS1-2 Use a model to describe that animals receive different types of information through their senses, process the information in their brain, and respond to the information in different ways.

Further Explanation: Emphasis is on systems of information transfer.

Engaging in Argument from Evidence, Information Processing, Systems and System Models

5-LS1-1 Support an argument that plants get the materials they need for growth chiefly from air and water.

Further Explanation: Emphasis is on the idea that plant matter comes mostly from air and water, not from the soil. Investigate Maine plants.

Engaging in Argument from Evidence, Organization for Matter and Energy Flow in Organisms, Energy and Matter

Strand Life Sciences (LS)
Standard LS1: From Molecules to Organisms: Structures and Processes
Early Adolescence
Grades 6-8
Performance Expectations

MS-LS1-1 Conduct an investigation to provide evidence that living things are made of cells; either one cell or many different numbers and types of cells.

Further explanation: Emphasis is on developing evidence that living things are made of cells, distinguishing between living and non-living things, and understanding that living things may be made of one cell or many and varied cells. Planning and carrying out investigations; structure and function; scale, proportion, and quantity

MS-LS1-2 Develop and use a model to describe the function of a cell as a whole and ways the parts of cells contribute to the function.

Further explanation: Emphasis is on the cell functioning as a whole system and the primary role of identified parts of the cell, specifically the nucleus, chloroplasts, mitochondria, cell membrane, and cell wall. Developing and using models; structure and function; structure and function

MS-LS1-3 Use argument supported by evidence for how the body is a system of interacting subsystems composed of groups of cells.

Further explanation: Emphasis is on conceptual understanding that cells form tissues and tissues form organs specialized for particular body functions. Examples could include the interaction of sub-systems within a system and the normal functioning of those systems. Engaging in argument from evidence; structure and function; system and system models

MS-LS1-4 Use argument based on empirical evidence and scientific reasoning to support an explanation for how characteristic animal behaviors and specialized plant structures affect the probability of successful reproduction of animals and plants, respectively.

Further explanation: Examples of behaviors that affect the probability of animal reproduction could include nest building to protect young from cold, herding of animals to protect young from predators, and vocalization of animals and colorful plumage to attract mates for breeding. Examples of animal behaviors that affect the probability of plant reproduction could include transferring pollen or seeds and creating conditions for seed germination and growth. Examples of plant structures could include bright flowers attracting butterflies that transfer pollen, flower nectar and odors that attract insects that transfer pollen, and hard shells on nuts that squirrels bury. Potential Maine connections could include herding of white-tail deer and caribou, vocalizations of moose and cardinals, and keystone species such as those on the coast (e.g. harbor seals and sea stars).

MS-LS1-5 Construct a scientific explanation based on evidence for how environmental and genetic factors influence the growth of organisms.

Further explanation: Examples of local environmental conditions could include availability of food, light, space, and water. Examples of genetic factors could include large breed cattle and species of grass affecting the growth of organisms. Examples of evidence could include drought decreasing plant growth, fertilizer increasing plant growth, different varieties of plant seeds growing at different rates in different conditions, and fish growing larger in large ponds than in small ponds. Examples could include winter and cold temperatures, hibernation (e.g. black bear), and the migration of hummingbirds and Canada geese. Constructing explanations and designing solutions; growth and development of organisms; cause and effect

MS-LS1-6 Construct a scientific explanation based on evidence for the role of photosynthesis in the cycling of matter and flow of energy into and out of organisms.

Further explanation: Emphasis is on tracing movement of matter and flow of energy.

Constructing explanations and designing solutions; organization for matter and energy flow in organisms; energy in chemical processes and everyday life; energy and matter

MS-LS1-7 Develop a model to describe how food is rearranged through chemical reactions forming new molecules that support growth and/or release energy as this matter moves through an organism.

Further explanation: Emphasis is on describing that molecules are broken apart and put back together and that in this process energy is released.

Developing and using models; organization for matter and energy flow in organisms; energy in chemical processes and everyday life; energy and matter

MS-LS1-8 Gather and synthesize information that sensory receptors respond to stimuli by sending messages to the brain for immediate behavior or storage as memories.

Obtaining, evaluating, and communicating information; information processing; cause and effect

Strand Life Sciences (LS)
Standard LS1: From Molecules to Organisms: Structures and Processes
Adolescence
Grades 9-Diploma
Performance Expectations

HS-LS1-1 Construct an explanation based on evidence for how the structure of DNA determines the structure of proteins which carry out the essential functions of life through systems of specialized cells.

Further explanation: Emphasis is on protein synthesis from DNA to codon to amino acid sequence. Constructing Explanations and Designing Solutions, Structure and Function, Structure and Function

HS-LS1-2 Develop and use a model to illustrate the hierarchical organization of interacting systems that provide specific functions within multicellular organisms.

Further explanation: Emphasis is on functions at the organism system level such as nutrient uptake, water delivery, and organism movement in response to neural stimuli. An example of an interacting system could be an artery depending on the proper function of elastic tissue and smooth muscle to regulate and deliver the proper amount of blood within the circulatory system. Another example could be the water and nutrient intake in soft shell clams. Developing and Using Models, Structure and Function, Systems and System Models

HS-LS1-3 Plan and conduct an investigation to provide evidence that feedback mechanisms maintain homeostasis.

Further explanation: Examples of investigations could include heart rate response to exercise, stomate response to moisture and temperature, and root development in response to water levels. Another example is commonly observed in the daphnia heart rate response to changes in temperature, caffeine, alcohol, or nicotine.

Planning and Carrying out Investigations, Structure and Function, Stability and Change

HS-LS1-4 Use a model to illustrate the role of cellular division (mitosis) and differentiation in producing and maintaining complex organisms.

Developing and Using Models, Growth and Development of Organisms, Systems and System Models

HS-LS1-5 Use a model to illustrate how photosynthesis transforms light energy into stored chemical energy.

Further explanation: Emphasis is on illustrating inputs and outputs of matter and the transfer and transformation of energy in photosynthesis by plants and other photosynthesizing organisms. Examples of models could include diagrams, chemical equations, and conceptual models. Models may focus on Maine based economy of photosynthetic organisms such as seaweeds, potatoes and pine trees. Developing and Using Models, Organization for Matter and Energy flow in Organisms, Energy and Matter

HS-LS1-6 Construct and revise an explanation based on evidence for how carbon, hydrogen, and oxygen from sugar molecules may combine with other elements to form amino acids and/or other large carbon-based molecules.

Further explanation: Emphasis is on using evidence from models and simulations to support explanations. Constructing Explanations and Designing Solutions, Organization for Matter and energy Flow in Organisms, Energy and Matter

HS-LS1-7 Use a model to illustrate that cellular respiration is a chemical process whereby the bonds of food molecules and oxygen molecules are broken and the bonds in new compounds are formed, resulting in a net transfer of energy.

Further explanation: Emphasis is on the conceptual understanding of the inputs and outputs of the process of cellular respiration. An example could be a moose eating a lily pad, the lily pad producing energy for the moose and the breathing of oxygen by the moose to enable the process of cellular respiration. Developing and Using Models, Organization for Matter and Energy Flow in Organisms, Energy and Matter

Strand Life Sciences (LS)
Standard LS2: Ecosystems: Interactions, Energy, and Dynamics
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

2-LS2-1 Plan and conduct an investigation to determine if plants need sunlight and water to grow.

Planning and Carrying out Investigations, Interdependent Relationships in Ecosystems, Cause and Effect

2-LS2-2 Develop a simple model that mimics the function of an animal in dispersing seeds or pollinating plants.

Further explanation: Examples of animals or insects that pollinate plants or disperse seeds could include bees, hummingbirds or bats. An example of a model could be using Velcro to show how seeds of burdocks are spread. Developing and Using Models, Interdependent Relationships in Ecosystems, Developing Possible Solutions, Structure and Function

Strand Life Sciences (LS)
Standard LS2: Ecosystems: Interactions, Energy, and Dynamics
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-LS2-1 Construct an argument that some animals form groups that help members survive.

Further explanation: Maine animals that form groups such as coyotes, deer herds, turkeys, bees, moose, salmon and alewives migration. Engaging in Argument from Evidence, Social Interactions and Group Behaviors, Cause and Effect

5-LS2-1 Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment.

Further Explanation: Emphasis is on the idea that matter that is not food (air, water, decomposed materials in soil) is changed by plants into matter that is food. Examples of systems could include organisms, ecosystems, and the Earth. Utilize Maine or Atlantic plants and animals to develop a model of a food chain or web. Developing and Using Models, Interdependent Relationships in Ecosystems, Cycles of Matter and Energy Transfer, Systems and System Models

Strand Life Sciences (LS)
Standard LS2: Ecosystems: Interactions, Energy, and Dynamics
Early Adolescence
Grades 6-8
Performance Expectations

MS-LS2-1 Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.

Further explanation: Emphasis is on cause and effect relationships between resources and the growth of individual organisms and the numbers of organisms in ecosystems during periods of abundant and scarce resources.

Analyzing and interpreting data; interdependent relationships in ecosystems; cause and effect

MS-LS2-2 Construct an explanation that predicts patterns of interactions among organisms across multiple ecosystems.

Further explanation: Emphasis is on predicting consistent patterns of interactions in different ecosystems in terms of the relationships among and between organisms and abiotic components of ecosystems. Examples of types of interactions could include competitive, predatory, and mutually beneficial. Potential Maine connections include predation: coyotes and house cats with smaller prey or white tail deer and wolves; mutualism in the union of algae and fungus to form lichen; parasitism in deer ticks on dogs; and commensalism when barnacles attach to minke whales or a grey squirrel makes a nest in a red oak tree. Constructing explanations and designing solutions; interdependent relationships in ecosystems; patterns

MS-LS2-3 Develop a model to describe the cycling of matter and flow of energy among living and nonliving parts of an ecosystem.

Further explanation: Emphasis is on describing the conservation of matter and flow of energy into and out of various ecosystems and on defining the boundaries of the system. Explore the reason behind burning blueberry fields biennially and the cycling of matter.

Developing and using models; cycle of matter and energy transfer in ecosystems; energy and matter

MS-LS2-4 Construct an argument supported by empirical evidence that changes to physical or biological components of an ecosystem affect populations.

Further explanation: Emphasis is on recognizing patterns in data and making warranted inferences about changes in populations and on evaluating empirical evidence supporting arguments about changes to ecosystems. Examples include the introduction of invasive species like the green crab or knotweed and their impact on native species. Explore the impacts of farming, urban sprawl and pollution. Engaging in argument from evidence; ecosystem dynamics, functioning, and resilience; stability and change

MS-LS2-5 Evaluate competing design solutions for maintaining biodiversity and ecosystem services.

Further explanation: Examples of ecosystem services could include water purification, nutrient recycling, and prevention of soil erosion. Examples of design solution constraints could include scientific, economic, and social considerations. Consider the balance of conservation with the logging of forests or with the lobster and blueberry industries.

Engaging in argument from evidence; ecosystem dynamics, functioning, and resilience; biodiversity and humans; developing possible solutions; stability and change

Strand Life Sciences (LS)
Standard LS2: Ecosystems: Interactions, Energy, and Dynamics
Adolescence
Grades 9-Diploma
Performance Expectations

HS-LS2-1 Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales.

Further Explanation: Emphasis is on quantitative analysis and comparison of the relationships among interdependent factors including boundaries, resources, climate, and competition. Examples of mathematical comparisons could include graphs, charts, histograms, and population changes gathered from simulations or historical data sets. Examples could include a look at historical data of the population of a species that has moved north into Maine, such as opossum, and how it has changed as the climate in Maine has changed. Observe data of the populations of harbor seals and the effect that a hunting ban has had on their population and the resulting increase in the number of large predatory sharks in the Gulf of Maine.

Using Mathematics and Computational Thinking, Interdependent Relationships in Ecosystems, Scale,

Proportion, and Quantity

HS-LS2-2 Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales.

Further explanation: Examples of mathematical representations include finding the average, determining trends, and using graphical comparisons of multiple sets of data. Examples could include a graphical analysis of historical data on the population of trout and/or landlocked salmon before and after the introduction of bass into Moosehead Lake. Or data on a variety of populations (biodiversity) affected by dredging for sea scallops. Using Mathematics and Computational Thinking, Interdependent Relationships in Ecosystems, Scale, Proportion, and Quantity

HS-LS2-3 Construct and revise an explanation based on evidence for the cycling of matter and flow of energy in aerobic and anaerobic conditions.

Further explanation: Emphasis is on conceptual understanding of the role of aerobic and anaerobic respiration in different environments. An example could include a classroom lab activity around a Winogradsky Column with groups changing a variable such as temperature or light. Additional examples could look at the fermentation processes when blue-green algae is grown in aerobic and anaerobic environments. Constructing Explanations and Designing Solutions, Cycles of Matter and Energy Transfer in Ecosystems, Energy and Matter

HS-LS2-4 Use mathematical representations to support claims for the cycling of matter and flow of energy among organisms in an ecosystem.

Further Explanation: Emphasis is on using a mathematical model of stored energy in biomass to describe the transfer of energy from one trophic level to another and that matter and energy are conserved as matter cycles and energy flows through ecosystems. Emphasis is on atoms and molecules such as carbon, oxygen, hydrogen and nitrogen being conserved as they move through an ecosystem. An example could include an illustration of a food pyramid students may find in Maine (e.g. seaweed ->snail ->fish ->shark, or grass ->insects ->turkeys ->foxes).

Using Mathematics and Computational Thinking, Cycles of Matter and Energy Transfer in Ecosystems, Energy and Matter

HS-LS2-5 Develop a model to illustrate the role of photosynthesis and cellular respiration in the cycling of carbon among the biosphere, atmosphere, hydrosphere, and geosphere.

Further explanation: Examples of models could include simulations and mathematical models. Models may include multi-media illustration of the carbon cycle to include a Maine ecosystem they are familiar with such as pond, seaside, farm, forest, etc.

Developing and Using Models, Cycles of Matter and Energy Transfer, Energy in Chemical Processes, Systems and System Models

HS-LS2-6 Evaluate the claims, evidence, and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem.

Further explanation: Examples of changes in ecosystem conditions could include modest biological or physical changes, such as moderate hunting or a seasonal flood; and extreme changes, such as volcanic eruption or sea level rise. Examples could include how the number of moose hunting licenses impacts other populations or how fishing limits or shortened seasons decreases the catch of many fish species and the effects on ground fish or smaller fish. Engaging in Argument from Evidence, Ecosystem Dynamics, Functioning, and Resilience, Stability and Change

HS-LS2-7 Design, evaluate, and refine a solution for reducing the impacts of human activities on the environment and biodiversity.

Further explanation: Examples of human activities can include urbanization, building dams, and dissemination of invasive species. Potential Maine connections include the effects of: salting the roads in winter, introducing green crabs into coastal waters, introducing invasive species into Maine lakes, or examining historical data on water pollution in the Androscoggin during the height of mill activity, closing of mills and legislation on water quality.

Constructing Explanations and Designing Solutions, Ecosystem Dynamics, Functioning, and Resilience, Biodiversity and Humans, Developing Possible Solutions, Stability and Change

HS-LS2-8 Evaluate the evidence for the role of group behavior on individual and species' chances to survive and reproduce.

Further explanation: Emphasis is on: (1) distinguishing between group and individual behavior, (2) identifying evidence supporting the outcomes of group behavior, and (3) developing logical and reasonable arguments based on evidence. Examples of group behaviors could include flocking, schooling, herding, and cooperative behaviors such as hunting, migrating, and swarming. Examples could include turkeys flocking to evade hunters or Canada geese migrating to and through Maine for breeding purposes. Engaging in Argument from Evidence, Social Interactions and Group Behavior, Cause and Effect

Strand Life Sciences (LS)
Standard LS3 Heredity: Inheritance and Variation of Traits
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

1-LS3-1 Make observations to construct an evidence-based account that young plants and animals are like, but not exactly like, their parents.

Further explanation: Examples of patterns could include features that plants or animals share. Examples of observations could include that leaves from the same kind of plant are the same shape but can differ in size and that a particular breed of dog looks like its parents but is not exactly the same. Constructing Explanations and Designing Solutions, Inheritance of Traits, Variation of Traits, Patterns

Strand Life Sciences (LS)
Standard LS3 Heredity: Inheritance and Variation of Traits
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-LS3-1 Analyze and interpret data to provide evidence that plants and animals have traits inherited from parents and that variation of these traits exists in a group of similar organisms.

Further Explanation: Patterns are the similarities and differences in traits shared between offspring and their parents, or among siblings. Emphasis is on organisms other than humans, such as lupins, apples or garden plants.

Analyzing and Interpreting Data, Inheritance of Traits, Variation of Traits, Patterns

3-LS3-2 Use evidence to support the explanation that traits can be influenced by the environment.

Further Explanation: Examples of the environment affecting a trait could include normally tall plants grown with insufficient water are stunted; and, a pet dog that is given too much food and little exercise may become overweight. In addition, hydrangea grown under higher acidic conditions will cause the petals to turn blue.

Constructing Explanations an Designing Solutions, Inheritance of Traits, Variation of Traits, Cause and Effect

Strand Life Sciences (LS)
Standard LS3 Heredity: Inheritance and Variation of Traits
Early Adolescence
Grades 6-8
Performance Expectations

MS-LS3-1 Develop and use a model to describe why structural changes to genes (mutations) located on chromosomes may affect proteins and may result in harmful, beneficial, or neutral effects to the structure and function of an organism.

Further explanation: Emphasis is on conceptual understanding that changes in genetic material may result in making different proteins.

Developing and using models; inheritance of traits; variation of traits; structure and function

MS-LS3-2 Develop and use a model to describe why asexual reproduction results in offspring with identical genetic information and sexual reproduction results in offspring with genetic variation.

Further explanation: Emphasis is on using models such as Punnett squares, diagrams, and simulations to describe the cause and effect relationship of gene transmission from parent(s) to offspring and the resulting genetic variation. Connections can be made to Maine agricultural crops, i.e. strawberries, blueberries, and potatoes.

Developing and using models; growth and development of organisms; inheritance of traits; variation of traits; cause and effect

Strand Life Sciences (LS)
Standard LS3 Heredity: Inheritance and Variation of Traits
Adolescence
Grades 9-Diploma
Performance Expectations

HS-LS3-1 Ask questions to clarify relationships about the role of DNA and chromosomes in coding the instructions for characteristic traits passed from parents to offspring

Further explanation: Emphasis is on the asking of clarifying questions about the general principles of genetics. An example is how cystic fibrosis (one of the most common autosomal recessive inherited diseases in Maine) is passed from parents to child. Asking Questions and Defining Problems, Structure and Function, Inheritance of Traits, Cause and Effect

HS-LS3-2 Make and defend a claim based on evidence that inheritable genetic variations may result from: (1) new genetic combinations through meiosis, (2) viable errors occurring during replication, and/or (3) mutations caused by environmental factors.

Further explanation: Emphasis is on using data to support arguments for the way variation occurs. Provide data on specific mutations caused by environmental factors.

Engaging in Argument from Evidence, Variation of Traits, Cause and Effect

HS-LS3-3 Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.

Further explanation: Emphasis is on the use of mathematics to describe the probability of traits as it relates to genetic and environmental factors in the expression of traits. An example would be the population of red fox in Maine and the incidences of the red allele vs. the sable allele.

Analyzing and Interpreting Data, Variation of Traits, Scale, Proportion, and Quantity

Strand Life Sciences (LS)
Standard LS4 Biological Evolution: Unity and Diversity
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

2-LS4-1 Make observations of plants and animals to compare the diversity of life in different habitats.

Further Explanation: Emphasis is on the diversity of living things in each of a variety of different habitats. Potential Maine connections include Maine habitats (e.g. ocean, lake/pond, mountains, forests, cities, etc.)

Planning and Carrying out Investigations, Biodiversity in Humans

Strand Life Sciences (LS)
Standard LS4 Biological Evolution: Unity and Diversity
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-LS4-1 Analyze and interpret data from fossils to provide evidence of the organisms and environments in which they lived long ago.

Further Explanation: Examples of data could include type, size, and distributions of fossil organisms. Examples of fossils and environments could include marine fossils found on dry land, tropical plant fossils found in Arctic areas, and fossils of extinct organisms. Analyzing and Interpreting Data, Evidence of Common Ancestry and Diversity, Scale, Proportion, and Quantity

3-LS4-2 Use evidence to construct an explanation for how the variations in characteristics among individuals of the same species may provide advantages in surviving, finding mates, and reproducing.

Further Explanation: Examples of cause and effect relationships could be plants that have larger thorns than other plants may be less likely to be eaten by predators and animals that have better camouflage coloration than other animals may be more likely to survive and therefore more likely to leave offspring such as yellow spotted salamanders and newts. Constructing Explanations an Designing Solutions, Natural Selection, Cause and Effect

3-LS4-3 Construct an argument with evidence that in a particular habitat some organisms can survive well, some survive less well, and some cannot survive at all.

Further Explanation: Examples of evidence could include needs and characteristics of the organisms (such as loons) and habitats involved. The organisms and their habitats make up a system in which the parts depend on each other. Potential Maine connections include the introduction of Pike and Bass into areas that are non-native to the species and their impact on native trout and other native species. Engaging in Argument from Evidence, Inheritance of Traits, Variation of Traits, Scale, Proportion, and Quantity, Cause and Effect

3-LS4-4 Make a claim about the merit of a solution to a problem caused when the environment changes and the types of plants and animals that live there may change.

Further Explanation: Examples of environmental changes could include changes in land characteristics, water distribution, temperature, food, and other organisms. Lobster migrate as a result of water temperature, Cod follow prey fish (Mackerel), Atlantic Salmon start life in streams and migrate to saltwater.

Engaging in Argument from Evidence, Biodiversity and Humans, Ecosystem Dynamics, Functioning, and Resilience, Systems and System Models

Strand Life Sciences (LS)
Standard LS4 Biological Evolution: Unity and Diversity
Early Adolescence
Grades 6-8
Performance Expectations

MS-LS4-1 Analyze and interpret data for patterns in the fossil record that document the existence, diversity, extinction, and change of life forms throughout the history of life on Earth under the assumption that natural laws operate today as in the past.

Further explanation: Emphasis is on finding patterns of changes in the level of complexity of anatomical structures in organisms and the chronological order of fossil appearance in rock layers. Analyzing and interpreting data; evidence of common ancestry and diversity; patterns

MS-LS4-2 Apply scientific ideas to construct an explanation for the anatomical similarities and differences among modern organisms and between modern and fossil organisms to infer evolutionary relationships.

Further explanation: Emphasis is on explanations of the evolutionary relationships among organisms in terms of similarities or differences of the gross appearance of anatomical structures.

Constructing explanations and designing solutions; evidence of common ancestry and diversity; patterns

MS-LS4-3 Analyze displays of pictorial data to compare patterns of similarities in the embryological development across multiple species to identify relationships not evident in the fully formed anatomy.

Further explanation: Emphasis is on inferring general patterns of relatedness among embryos of different organisms by comparing the macroscopic appearance of diagrams or pictures. Analyzing and interpreting data; evidence of common ancestry and diversity; patterns

MS-LS4-4 Construct an explanation based on evidence that describes how genetic variations of traits in a population increase some individuals' probability of surviving and reproducing in a specific environment.

Further explanation: Emphasis is on using simple probability statements and proportional reasoning to construct explanations.

Constructing explanations and designing solutions; natural selection; cause a nd effect

MS-LS4-5 Gather and synthesize information about the technologies that have changed the way humans influence the inheritance of desired traits in organisms.

Further explanation: Emphasis is on synthesizing information from reliable sources about the influence of humans on genetic outcomes in artificial selection (such as genetic modification, animal husbandry, and gene therapy) and on the impacts these technologies have on society as well as the technologies leading to these scientific discoveries. Obtaining, evaluating, and communicating information; natural selection; cause and effect

MS-LS4-6 Use mathematical representations to support explanations of how natural selection may lead to increases and decreases of specific traits in populations over time.

Further explanation: Emphasis is on using mathematical models, probability statements, and proportional reasoning to support explanations of trends in changes to populations over time. Using mathematics and computational thinking; adaptation; cause and effect

Strand Life Sciences (LS)
Standard LS4 Biological Evolution: Unity and Diversity
Adolescence
Grades 9-Diploma
Performance Expectations

HS-LS4-1 Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence.

Further explanation: Emphasis is on a conceptual understanding of the role each line of evidence has relating to common ancestry and biological evolution. Examples of evidence could include similarities in DNA sequences, anatomical structures, and order of appearance of structures in embryological development. Obtaining, Evaluating, and Communicating Information, Evidence of Common Ancestry and Diversity, Patterns

HS-LS4-2 Construct an explanation based on evidence that the process of evolution primarily results from four factors: (1) the potential for a species to increase in number, (2) the heritable genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for limited resources, and (4) the proliferation of those organisms that are better able to survive and reproduce in the environment.

Further explanation: Emphasis is on using evidence to explain the influence each of the four factors has on number of organisms, behaviors, morphology, or physiology in terms of ability to compete for limited resources and subsequent survival of individuals and adaptation of species. Examples of evidence could include mathematical models such as simple distribution graphs and proportional reasoning. Constructing Explanations and Designing Solutions, Adaptation, Cause and Effect

HS-LS4-3 Apply concepts of statistics and probability to support explanations that organisms with an advantageous heritable trait tend to increase in proportion to organisms lacking this trait.

Further explanation: Emphasis is on analyzing shifts in numerical distribution of traits and using these shifts as evidence to support explanations. Observe historical data for the distribution of humpback whales in the Gulf of Maine looking specifically at skin pigmentation. Analyzing and Interpreting Data, Natural Selection, Adaptation, Patterns

HS-LS4-4 Construct an explanation based on evidence for how natural selection leads to adaptation of populations.

Further explanation: Emphasis is on using data to provide evidence for how specific biotic and abiotic differences in ecosystems (such as ranges of seasonal temperature, long-term climate change, acidity, light,geographic barriers, or evolution of other organisms) contribute to a change in gene frequency over time,leading to adaptation of populations.

Constructing Explanations and Designing Solutions, Adaptation, Cause and Effect

HS-LS4-5 Evaluate the evidence supporting claims that changes in environmental conditions may result in: (1) increases in the number of individuals of some species, (2) the emergence of new species over time, and (3) the extinction of other species.

Further explanation: Emphasis is on determining cause and effect relationships for how changes to the environment such as deforestation, fishing, application of fertilizers, drought, flood, and the rate of change of the environment affect distribution or disappearance of traits in species. Engaging in Argument from Evidence, Adaptation, Cause and Effect

HS-LS4-6 Create or revise a simulation to test a solution to mitigate adverse impacts of human activity on biodiversity.

Further explanation: Emphasis is on designing solutions for a proposed problem related to threatened or endangered species, or to genetic variation of organisms for multiple species.

Using Mathematics and Computational Thinking, Biodiversity and Humans, Developing Possible Solutions, Cause and Effect

Strand Earth and Space Sciences (ESS)
Standard ESS1 Earth's Place in the Universe
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

1-ESS1-1 Use observations of the sun, moon, and stars to describe patterns that can be predicted.

Further explanation: Examples of patterns could include that the sun and moon appear to rise in one part of the sky, move across the sky, and set and that stars other than our sun are visible at night but not during the day. Analyzing and Interpreting Data, The Universe and Its Stars, Patterns

1-ESS1-2 Make observations at different times of the year to relate the amount of daylight to the time of year.

Further explanation: Emphasis is on relative comparisons of the amount of daylight in the winter or summer to the amount in the spring or fall. Planning and Carrying out Investigations, Earth and the Solar System, Patterns

2-ESS1-1 Use information from several sources to provide evidence that Earth events can occur quickly or slowly.

Further Explanation: Examples of events and timescales could include volcanic explosions and earthquakes, which happen quickly, and erosion of rocks, which occurs slowly. Examples of Maine phenomena (e.g. flash floods, erosion and tides). Constructing Explanations and Designing Solutions, The History of Planet Earth, Stability and Change

Strand Earth and Space Sciences (ESS)
Standard ESS1 Earth's Place in the Universe
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

4-ESS1-1 Identify evidence from patterns in rock formations and fossils in rock layers to support an explanation for changes in a landscape over time.

Further Explanation: Examples of evidence from patterns could include rock layers with marine shell fossils above rock layers with plant fossils and no shells, indicating a change from land to water over time and a canyon with different rock layers in the walls and a river in the bottom, indicating that over time a river cut through the rock. Constructing Explanations and Designing Solutions, The History of Planet Earth, Patterns

5-ESS1-1 Support an argument that differences in the apparent brightness of the sun compared to other stars is due to their relative distances from Earth.

Engaging in Argument from Evidence, The Universe and its Stars, Scale Proportion and Quantity

5-ESS1-2 Represent data in graphical displays to reveal patterns of daily changes in length and direction of shadows, day and night, and the seasonal appearance of some stars in the night sky.

Further Explanation: Examples of patterns could include the position and motion of Earth with respect to the sun and selected stars that are visible only in particular months. Analyzing and Interpreting Data, Earth and the Solar System, Patterns

Strand Earth and Space Sciences (ESS)
Standard ESS1 Earth's Place in the Universe
Early Adolescence
Grades 6-8
Performance Expectations

MS-ESS1-1 Develop and use a model of the Earth-sun-moon system to describe the cyclic patterns of lunar phases, eclipses of the sun and moon, and seasons.

Further explanation: Examples of models can be physical, graphical, or conceptual. Examples could incorporate latitude and season connections, why Lubec is the first town in the continental U.S. to see the sunrise, and tides (king, neap, spring). Developing and using models; the universe and its stars; earth and the solar system; patterns

MS-ESS1-2 Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system.

Further explanation: Emphasis for the model is on gravity as the force that holds together the solar system and Milky Way galaxy and controls orbital motions within them. Examples of models can be physical (such as the analogy of distance along a football field or computer visualizations of elliptical orbits) or conceptual (such as mathematical proportions relative to the size of familiar objects such as students' school or state). Developing and using models; the universe and its stars; earth and the solar system; systems and system models

MS-ESS1-3 Analyze and interpret data to determine scale properties of objects in the solar system.

Further explanation: Emphasis is on the analysis of data from Earth-based instruments, space-based telescopes, and spacecraft to determine similarities and differences among solar system objects. Examples of scale properties include the sizes of an object's layers (such as crust and atmosphere), surface features (such as volcanoes), and orbital radius. Examples of data include statistical information, drawings and photographs, and models. Analyzing and interpreting data; earth and the solar system; scale, proportion, and quantity

MS-ESS1-4 Construct a scientific explanation based on evidence from rock strata for how the geologic time scale is used to organize Earth's 4.6-billion-year-old history.

Further explanation: Emphasis is on how analysis of rock formations and the fossils they contain are used to establish relative ages of major events in Earth's history. Examples of Earth's major events could range from being very recent (such as the last Ice Age or the earliest fossils of homo sapiens) to very old (such as the formation of Earth or the earliest evidence of life). Examples can include the formation of mountain chains and ocean basins, the evolution or extinction of particular living organisms, or significant volcanic eruptions. Constructing explanations and designing solutions; the history of planet earth; scale, proportion, and quantity

Strand Earth and Space Sciences (ESS)
Standard ESS1 Earth's Place in the Universe
Adolescence
Grades 9-Diploma
Performance Expectations

HS-ESS1-1 Develop a model based on evidence to illustrate the life span of the sun and the role of nuclear fusion in the sun's core to release energy that eventually reaches Earth in the form of radiation.

Further explanation: Emphasis is on the energy transfer mechanisms that allow energy from nuclear fusion in the sun's core to reach Earth. Examples of evidence for the model include observations of the masses and lifetimes of other stars, as well as the ways that the sun's radiation varies due to sudden solar flares ("space weather"), the 11- year sunspot cycle, and non-cyclic variations over centuries.

Developing and Using Models, The Universe and its Stars, Energy in Chemical Processes and Everyday Life, Scale, Proportion and Quantity

HS-ESS1-2 Construct an explanation of the Big Bang theory based on astronomical evidence of light spectra, motion of distant galaxies, and composition of matter in the universe.

Further explanation: Emphasis is on the astronomical evidence of the red shift of light from galaxies as an indication that the universe is currently expanding, the cosmic microwave background as the remnant radiation from the Big Bang, and the observed composition of ordinary matter of the universe, primarily found in stars and interstellar gases (from the spectra of electromagnetic radiation from stars), which matches that predicted by the Big Bang theory (3/4 hydrogen and 1/4 helium).

Constructing Explanations and Designing Solutions, The Universe and its Stars, Electromagnetic Radiation, Energy and Matter

HS-ESS1-3 Communicate scientific ideas about the way stars, over their life cycle, produce elements.

Further explanation: Emphasis is on the way nucleosynthesis, and therefore the different elements created, varies as a function of the mass of a star and the stage of its lifetime.

Obtaining, Evaluating, and Communicating Information, The Universe and its Stars, Energy and Matter

HS-ESS1-4 Use mathematical or computational representations to predict the motion of orbiting objects in the solar system.

Further explanation: Emphasis is on Newtonian gravitational laws governing orbital motions, which apply to

human-made satellites as well as planets and moons.

Using Mathematical and Computational Thinking, Earth and the Solar System, Scale, Proportion, and Quantity

HS-ESS1-5 Evaluate evidence of the past and current movements of continental and oceanic crust and the theory of plate tectonics to explain the ages of crustal rocks.

Further explanation: Emphasis is on the ability of plate tectonics to explain the ages of crustal rocks. Examples include evidence of the ages oceanic crust increasing with distance from mid-ocean ridges (a result of plate spreading) and the ages of North American continental crust increasing with distance away from a central ancient core (a result of past plate interactions). Examples could also be found from looking at differences between coastal Maine and interior Maine rock types and their ages as evidence to explain the formation of land structures and plate boundaries that cause them.

Engaging in Argument from Evidence, The History of Planet Earth, Plate Tectonics and Large-Scale System Interactions, Nuclear Processes, Patterns

HS-ESS1-6 Apply scientific reasoning and evidence from ancient Earth materials, meteorites, and other planetary surfaces to construct an account of Earth's formation and early history.

Further explanation: Emphasis is on using available evidence within the solar system to reconstruct the early history of Earth, which formed along with the rest of the solar system 4.6 billion years ago. Examples of evidence include the absolute ages of ancient materials (obtained by radiometric dating of meteorites, moon rocks, and Earth's oldest minerals), the sizes and compositions of solar system objects, and the impact cratering record of planetary surfaces. Constructing Explanations and Designing Solutions, The History of Planet Earth, Stability and Change

Strand Earth and Space Sciences (ESS)
Standard ESS2 Earth's Systems
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

K-ESS2-1 Use and share observations of local weather conditions to describe patterns over time.

Further explanation: Examples of qualitative observations could include descriptions of the weather (such as sunny, cloudy, rainy, and warm); examples of quantitative observations could include graphing the number of sunny, windy, and rainy or snowy days in a month. Examples of patterns could include that it is usually cooler in the morning than in the afternoon and the number of sunny days versus cloudy days in different months. Analyzing and Interpreting Data, Weather and Climate, Patterns

K-ESS2-2 Construct an argument supported by evidence for how plants and animals (including humans) can change the environment to meet their needs.

Further explanation: Examples of plants and animals changing their environment could include a squirrel digging in the ground to hide its food and tree roots can break concrete. Examples could include ways that humans change their environment to meet their needs (cutting down trees to provide heat, farming to provide food, and the process of snow removal, e.g. sanding/salting the roads, snowplowing, etc.).

Engaging in Argument from Evidence, Biogeology, Human Impacts on Earth

2-ESS2-1 Compare multiple solutions designed to slow or prevent wind or water from changing the shape of the land.

Further Explanation: Examples of solutions could include different designs of dikes and windbreaks to hold back wind and water and different designs for using shrubs, grass, and trees to hold back land.

Constructing Explanations and Designing Solutions, Earth Materials and Systems, Optimizing the Design Solution, Stability and Change

2-ESS2-2 Develop a model to represent the shapes and kinds of land and bodies of water in an area.

Developing and Using Models, Plate Tectonics and the Large-Scale System Interactions, Patterns

2-ESS2-3 Obtain information to identify where water is found on Earth and that it can be solid or liquid.

Obtaining, Evaluating, and Communicating Information, The Roles of Water in Earth's Surface Processes, Patterns

Strand Earth and Space Sciences (ESS)
Standard ESS2 Earth's Systems
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-ESS2-1 Represent data in tables and graphical displays to describe typical weather conditions expected during a particular season.

Further Explanation: Examples of data could include average temperature, precipitation, and wind direction Analyzing and Interpreting Data, Weather and Climate, Patterns

3-ESS2-2 Obtain and combine information to describe climates in different regions of the world.

Obtaining, Evaluating, and Communicating Information, Weather and Climate, Patterns

4-ESS2-1 Make observations and/or measurements to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation.

Further Explanation: Examples of variables to test could include angle of slope in the downhill movement of water, amount of vegetation, speed of wind, relative rate of deposition, cycles of freezing and thawing of water, cycles of heating and cooling, and volume of water flow. Maine pot holes and frost heaves are evidence of the effects of weathering and explain why roads in Maine are repaved more frequently than roads in Florida. Planning and Carrying out Investigations, Earth Materials and Systems, Biogeology, Cause and Effect

4-ESS2-2 Analyze and interpret data from maps to describe patterns of Earth's features.

Further Explanation: Maps can include topographic maps of Earth's land and ocean floor, as well as maps of the locations of mountains, continental boundaries, volcanoes, and earthquakes. Investigate the formation of the Appalachian Mountains and compare them to the formation of the Rocky or Cascade Mountain Ranges. Analyzing and Interpreting Data, Plate Tectonics and Large-Scale System Interactions, Patterns

5-ESS2-1 Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact.

Further Explanation: Examples could include the influence of the ocean on ecosystems, landform shape, and climate; the influence of the atmosphere on landforms and ecosystems through weather and climate; and the influence of mountain ranges on winds and clouds in the atmosphere. The geosphere, hydrosphere, atmosphere, and biosphere are each a system. Developing and Using Models, Earth's Materials and Systems, Systems and System Models

5-ESS2-2 Describe and graph the amounts and percentages of water and fresh water in various reservoirs to provide evidence about the distribution of water on Earth.

Using Mathematics and Computational Thinking, The Roles of Water in Earth's Surface Processes, Scale, Proportion, and Quantity

Strand Earth and Space Sciences (ESS)
Standard ESS2 Earth's Systems
Early Adolescence
Grades 6-8
Performance Expectations

MS-ESS2-1 Develop a model to describe the cycling of Earth's materials and the flow of energy that drives this process

Further explanation: Emphasis is on the processes of melting, crystallization, weathering, deformation, and sedimentation, which act together to form minerals and rocks through the cycling of Earth's materials. Potential Maine connections include Deer Isle granite, Rockland limestone, Maine tourmaline, Acadia National Park pink granite, along with Maine mining history at Bald Mountain or Katahdin Iron Works. Developing and using models, earth's materials and systems, stability and change

MS-ESS2-2 Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales.

Further explanation: Emphasis is on how processes change Earth's surface at time and spatial scales that can be large (such as slow plate motions or the uplift of large mountain ranges) or small (such as rapid landslides or microscopic geochemical reactions), and how many geoscience processes (such as earthquakes, volcanoes, and meteor impacts) usually behave gradually but are punctuated by catastrophic events. Examples of geoscience processes include surface weathering and deposition by the movements of water, ice, and wind. Emphasis is on geoscience processes that shape local geographic features, where appropriate. Potential Maine connections include the Desert of Maine, glacial erratics, alluvial fans, Appalachian Trail and Baxter State Park, and the fjord on Mount Desert Island.

Constructing explanations and designing solutions, earth's materials and systems, the roles of water in earth's surface processes, scale proportion and quantity

MS-ESS2-3 Analyze and interpret data on the distribution of fossils and rocks, continental shapes, and seafloor structures to provide evidence of the past plate motions.

Further explanation: Examples of data include similarities of rock and fossil types on different continents, the shapes of the continents (including continental shelves), and the locations of ocean structures (such as ridges, fracture zones, and trenches). Potential Maine connections can be found in the Gulf of Maine, Georges Bank and the inner continental shelf.

Analyzing and interpreting data, the history of planet earth, plate tectonics and large-scale system interactions, patterns

MS-ESS2-4 Develop a model to describe the cycling of water through Earth's systems driven by energy from the sun and the force of gravity.

Further explanation: Emphasis is on the ways in which water changes its state as it moves through the multiple pathways of the hydrologic cycle. Examples of models can be conceptual or physical. Developing and using models, the roles of water in earth's surface processes, energy and matter

MS-ESS2-5 Collect data to provide evidence for how the motions and complex interactions of air masses result in changes in weather conditions.

Further explanation: Emphasis is on how air masses flow from regions of high pressure to low pressure, causing weather (defined by temperature, pressure, humidity, precipitation, and wind) at a fixed location to change over time and how sudden changes in weather can result when different air masses collide. Emphasis is on how weather can be predicted within probabilistic ranges. Examples of data can be provided to students (such as weather maps, diagrams, and visualizations) or obtained through laboratory experiments (such as with condensation). Potential Maine connections include "Bombogenesis" snow storms, coastal fog, Nor'easters, sea smoke and valley fog.

Planning and carrying out investigations, the roles of water in earth's surface processes, weather and climate, cause and effect

MS-ESS2-6 Develop and use a model to describe how unequal heating and rotation of the Earth cause patterns of atmospheric and oceanic circulation that determine regional climates.

Further explanation: Emphasis is on how patterns vary by latitude, altitude, and geographic land distribution. Emphasis of atmospheric circulation is on the sunlight-driven latitudinal banding, the Coriolis effect, and resulting prevailing winds; emphasis of ocean circulation is on the transfer of heat by the global ocean convection cycle, which is constrained by the Coriolis effect and the outlines of continents. Examples of models can be diagrams, maps and globes, or digital representations.

Developing and using models, the roles of water in earth's surface processes, weather and climate, systems and system models

Strand Earth and Space Sciences (ESS)
Standard ESS2 Earth's Systems
Adolescence
Grades 9-Diploma
Performance Expectations

HS-ESS2-1 Develop a model to illustrate how Earth's internal and surface processes operate at different spatial and temporal scales to form continental and ocean-floor features.

Further explanation: Emphasis is on how the appearance of land features (such as mountains, valleys, and plateaus) and sea floor features (such as trenches, ridges, and seamounts) are a result of both constructive forces (such as volcanism, tectonic uplift, and orogeny) and destructive mechanisms (such as weathering, mass wasting, and coastal erosion). An example could be to utilize Maine Geologic maps, including tectonic maps, as data to create a model to illustrate how Maine's land features or oceanic features were formed. Consider looking to Maine's glacial history, features formed and materials deposited by glaciers. Developing and Using Models, Plate Tectonics and Large-Scale System Interactions, Earth Materials and Systems, Stability and Change

HS-ESS2-2 Analyze geoscience data to make the claim that one change to Earth's surface can create feedbacks that cause changes to other Earth systems.

Further explanation: Examples should include climate feedbacks, such as how an increase in greenhouse gases causes a rise in global temperatures that melts glacial ice, which reduces the amount of sunlight reflected from Earth's surface, increasing surface temperatures and further reducing the amount of ice. Examples could also be taken from other system interactions, such as how the loss of ground vegetation causes an increase in water runoff and soil erosion; how dammed rivers increase groundwater recharge, decrease sediment transport, and increase coastal erosion; and how the loss of wetlands causes a decrease in local humidity that further reduces the wetlands' extent. An example could consider timber harvesting practices related to erosion and water runoff issues, river damming, or coastal erosion of Maine's beaches and dunes. Analyzing and Interpreting Data, Earth Materials and Systems, Stability and Change

HS-ESS2-3 Develop a model based on evidence of Earth's interior to describe the cycling of matter by thermal convection.

Further explanation: Emphasis is on both a one-dimensional model of Earth, with radial layers determined by density, and a three-dimensional model, which is controlled by mantle convection and the resulting plate tectonics. Examples of evidence include maps of Earth's three-dimensional structure obtained from seismic waves, records of the rate of change of Earth's magnetic field (as constraints on convection in the outer core), and identification of the composition of Earth's layers from high-pressure laboratory experiments. Developing and Using Models, Earth Materials and Systems, Plate Tectonics and Large-Scale System Interactions, Wave Properties, Energy and Matter

HS-ESS2-4 Use a model to describe how variations in the flow of energy into and out of Earth's systems result in changes in climate.

Further explanation: Examples of the causes of climate change differ by timescale, over 1-10 years; large volcanic eruptions, ocean circulation; 10s to 100s of years: changes in human activity, ocean circulation, solar output; 10s a-100s of thousands of years: changes to Earth's orbit and the orientation of its axis; and 10s-100s of millions of years: long-term changes in atmospheric composition. Consider the climatic impacts of the Gulf stream and the Labrador currents on the Gulf of Maine, e.g. water temperature changes and fishing industry disruptions.

Developing and Using Models, Earth and the Solar System, Earth Materials and Systems, Weather and Climate, Scale, Proportion, and Quantity

HS-ESS2-5 Plan and conduct an investigation of the properties of water and its effects on Earth materials and surface processes.

Further explanation: Emphasis is on mechanical and chemical investigations with water and a variety of solid materials to provide evidence for the connections between the hydrologic cycle and system interactions commonly known as the rock cycle. Examples of mechanical investigations include stream transportation and deposition using a stream table, erosion using variations in soil moisture content, and frost wedging by the expansion of water as it freezes. Examples of chemical investigations include chemical weathering and recrystallization (by testing the solubility of different materials) or melt generation (by examining how water lowers the melting temperature of most solids). Draw connections to Maine phenomena such as ice jams, frost heaves and potholes.

Planning and Carrying Out Investigations, The Role of Water in Earth's Surface Processes, Structure and Function

HS-ESS2-6 Develop a quantitative model to describe the cycling of carbon among the hydrosphere, atmosphere, geosphere, and biosphere.

Further explanation: Emphasis is on modeling biogeochemical cycles that include the cycling of carbon through the ocean, atmosphere, soil, and biosphere (including humans), providing the foundation for living organisms. Developing and Using Models, Weather and Climate, Energy and Matter

HS-ESS2-7 Construct an argument based on evidence about the simultaneous coevolution of Earth's systems and life on Earth.

Further explanation: Emphasis is on the dynamic causes, effects, and feedbacks between the biosphere and Earth's other systems, whereby geoscience factors control the evolution of life, which in turn continuously alters Earth's surface. Examples include how photosynthetic life altered the atmosphere through the production of oxygen, which in turn increased weathering rates and allowed for the evolution of animal life; how microbial life on land increased the formation of soil, which in turn allowed for the evolution of land plants; and how the evolution of corals created reefs that altered patterns of erosion and deposition along coastlines and provided habitats for the evolution of new life forms. Engaging in Argument from Evidence, Weather and Climate, Biogeology, Stability and Change

Strand Earth and Space Sciences (ESS)
Standard ESS3 Earth and Human Activity
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

K-ESS3-1 Use a model to represent the relationship between the needs of different plants or animals (including humans) and the places they live.

Further explanation: Examples of relationships could include that deer eat buds and leaves and therefore usually live in forested areas and that grasses need sunlight so they often grow in meadows. Plants, animals, and their surroundings make up a system. Examples could include coastal tidepools, humans in Maine live in insulated buildings for protection during cold months, or uninsulated structures during warm months (e.g. camping in a tent). Examples of animals that migrate include monarch butterflies, ducks, Canada geese, etc.

Developing and Using Models, Natural Resources, Systems and System Models

K-ESS3-2 Ask questions to obtain information about the purpose of weather forecasting to prepare for, and respond to, severe weather.

Further explanation: Emphasis is on local forms of severe weather. Examples could include local forms of severe weather (flooding, ice, blizzards, heat, etc.) and checking the weather forecast to determine proper clothing to wear. Asking Questions and Defining Problems, Obtaining, Evaluating, and Communicating Information, Natural Hazards, Defining and Delimiting an Engineering Problem, Cause and Effect

K-ESS3-3 Communicate solutions that will reduce the impact of humans on the land, water, air, and/or other living things in the local environment.

Further explanation: Examples of human impact on land could include cutting trees to produce paper and using resources to produce bottles. Examples of solutions could include reusing paper and recycling cans and bottles. Examples could also include what we can do to clean public areas (e.g. beaches, parks, lakes, trails, etc.).

Obtaining, Evaluating, and Communicating Information, Developing Possible Solutions, Human Impacts on Earth Systems, Cause and Effect

Strand Earth and Space Sciences (ESS)
Standard ESS3 Earth and Human Activity
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-ESS3-1 Make a claim about the merit of a design solution that reduces the impacts of a weather-related hazard.

Further Explanation: Examples of design solutions to weather-related hazards could include barriers to prevent flooding, wind resistant roofs, and lightning rods. Potential Maine connections include the construction of seawalls in southern Maine to prevent damage to homes from strong ocean storms. Engaging in Argument from Evidence, Natural Hazards, Cause and Effect

4-ESS3-1 Obtain and combine information to describe that energy and fuels are derived from natural resources and their uses affect the environment.

Further Explanation: Examples of renewable energy resources could include wind energy, water behind dams, and sunlight; nonrenewable energy resources are fossil fuels and fissile materials. Examples of environmental effects could include loss of habitat due to dams, loss of habitat due to surface mining, and air pollution from burning of fossil fuels. Investigate the pros and cons of heating homes with wood, fossil fuels, and solar energy. Investigate what a wind or solar farm is and why they are controversial in Maine. Obtaining, Evaluating, and Communicating Information, Natural Resources, Cause and Effect

4-ESS3-2 Generate and compare multiple solutions to reduce the impacts of natural Earth processes on humans.

Further Explanation: Examples of solutions could include designing an earthquake resistant building and improving monitoring of volcanic activity. Design a microburst resistant building or design a telephone/electric pole that could sustain less damage in an ice storm.

Constructing Explanations and Designing Solutions, Natural Hazards, Designing Solutions to Engineering Problems, Cause and Effect

5-ESS3-1 Obtain and combine information about ways individual communities use science ideas to protect the Earth's resources and environment.

Obtaining, Evaluating and Communicating Information, Human Impacts on Earth systems, Systems and System Models

Strand Earth and Space Sciences (ESS)
Standard ESS3 Earth and Human Activity
Early Adolescence
Grades 6-8
Performance Expectations

MS-ESS3-1 Construct a scientific explanation based on evidence for how the uneven distributions of Earth's mineral, energy, and groundwater resources are the result of past and current geoscience processes.

Further explanation: Emphasis is on how these resources are limited and typically non-renewable and on how their distributions are significantly changing as a result of removal by humans. Examples of uneven distributions of resources as a result of past processes include but are not limited to petroleum (locations of the burial of organic marine sediments and subsequent geologic traps), metal ores (locations of past volcanic and hydrothermal activity associated with subduction zones), and soil (locations of active weathering and/or deposition of rock). Constructing explanations and designing solutions, natural resources, cause and effect

MS-ESS3-2 Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their effects.

Further explanation: Emphasis is on how some natural hazards, such as volcanic eruptions, and severe weather, are preceded by phenomena that allow for reliable predictions, but others, such as earthquakes, occur suddenly and with no notice and thus are not yet predictable. Examples of natural hazards can be taken from interior processes (such as earthquakes and volcanic eruptions), surface processes (such as mass wasting and tsunamis), or severe weather events (such as hurricanes, tornadoes, and floods). Examples of data can include the locations, magnitudes, and frequencies of the natural hazards. Examples of technologies can be global (such as satellite systems to monitor hurricanes or forest fires) or local (such as building basements in tornado-prone regions or reservoirs to mitigate droughts). Analyzing and interpreting data, natural hazards, patterns

MS-ESS3-3 Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment.

Further explanation: Examples of the design process include examining human environmental impacts, assessing the kinds of solutions that are feasible, and designing and evaluating solutions that could reduce that impact. Examples of human impacts can include water usage (such as the withdrawal of water from streams and aquifers or the construction of dams and levees), land usage (such as urban development, agriculture, or the removal of wetlands), and pollution (such as of the air, water, or land). Constructing explanations and designing solutions, human impacts on earth systems, cause and effect

MS-ESS3-4 Construct an argument supported by evidence for how increases in human population and per-capita consumption of natural resources impact Earth's systems.

Further explanation: Examples of evidence include grade-appropriate databases on human populations and the rates of consumption of food and natural resources (such as freshwater, mineral, and energy). Examples of impacts can include changes to the appearance, composition, and structure of Earth's systems as well as the rates at which they change. The consequences of increases in human populations and consumption of natural resources are described by science, but science does not make the decisions for the actions society takes. Engaging in argument from evidence, human impacts on earth systems, cause and effect

MS-ESS3-5 Ask questions to clarify evidence of the factors that have caused the rise in global temperatures over the past century.

Further explanation: Examples of factors include human activities (such as fossil fuel combustion, cement production, and agricultural activity) and natural processes (such as changes in incoming solar radiation or volcanic activity). Examples of evidence can include tables, graphs, and maps of global and regional temperatures, atmospheric levels of gases such as carbon dioxide and methane, and the rates of human activities. Emphasis is o n the major role that human activities play in causing the rise in global temperatures. Asking questions and defining problems, global climate change, stability and change

Strand Earth and Space Sciences (ESS)
Standard ESS3 Earth and Human Activity
Adolescence
Grades 9-Diploma
Performance Expectations

HS-ESS3-1 Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity.

Further explanation: Examples of key natural resources include access to fresh water (such as rivers, lakes, and groundwater), regions of fertile soils such as river deltas, and high concentrations of minerals and fossil fuels. Examples of natural hazards can be from interior processes (such as volcanic eruptions and earthquakes), surface processes (such as tsunamis, mass wasting and soil erosion), and severe weather (such as hurricanes, floods, and droughts). Examples of the results of changes in climate that can affect populations or drive mass migrations include changes to sea level, regional patterns of temperature and precipitation, and the types of crops and livestock that can be raised. Other examples include the impacts of climate change on Maine's ski industry, fishing industry, maple sugar industry and on sea levels or droughts. Constructing Explanations and Designing Solutions, Natural Resources, Natural Hazards, Cause and Effect

HS-ESS3-2 Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.

Further explanation: Emphasis is on the conservation, recycling, and reuse of resources (such as minerals and metals) where possible, and on minimizing impacts where it is not. Examples include developing best practices for agricultural soil use (for farming, timber industry, blueberry and potato crops), mining (for coal, tar sands, and oil shales), and pumping (for petroleum and natural gas). Science knowledge indicates what can happen in natural systems-not what should happen. Engaging in Argument from Evidence, Natural Resources, Developing Possible Solutions

HS-ESS3-3 Create a computational simulation to illustrate the relationships among management of natural resources, the sustainability of human populations, and biodiversity.

Further explanation: Examples of factors that affect the management of natural resources include costs of resource extraction and waste management, per-capita consumption, and the development of new technologies. Examples of factors that affect human sustainability include agricultural efficiency, levels of conservation, and urban planning. Consider the effects of urban sprawl and the loss of farmland. Using Mathematics and Computational Thinking, Human Impacts on Earth Systems, Stability and Change

HS-ESS3-4 Evaluate or refine a technological solution that reduces impacts of human activities on natural systems.

Further explanation: Examples of data on the impacts of human activities could include the quantities and types of pollutants released, changes to biomass and species diversity, or areal changes in land surface use (such as for urban development, agriculture and livestock, or surface mining). Examples for limiting future impacts could range from local efforts (such as reducing, reusing, and recycling resources) to large-scale geoengineering design solutions (such as altering global temperatures by making large changes to the atmosphere or ocean). Other examples include the use of propane-powered buses in Acadia (evaluate pros and cons). Constructing Explanations and Designing Solutions, Developing Possible Solutions, Stability and Change

HS-ESS3-5 Analyze geoscience data and the results from global climate models to make an evidence-based forecast of the current rate of global or regional climate change and associated future impacts to Earth's systems.

Further explanation: Examples of evidence, for both data and climate model outputs, are for climate changes (such as precipitation and temperature) and their associated impacts (such as on sea level, glacial ice volumes, or atmosphere and ocean composition). Analyzing and Interpreting Data, Global Climate Change, Stability and Change

HS-ESS3-6 Use a computational representation to illustrate the relationships among Earth systems and how those relationships are being modified due to human activity.

Further explanation: Examples of Earth systems to be considered are the hydrosphere, atmosphere, cryosphere, geosphere, and/or biosphere. An example of the far-reaching impacts from a human activity is how an increase in atmospheric carbon dioxide results in an increase in photosynthetic biomass on land and an increase in ocean acidification, with resulting impacts on sea organism health and marine populations. Use and interpret graphs and data of carbon dioxide levels in the Gulf of Maine for oysters and sea scallops. Consider the impacts of ocean acidification on shellfish. Using Mathematics and Computational Thinking, Weather and Climate, Global Climate Change, Systems andSystem Models

Strand Engineering, Technology, and Applications of Science (ETS)
Standard ETS1 Engineering Design
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

K-2-ETS1-1 Ask questions, make observations, and gather information about a situation people want to change to define a simple problem that can be solved through the development of a new or improved object or tool.

Asking Questions and Defining Problems, Defining and Delimiting Engineering Problems

K-2-ETS1-2 Develop a simple sketch, drawing, or physical model to illustrate how the shape of an object helps it function as needed to solve a given problem.

Developing and Using Models, Developing Possible Solutions, Structure and Function

K-2-ETS1-3 Analyze data from tests of two objects designed to solve the same problem to compare the strengths and weaknesses of how each performs.

Analyzing and Interpreting Data, Optimizing the Design Solution

Strand Engineering, Technology, and Applications of Science (ETS)
Standard ETS1 Engineering Design
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

3-5-ETS1-1 Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.

Asking Questions and Defining Problems, Defining and Delimiting Engineering Problems, Influence of Engineering, Technology, and Science on Society and the Natural World

3-5-ETS1-2 Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.

Constructing Explanations and Designing Solutions, Developing Possible Solutions, Influence of Engineering, Technology, and Science on Society and the Natural World

3-5-ETS1-3 Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model or prototype that can be improved.

Planning and Carrying out Explanations, Developing Possible Solutions, Optimizing the Design Solution

Strand Engineering, Technology, and Applications of Science (ETS)
Standard ETS1 Engineering Design
Early Adolescence
Grades 6-8
Performance Expectations

MS-ETS1-1 Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

Further explanation: To solve a problem it needs to have clearly defined set goals and limits. The more limitations applied to a problem, the more elegant and successful the solution is likely to be. Limitations would take into account potential impacts on the environment, social/cultural norms, and allowable interactions. The application of science principles is to be used as a tool to verify solutions. Examples could include hydroelectric dams as a viable, cost effective and ecologically friendly way to generate electrical power. However, the dam holds fish populations from traveling freely through the environment. There is a need to provide a safe way for aquatic life to pass by the hydroelectric turbine in a way that does not impact the electrical generation, the original water flow of the river dammed, is cost effective to existing dam models, and has no negative impact on human populations.

Asking questions and defining problems, defining and delimiting engineering problems, influence of science, engineering, and technology on society and the natural world

MS-ETS1-2 Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

Further explanation: When designing a solution to a problem, there need to be many possible solutions explored, tested, verified, and compared, and the use of some tool to determine the validity of competing designs in meeting the design criteria. These tools would be used to make testing data understandable, comparable, and accessible.

Engaging in argument from evidence, deve loping possible solutions

MS-ETS1-3 Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success.

Further explanation: Testing and data is used to evaluate the solutions or part of the solutions that best solve the given problem. The data needs to be assessed and then used to modify, combine, and deny solutions and then retested to arrive at the best possible solution within the constraints of the problem. Examples could include tables, graphs, matrices, check lists, spreadsheets, public polls, Venn diagrams, mathematical models, etc. Analyzing and interpreting data, developing possible solutions, optimizing design solution

MS-ETS1-4 Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.

Further explanation: Developing the proper test to verify which solutions meet and which excel when applied against the constraints. That test is then applied to a prototype or model to allow faults to be identified and then corrected, frequently the combination of two or more solutions can produce a better solution and then retest it to see if it is the best solution. Examples could include materials science testing (shear strength, compression testing, tension testing, etc.), weather testing (temperature, rain, snow, wind, sun exposure), wind tunnel, failure or destructive testing, mathematical models, etc. Developing and using models, developing possible solutions, optimizing design solution

Strand Engineering, Technology, and Applications of Science (ETS)
Standard ETS1 Engineering Design
Adolescence
Grades 9-Diploma
Performance Expectations

HS-ETS1-1 Analyze a major global challenge to specify qualitative and quantitative criteria and constraints for solutions that account for societal needs and wants.

Further explanation: Examples of challenges include local and global climate change issues, biodiversity loss or United Nations sustainable development goals.

Asking Questions and Defining Problems, Defining and Delimiting Engineering Problems

HS-ETS1-2 Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

Further explanation: Examples could include transportation issues, dams, green energy and wind power in Maine.

Constructing Explanations and Designing Solutions, Optimizing the Design Solution

HS-ETS1-3 Evaluate a solution to a complex real-world problem based on prioritized criteria and tradeoffs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts.

Further explanation: Examples could include lobstering and exports of lobster, dry wells and water conservation in Maine, or saltwater intrusion in coastal Maine wells.

Constructing Explanations and Designing Solutions, Developing Possible Solutions

HS-ETS1-4 Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints on interactions within and between systems relevant to the problem.

Using Mathematics and Computational Thinking, Developing Possible Solutions, Systems and System Models

SOCIAL STUDIES

Introduction

The great architects of American public education, such as Thomas Jefferson, Horace Mann, and John Dewey, believed that every student must be well versed in our nation's history, the principles and practices which support and sustain citizenship, and the institutions that define our government. Understandings of commerce and geography were critical to their thinking as well. In essence, Jefferson, Mann, and Dewey viewed the study of social studies as critical to the mission of public schools. According to the National Council for the Social Studies: advocates of citizenship education cross the political spectrum, but they are bound by a common belief that our democratic republic will not sustain unless students are aware of their changing cultural and physical environments; know the past; read, write, and think deeply; and act in ways that promote the common good. (C3 Framework for Social Studies, 2013).

A strong Social Studies education depends upon a clear understanding of its interrelated disciplines and inclusion of Maine's Guiding Principles. Without knowledge of the geography and economics of earlier times, history offers only lists of people, events, and dates. Without knowledge of history, the institutions of American government and the dynamics of today's global economy are difficult to understand. Although social studies curricula vary in their breadth and depth, the Social Studies Standards reflect a focus on government, history, geography, personal finance and economics as the pillars of the content, with other disciplines within the social sciences deemed important, but not essential.

Guiding Principles

The Guiding Principles guide education in Maine and should be reflected throughout Social Studies curriculum. Examples of how students can show evidence of those guiding principles in Social Studies may include:

A. Clear and Effective Communicator: Students research and use background knowledge to give audiovisual presentations about current and historical issues.
B. Self-Directed and Lifelong Learner: Students generate questions and explore primary and secondary sources to answer those questions while demonstrating a growth mindset.
C. Creative and Practical Problem Solver: Students draw conclusions about current and historical problems using valid research and critical thinking.
D. Responsible and Involved Citizen: Students practice and apply the duties of citizenship through the exercise of constitutional rights.
E. Integrative and Informed Thinker: Students compare and contrast to analyze point of view and differentiate between reliable and unreliable primary and secondary sources.

Performance Expectations that include the application of the Guiding Principles through Social Studies knowledge and skills are denoted in the standards with an asterisk (*).

Skills in Social Studies:

The application of skills in Social Studies is crucial to any curriculum. Best practices in Social Studies reflect curriculum, instruction, and assessment that give students opportunities to demonstrate research and develop positions on current Social Studies issues. Students will be asked to identify key words and concepts related to research questions and locate and access information by using text features. Additionally, students will demonstrate facility with note-taking, organizing information, and creating bibliographies. Students will distinguish between primary and secondary sources as well as evaluate and verify the credibility of the information found in print and non-print sources. Equally important is that students use additional sources to resolve contradictory information.

Key Ideas in the Social Studies Standards:

Growth mindset - Our mindset includes beliefs about our abilities and qualities that include intelligence, creativity or musicality. Having a growth mindset means that students know that their abilities and strengths can change or develop, and that those changes are within their control.

Understand - The word "understand" appears in performance expectations throughout the Social Studies Standards. It refers to a variety of different levels of thinking and was used intentionally to serve as an umbrella term for the cognitive demand that is described by the descriptors beneath the performance expectations. Look to the grade level expectation for grades K-5 or to the grade span expectations in spans 6-8 and 9-12 (Foundational or Developmental as noted by "F" or "D") to define the level of cognitive demand for student performance.

Various -The Social Studies Standards refer to "various" peoples, nations, regions of the world, historical eras, and enduring themes. School administrative units should develop a local curriculum that assists students in gaining a coherent, broad perspective on a variety of peoples, nations, regions, historical eras, and enduring themes.

Major Enduring Themes - The term "major enduring themes" is used in several places in the Social Studies Standards. This term refers to general topics or issues that have been relevant over a long period of time. Using a consistent set of themes can serve as a framework within which other concepts, topics, and facts can be organized. It can also help students make connections between events within and across historical eras, and use history to help make informed decisions. The Civics and Government, Personal Finance and Economics, Geography, and History Standards all include performance expectations that address individual, cultural, international, and global connections. It will be up to the School Administrative Units to determine whether they use these performance expectations as an opportunity to integrate across the disciplines of the social studies or address them separately. The "enduring themes," some of which overlap, include:

Freedom and Justice Conflict and Compromise Technology and Innovation Unity and Diversity Continuity and Change Over Time Supply and Demand

Eras - School Administrative Units (SAU) should develop a coherent curriculum that provides students with a balanced exposure to the major eras of United States and World History. The term "various eras" in this document refers to those eras that are selected by an SAU to build a cohesive, balanced understanding. The "eras," some of which overlap, include:

Eras in United States History* Eras in World History*

1. Beginnings to 1607: Migration, contact, and exchange between Native Americans, Africans , and Europeans.

2. 1607 to 1754: Conflict and competition -- Europeans and Native Americans; emergence of distinctive Colonial and Native societies.

3. 1754 to 1800: Social, political, and economic tensions --Revolution and the Early National Period.

4. 1800 to 1848: Defining and extending democratic ideals during rapid economic, territorial, and demographic changes.

5. 1844 to 1877: Regional tensions and civil war.

6. 1865 to 1898: Move from agricultural to industrialized society.

7. 1890 to 1945: Domestic and global challenges; debate over Government's role and the role of the US in the world.

8. 1945 to 1980: Challenges with prosperity, living up to ideals, and unfamiliar international responsibilities.

9. 1980 to present: Cultural debates, adaptation to economic globalization and revolutionary changes in science and technology.

*All eras are circa.

1. Beginnings to 600 BCE: Technological and environmental transformations.

2. 600 BCE to 600 CE: Organization and reorganization of human societies.

3. 600 to 1450: Regional and interregional interactions.

4. 1450 to 1750: Political, social, economic and global interactions led to revolutions.

5. 1750 to 1900: Industrialization and global integration.

6. 1900 to present: Accelerating global change and realignments.

Spiraling K-12 - A course of study in which students will see the same topics throughout their school career, with each encounter increasing in complexity and reinforcing previous learning. The Social Studies Standards and performance expectations have been created in order to reflect a progression of increasing complexity from K-5 and between the 6-8, and 9-diploma grade spans.

Maine Statutes Related to Social Studies

Title 20-A: Education §4722. High school diploma standards.

1. Minimum instructional requirements. A comprehensive program of instruction must include a minimum 4-year program that meets the curriculum requirements established by this chapter and any other instructional requirements established by the commissioner and the school board. [2009, c. 313, §15 (AMD).]
2. Required subjects. Courses in the following subjects shall be provided in separate or integrated study programs to all students and required for a high school diploma: .... Social studies and history, including American history, government, civics and personal finance--2 years; [2013, c. 244, §1 (AMD).]

Title 20-A MRSA §4706, as amended by PL 1991, c. 655, §4, is further amended to read:

§4706. Instruction in American history, Maine studies and Maine Native American history.

The following subjects are required: .... Maine Studies... American History... Maine Native American history (including Maine tribal governments, Maine Native American culture, Maine Native American territories, and Maine Native American economic systems). Maine Native American history and culture must be taught in all elementary and secondary schools, both public and private.

Maine Native Americans - The phrase "Maine Native Americans" refers to the four Maine Native American tribes - the Penobscot, the Passama quoddy, the Micmac, and the Maliseet.

Strand

Civics & Government

Standard

Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world.

Childhood

Kindergarten

Grade 1

Grade 2

Performance Expectations

Civics & Government 1: Students understand key ideas and processes that characterize democratic government in the community and the United States by identifying community workers and volunteers and the roles they play in promoting the common good.

Civics & Government 2: Students understand key ideas and processes that characterize democratic government in the community and the United States by recognizing symbols, monuments, celebrations, and leaders of local government.

Civics & Government 3: Students understand the concepts of rights, duties, responsibilities, and participation by explaining the purpose of school/classroom rules and local laws encountered in daily experiences to promote the common good and the peaceful resolution of conflict.

Civics & Government 4: Students understand the concepts of rights, duties, responsibilities, and participation by describing classroom rights, duties, and responsibilities including how students participate in some classroom decisions and are obliged to follow classroom rules.

Civics & Government 5: Students understand civic aspects of classroom traditions and decisions by identifying and comparing diverse interests and opinions related to classroom traditions and decisions.

Civics & Government 1: Students understand key ideas and processes that characterize democratic government in the community and the United States by recognizing symbols, monuments, celebrations, and leaders of State government.

Civics & Government 2: Students understand the concepts of rights, duties, responsibilities, and participation by explaining the purpose of school/classroom rules and state laws encountered in daily experiences to promote the common good and the peaceful resolution of conflict.

Civics & Government 3: Students understand Maine Native Americans by explaining their traditions and customs.

Civics & Government 1: Students understand key ideas and processes that characterize democratic government in the community and the United States by describing and providing examples of democratic ideals

Civics & Government 2: Students understand key ideas and processes that characterize democratic government in the community and the United States by recognizing symbols, monuments, celebrations, and leaders of national government.

Civics & Government 3: Students understand the concepts of rights, duties, responsibilities, and participation by explaining the purpose of school/classroom rules and national laws encountered in daily experiences to promote the common good and the peaceful resolution of conflict through selecting, planning, and participating in a civic action or service-learning project based on a classroom or school asset or need, and describing the project's potential civic contribution. *

Civics & Government 4: Students understand the traditions of Maine Native Americans and various cultures by comparing national traditions and customs.

Strand

Civics & Government

Standard

Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world.

Childhood

Grade 3

Grade 4

Grade 5

Performance Expectations

Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining that the study of government includes how governments are organized and how citizens participate.

Civics & Government 2: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining how leaders are elected and how laws are made and implemented.

Civics & Government 3: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by identifying the rights, duties, and responsibilities of citizens within the class, school, or community.

Civics & Government 4: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by providing examples of how people influence government and work for the common good including voting and writing to legislators.

Civics & Government 5: Students understand civic aspects of unity and diversity in the daily life of various cultures in Maine and the United States by identifying examples of unity (sameness) and diversity (variety).

Civics & Government 6: Students understand civic aspects of unity and diversity in the daily life of Maine Native Americans and other various cultures in Maine by describing civic beliefs and activities in the daily life of diverse cultures of Maine.

Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining and providing examples of democratic ideals and constitutional principles to include the rule of law, legitimate power, and common good.

Civics & Government 2: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine by explaining and giving examples of governmental structures including the legislative, executive, and judicial branches and the local and State levels of government.

Civics & Government 3: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine by explaining that the structures and processes of government are described in documents, including the Constitution of Maine. Civics & Government 4: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by providing examples of how people influence government and work for the common good, including selecting, planning, and participating in a civic action or service-learning project based on a classroom, school, or local community asset or need, and describe evidence of the project's effectiveness and civic contribution. *

Civics & Government 5: Students understand civic aspects of unity and diversity in the daily life of various cultures in Maine and the United States, by identifying examples of unity and diversity in the United States that relate to how laws protect individuals or groups to support the common good.

Civics & Government 6: Students understand civic aspects of unity and diversity in the daily life of various cultures in the United States by describing civic beliefs and activities in the daily life of diverse cultures.

Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining that the structures and processes of government are described in documents, including the Constitution of the United States.

Civics & Government 2: Students understand the basic ideals, purposes, principles, structures, and processes of democratic government in Maine and the United States by explaining and giving examples of governmental structures including the legislative, executive, and judicial branches at national levels of government.

Civics & Government 3: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by identifying and describing the United States Constitution and Bill of Rights as documents that establish government and protect the rights of the individual United States citizen.

Civics & Government 4: Students understand the basic rights, duties, responsibilities, and roles of citizens in a democratic republic by providing examples of how people influence government and work for the common good, including engaging in civil disobedience.

Civics & Government 5: Students understand civic aspects of unity and diversity in the daily life of various cultures in the world, by identifying examples of unity and diversity in the United States that relate to how laws protect individuals or groups to support the common good. Civics & Government 6: Students understand civic aspects of unity and diversity in the daily life of various cultures of the world by describing civic beliefs and activities in the daily life of diverse cultures.

Strand

Civics & Government

Standard

Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world.

Early Adolescence

Grades 6-8

Performance Expectations

Civics & Government 1: Students understand the basic ideals, purposes, principles, structures, and processes of constitutional government in Maine and the United States as well as examples of other forms of government in the world by:

(F1) Explaining that the study of government includes the structures and functions of government and the political and civic activity of citizens.

(F2) Describing the structures and processes of United States government and government of the State of Maine and how these are framed by the United States Constitution, the Maine Constitution, and other primary sources.

(F3) Explaining the concepts of federalism and checks and balances and the role these concepts play in the governments of the United States and Maine as framed by the United States Constitution, the Maine Constitution and other primary sources.

(D1) Comparing the structures and processes of United States government with examples of other forms of government.

(D2) Comparing how laws are made in Maine and at the federal level in the United States.

(D3) Analyze examples of democratic ideals and constitutional principles that include the rule of law, legitimate power, and common good.

Civics & Government 2: Students understand constitutional and legal rights, civic duties and responsibilities, and roles of citizens in a constitutional democracy by:

(F1) Explaining the constitutional and legal status of "citizen" and provide examples of rights, duties, and responsibilities of citizens.

(F2) Describing how the powers of government are limited to protect individual rights and minority rights as described in the United States Constitution and the Bill of Rights.

(D1) Analyzing examples of the protection of rights in court cases or from current events.

(D2) Analyzing how people influence government and work for the common good including voting, writing to legislators, performing community service, and engaging in civil disobedience through selecting, planning, and implementing a civic action or service-learning project based on a school, community, or state asset or need, and analyze the project's effectiveness and civic contribution. *

Civics & Government 3: Students understand political and civic aspects of cultural diversity by:

(F1) Explaining basic civic aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations.

(F2) Describing the political structures and civic responsibilities of the diverse historic and current cultures of Maine, including Maine Native Americans.

(D1) Explaining constitutional and political aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations.

(D2) Describing the political structures and civic responsibilities of the diverse historic and current cultures of the United States and the world.

Strand Civics & Government
Standard Students draw on concepts from civics and government to understand political systems, power, authority, governance, civic ideals and practices, and the role of citizens in the community, Maine, the United States, and the world.
Adolescence
Grades 9-Diploma
Performance Expectations Civics & Government 1: Students understand the ideals, purposes, principles, structures, and processes of constitutional government in the United States and in the American political system, as well as examples of other forms of government and political systems in the world by:

(F1) Explaining that the study of government includes the structures, functions, institutions, and forms of government.

(F2) Explaining how and why democratic institutions and interpretations of democratic ideals and constitutional principles change over time.

(F3) Describing the purpose, structures, and processes of the American political system.

(D1) Evaluating and comparing the relationship of citizens with government in the United States and other regions of the world.

(D2) Evaluating current issues by applying democratic ideals and constitutional principles of government in the United States, including checks and balances, federalism, and consent of the governed as put forth in founding documents.

(D3) Comparing the American political system with examples of political systems from other parts of the world.

Civics & Government 2: Students understand the constitutional and legal rights, the civic duties and responsibilities, and roles of citizens in a constitutional democracy and the role of citizens li ving under other forms of government in the world by:

(F1) Exp laining the relationship between constitutional and legal rights, and civic duties and responsibilities in a constitutional democracy.

(F2) Evaluating the relationship between the government and the individual as evident in the United States Constitution, the Bill of Rights, and landmark court cases.

(F3) Evaluating how people influence government and work for the common good, including voting, writing to legislators, performing community service, and engaging in civil disobedience.

(D1) Comparing the rights, duties, and responsibilities of United States citizens with those of citizens from other nations.

(D2) Analyzing the constitutional principles and the roles of the citizen and the government in major laws or cases.

Civics & Government 3: Students understand political and civic aspects of cultural diversity by:

(F1) Explaining basic civic aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations.

(F2) Describing the political structures and civic responsibilities of the diverse historic and current cultures of Maine, including Maine Native Americans.

(D1) Analyzing constitutional and political aspects of historical and/or current issues that involve unity and diversity in Maine, the United States, and other nations through selecting, planning, and implementing a civic action or service-learning project based on a community, school, state, national, or international asset or need, and evaluate the project's effectiveness and civic contribution. *

(D2) Analyzing the political structures, political power, and political perspectives of the diverse historic and current cultures of the United States and the world.

Strand Personal Finance & Economics
Standard Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing how money has value and can be traded for goods and services.

Economics: Students understand the nature of economics as well as key foundational ideas by describing how people make choices to meet their needs and wants.

Global Connections: Students understand the influence of economics on individuals and groups in the United States and the World, including Maine Native Americans, by identifying how individuals, families, and communities are part of an economy.

Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing how spending, saving, and sharing are ways to use money.

Economics: Students understand the nature of economics as well as key foundational ideas by explaining and making decisions about how to use scarce resources to meet their needs and wants. *

Global Connections: Students understand the influence of economics on individuals and groups in the United States and the World, including Maine Native Americans by identifying how individuals, families, and communities are influenced by economic factors.

Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing how planning for the future is important to managing money.

Economics: Students understand the nature of economics as well as key foundational ideas by explaining how people make choices about how to use scarce resources and make individual and collaborative plans to meet their own needs and wants. *

Global Connections: Students understand the influence of economics on individuals and groups in the United States and the World, including Maine Native Americans by describing the work and contributions of various groups to the economics of the local community in the past and present.

Strand Personal Finance & Economics
Standard Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world.
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

Personal Finance: Students understand the nature of personal finance as well as key foundational ideas by describing situations in which personal choices are related to the use of money.

Economics: Students understand economics and the basis of the economies of the community, Maine, the United States, and various regions of the world by explaining how scarcity leads to choices about what goods and services are produced and for whom they are produced.

Global Connections: Students understand economic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities by describing economic similarities and differences within the community, Maine, and the United States.

Personal Finance: Students understand the principles and process of personal finance by describing situations in which financial institutions can be used to manage money.

Economics: Students understand economics and the basis of the economies of the community, Maine, the United States, and various regions of the world by explaining how scarcity leads to choices about how goods and services are consumed and distributed, and by making a real or simulated decision related to scarcity. *

Global Connections: Students understand economic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities by identifying economic processes, economic institutions, and economic influences related to Maine Native Americans and various cultures in the United States and the world.

Personal Finance: Students understand the principles and process of personal finance by describing situations in which choices are related to the use of financial resources and financial institutions.

Economics: Students understand the basis of the economies of the community, Maine, the United States, and various regions of the world by examining different ways producers of goods and services help satisfy the wants and needs of consumers in a market economy by using entrepreneurship, natural, human and capital resources, as well as collaborating to make a decision. *

Global Connections: Students understand economic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities, by explaining economic processes, economic institutions, and economic influences related to Maine Native Americans and various cultures in the United States and the world.

Strand Personal Finance & Economics
Standard Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world.
Early Adolescence
Grades 6-8
Performance Expectations Personal Finance: Students understand the principles and processes of personal finance by:

(F1) Explaining how scarcity influences choices and relates to the market economy.

(F2) Identifying factors that contribute to spending and savings decisions.

(D1) Using a process for making spending and savings decisions based on work, wages, income, expenses, and budgets as they relate to the study of individual financial choices. *
Economics: Students understand the principles and processes of personal economics, the influence of economics on personal life and business, and the economic systems of Maine, the United States, and various regions of the world by:

(F1) Describing the functions of financial institutions.

(F2) Describing the function and process of taxation.

(D1) Explaining how scarcity requires choices and relates to the market economy, entrepreneurship, supply and demand.
Global Connections: Students understand economic aspects of unity and diversity in Maine, the United States, and various world cultures, including Maine Native Americans, by:
(F1) Researching the pros and cons of economic processes, economic institutions, and economic influences of diverse cultures, including Maine Native Americans, various historical and recent immigrant groups in the United States, and various cultures in the world to propose a solution to an economic problem. * (D1) Describing factors in economic development, and how states, regions, and nations have worked together to promote economic unity and interdependence.

Strand Personal Finance & Economics
Standard Students draw from concepts and processes in personal finance to understand issues of money management, saving, investing, credit, and debt; students draw from concepts and processes in economics to understand issues of production, distribution, consumption in the community, Maine, the United States, and the world.
Adolescence
Grades 9-Diploma
Performance Expectations Personal Finance: Students understand the principles and process of personal finance by:

(F1) Explaining how personal finance involves the use of economics as the basis for saving, investing and managing money.

(F2) Identifying factors that impact consumer credit.

(D1) Evaluating ways credit can be used.

(D2) Evaluating different strategies for money and risk management.

Economics: Students understand the principles and processes of personal economics, the role of markets, the economic system of the United States, other economic systems in the world, and how economics serves to inform decisions in the present and future by:

(F1) Analyzing the role of financial institutions, the financial markets, and government including fiscal, monetary, and trade policies.

(F2) Identifying and explaining various economic indicators and how they represent and influence economic activity.

(D1) Analyzing economic activities and policies in relationship to freedom, efficiency, equity, security, growth, and sustainability.

(D2) Explaining and applying the concepts of specialization, economic interdependence, and comparative advantage.

(D3) Proposing a solution to a problem using the theory of supply and demand. *

Global Connections: Students understand economic aspects of unity and diversity in Maine, the United States, and the world, including Maine Native American communities, by:

(F1) Comparing a variety of economic systems and strategies of economic development.

(F1) Analyzing how resource distribution effects wealth, poverty, and other economic factors.

(D2) Analyzing multiple views on how resource distribution has affected wealth, poverty, and other economics factors and present an argument as to the role of regional, international, and global organizations that are engaged in economic development. *

Strand Geography
Standard Students draw on concepts and processes from geography to understand issues involving people, places, and environments in the community, Maine, the United States, and the world.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

Geography 1: Students understand the nature and basic ideas of geography by identifying questions about their world and explaining that geography is the study of the Earth's surface and peoples. *

Geography 2: Students understand the influence of geography on individuals and their immediate surroundings by identifying the impacts of geographic features on individuals and families.

Geography 1: Students understand the nature and basic ideas of geography by gathering information about their immediate neighborhood and community, including maps, photographs, charts and graphs, and then create visual representations of their findings. *

Geography 2: Students understand the influence of geography on communities by identifying the impacts of geographic features on communities.

Geography 1: Students understand the nature and basic ideas of geography by using basic maps and globes to identify local and distant places and locations, directions (including N, S, E, and W), and basic physical, environmental, and cultural features.

Geography 2: Students understand the influence of geography on individuals and groups in Maine, including Maine Native Americans, the United States and the world by identifying the impacts of geographic features on individuals and groups in those communities.

Grade 3 Grade 4 Grade 5
Performance Expectations

Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world by explaining that geography includes the study of Earth's physical features including climate and the distribution of plant, animal, and human life.

Geography 2: Students understand geographic aspects of unity and diversity in the community and in Maine, including Maine Native American communities by collecting, evaluating, and organizing information about the impacts of geographic features on the daily life of various cultures, including Maine Native Americans and other cultures and communities. *

Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world by communicating their findings by creating visual representations of the world, showing a basic understanding of the geographic grid, including the equator and prime meridian. *

Geography 2: Students understand geographic aspects of unity and diversity in various regions of the United States and the world by describing impacts of geographic features on the daily life of various cultures in the United States and the world.

Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world by identifying the Earth's major geographic features such as continents, oceans, major mountains, and rivers using a variety of geographic tools including digital mapping tools; and by explaining examples of changes in the Earth's physical features and their impact on communities and regions.

Geography 2: Students understand geographic aspects of unity and diversity in the community, Maine, and regions of the United States and the world, including Maine Native American communities, by identifying examples through inquiry of how geographic features unify communities and regions as well as support diversity using print and non-print sources. *

Early Adolescence
Grades 6-8
Performance Expectations Geography 1: Students understand the geography of the community, Maine, the United States, and various regions of the world and the geographic influences on life in the past, present, and future by:

(F1) Using the geographic grid and a variety of types of maps, including digital sources, to locate and access relevant geographic information that reflects multiple perspectives. *

(F2) Identifying the major regions of the Earth and their major physical features and political boundaries using a variety of geographic tools including digital tools and resources. *

(F3) Evaluating a geographic issue of physical, environmental, or cultural importance. *

(D1) Identifying consequences of geographic influences through inquiry and formulating predictions.

(D2) Describing the impact of change on the physical and cultural environment.

Geography 2: Students understand geographic aspects of unity and diversity in Maine, the United States, and various world cultures, including Maine Native Americans by:
(F1) Explaining how geographic features have impacted unity and diversity in Maine, the United States, and other nations. * (D1) Summarizing and interpreting the relationship between geographic features and cultures of Maine Native Americans, and historical and recent immigrant groups in Maine, United States, and the world. *

Adolescence
Grades 9-Diploma
Performance Expectations Geography 1: Students understand the geography of the United States and various regions of the world and the effect of geographic influences on decisions about the present and future by:

(F1) Analyzing local, national, a nd global geographic data on physical, environmental, and cultural processes that shape and change places and regions. *

(F2) Evaluating and developing a well-supported position about the impact of change on the physical and cultural environment. *

(D1) Proposing a solution to a geographic issue that reflects physical, environmental, and cultural features at local, state, national, and global levels. *

(D2) Using inquiry to predict and evaluate consequences of geographic influences.

(D3) Describing the major regions of the Earth and their major physical, environmental, and cultural features using a variety of geographic tools including digital tools and resources. *

Geography 2: Students understand geographic aspects of unity and diversity in Maine, the United States, and the world, including Maine Native American communities by:
(F1) Analyzing geographic features that have impacted unity and diversity in the United States and other nations. * (D1) Summarizing and interpreting the relationship between geographic features and cultures of Maine Native Americans, and historical and recent immigrant groups in Maine, United States, and the world. *

Strand History
Standard Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world.
Childhood
Kindergarten Grade 1 Grade 2
Performance Expectations

History 1: Students understand the nature of history by describing history as stories of the past and identifying questions related to social studies. *

History 2: Students understand the nature of history as well as the key foundation of ideas by applying terms such as "before" and "after" in sequencing events.

History 3: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans, by explaining how individuals and families share both common and unique aspects of culture, values, and beliefs through stories, traditions, religion, celebrations, or the arts.

History 1: Students understand the nature of history as well as the key foundation of ideas by identifying past, present, and future in stories, pictures, poems, songs, and video.

History 2: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans by explaining how individuals and families share both common and unique aspects of culture, values, and beliefs through stories, traditions, religion, celebrations, or the arts. Students organize findings at a developmentally appropriate manner and share gathered information using oral and visual examples *

History 3: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans, by describing traditions of Maine Native Americans and various historical and recent immigrant groups and traditions common to all.

History 1: Students understand the nature of history as well as the key foundation of ideas by following an established procedure to locate sources appropriate to reading level* and identifying a few key figures and events from personal history and the history of the community, the state, and the United States, especially those associated with historically-based traditions.

History 2: Students understand the nature of history as well as the key foundation of ideas by creating a brief historical account about family, the local community, or the nation by locating and collecting information from sources including maps, charts, graphs, artifacts, photographs*, or stories of the past.

History 3: Students understand historical aspects of the uniqueness and commonality of individuals and groups, including Maine Native Americans, by describing traditions of Maine Native Americans and various historical and recent immigrant groups and traditions common to all.

Strand History
Standard Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world.
Childhood
Grade 3 Grade 4 Grade 5
Performance Expectations

History 1: Students understand various major eras in the history of the community, Maine, and the United States by explaining that history includes the study of past human experience based on available evidence from a variety of primary and secondary sources. *

Students make real or simulated decisions related to the local community or civic organizations by applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information. *

History 2: Students understand historical aspects of unity and diversity in the community, the state, Maine Native American communities, and the United States by identifying research questions, seeking multiple perspectives from varied sources *, and describing examples in the history of the United States of diverse and shared values and traditions.

History 1: Students understand various major eras in the history of the community, Maine, and the United States by identifying major historical eras, major enduring themes, turning points, events, consequences, persons, and timeframes, in the history of the community, the state, and the United States.

Students make real or simulated decisions related to the state of Maine or civic organizations by applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information. *

Students distinguish between facts and opinions/interpretations in sources. *

History 2: Students understand historical aspects of unity and diversity in the community, the state, Maine Native American communities, and the United States by describing various cultural traditions and contributions of Maine Native Americans and various historical and recent immigrant groups in the community and the state.

History 1: Students understand various major eras in the history of the community, Maine, and the United States by tracing and explaining how the history of democratic principles is preserved in historic symbols, monuments, and traditions important in the community, Maine and the United States.

Students make real or simulated decisions related to the United States, world, or civic organizations by applying appropriate and relevant social studies knowledge and skills, including research skills, and other relevant information. *

Students communicate findings from a variety of print and non-print sources, describe plagiarism and demonstrate appropriate citation. *

History 2: Students understand historical aspects of unity and diversity in the community, the state, including Maine Native American communities, by describing various cultural traditions and contributions of Maine Native Americans and other cultural groups within the United States.

Strand History
Standard Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world.
Early Adolescence
Grades 6-8
Performance Expectations History 1: Students understand major eras, major enduring themes, and historic influences in the history of Maine, the United States, and various regions of the world by:

(F1) Explaining that history includes the study of past human experience based on available evidence from a variety of primary and secondary sources; and explaining how history can help one better understand and make informed decisions about the present and future. *

(F2) Identifying major historical eras, major enduring themes, turning points, events, consequences, and people in the history of Maine, the United States and various regions of the world. *

(F3) Tracing the history of democratic ideals and constitutional principles and their importance in the history of the United States and the world. *

(F4) Proposing and revising research questions related to a current social studies issue. *

(D1) Analyzing interpretations of historical events that are based on different perspectives and evidence from primary and secondary sources. *

(D2) Analyzing major historical eras, major enduring themes, turning points, events, consequences, and people in the history of Maine, the United States and various regions of the world. *

(D3) Explaining the history of democratic ideals and constitutional principles and their importance in the history of the United States and the world. *

(D4) Making decisions related to the classroom, school, community, civic organization, Maine, or beyond; applying appropriate and relevant social studies knowledge and skills, including research skills, and othe r relevant information. *

History 2: Students understand historical aspects of unity and diversity in the community, the state, including Maine Native American communities, and the United States by:

(F1) Explaining how both unity and diversity have played and continue to play important roles in the history of Maine and the United States.

(F2) Identifying a variety of cultures through time, including comparisons of native and immigrant groups in the United States, and eastern and western societies in the world.

(F3) Identifying major turning points and events in the history of Maine Native Americans and various historical and recent immigrant groups in Maine, the United States, and other cultures in the world.

(D1) Explaining how both unity and diversity have played and continue to play important roles in the history of the World.

(D2) Comparing a variety of cultures through time, including comparisons of native and immigrant groups in the United States, and eastern and western societies in the world.

(D3) Describing major turning points and events in the history of Maine Native Americans and various historical and recent immigrant groups in Maine, the United States, and other cultures in the world.

Strand History
Standard Students draw on concepts and processes using primary and secondary sources from history to develop historical perspective and understand issues of continuity and change in the community, Maine, the United States, and the world.
Adolescence
Grades 9-Diploma
Performance Expectations History 1: Students understand major eras, major enduring themes, and historic influences in United States and world history, including the roots of democratic philosophy, ideals, and institutions in the world by:

(F1) By explaining that history includes the study of the past based on the examination of a variety of primary and secondary sources and how history can help one better understand and make informed decisions about the present and future. *

(F2) Analyzing and critiquing major historical eras: major enduring themes, turning points, events, consequences, and people in the history of the United States and the implications for the present and future.

(F3) Tracing and critiquing the roots and evolution of democratic ideals and constitutional principles in the history of the United States using historical sources.

(F4) Developing individual and collaborative decisions/plans by considering multiple points of view, weighing pros and cons, building on the ideas of others, and sharing information in an attempt to sway the opinions of others. *

(D1) Analyzing and critiquing varying interpretations of historic people, issues, or events, and explain how evidence from primary and secondary sources is used to support and/or refute different interpretations. *

(D2) Analyzing and critiquing major historical eras: major enduring themes, turning points, events, consequences, and people in the history of the world and the implications for the present and future.

(D3) Tracing and critiquing the roots and evolution of democratic ideals and constitutional principles in the history of the world using historical sources.

(D4) Making a decision related to the classroom, school, community, civic organization, Maine, United States, or international entity by applying appropriate and relevant social studies knowledge and skills, including research skills, ethical reasoning skills, and other relevant information. *

History 2: Students understand historical aspects of unity and diversity in the United States, the world, and Native American communities by:

(F1) Identifying and critiquing issues characterized by unity and diversity in the history of the United States, and describing their effects, using primary and secondary sources. *

(F2) Identifying and analyzing major turning points and events in the history of Native Americans and various historical and recent immigrant groups in the United States, making use of primary and secondary sources. *

(D1) Identifyi ng and critiquing issues characterized by unity and diversity in the history of other nations, and describing their effects, using primary and secondary sources. *

(D2) Making use of primary and secondary sources, identifying and analyzing major turning points and events in the history of world cultures as it pertains to various historical and recent migrant groups. *

Definitions:

Strand: A body of knowledge in a content area identified by a simple title.

Standard: Enduring understandings and skills that students can apply and transfer to contexts that are new to the student.

Performance Expectation: Building blocks to the standard and measurable articulations of what the student understands and can do.

VISUAL AND PERFORMING ARTS

The visual and performing arts are an essential part of every child's education. Engagement in the visual and performing arts deepens students' overall knowledge and skills, as well as their social and emotional development. Research shows that students involved in the visual and performing arts are more successful in school, more involved in their communities, and perform better on standardized tests.

The National Standards for Arts Education includes separate standards for dance, music, theatre, and visual arts. In 1997, the National Assessment of Educational Progress (NAEP) Arts assessment was developed with separate assessments in these disciplines. These four visual and performing arts disciplines are uniquely different from each other in literacy as well as creation and performance. Standards A and B of the Visual and Performing Arts Standards of the Maine Learning Results each include four separate strands (dance, music, theatre, and visual arts). In contrast, standards C, D, and E are representative of skills and knowledge in all four disciplines of the visual and performing arts. This format best represents both the unique and common aspects of the visual and performing arts. The decision about the breadth of the programming in the visual and performing arts resides with the School Administrative Units (SAU).

These Visual and Performing Arts Standards outline a comprehensive pathway to enable every high school graduate to exhibit proficiency in one or more of the visual and performing arts disciplines. The key to success is local commitment to the visual and performing arts. Staffing, scheduling, and resources vary from SAU to SAU. Research supports the implementation of a comprehensive visual and performing arts education curriculum to meet the learning needs of all students. Connecting the visual and performing arts with other content areas of the curriculum improves teaching and learning.

This document guides SAUs in developing comprehensive and sequential standards-based visual and performing arts curricula for student learning. The use of these standards may assist in the improvement of instruction generally, and impact student learning, not only in the visual and performing arts but in other content areas, as well.

OUTLINE OF VISUAL AND PERFORMING ARTS STANDARDS AND PERFORMANCE INDICATOR LABELS

A. Disciplinary Literacy

Dance:

1. Terminology
2. Space
3. Time
4. Energy
5. Locomotor and Non-Locomotor Movement
6. Compositional Forms

Music:

1. Music Difficulty
2. Notation and Terminology
3. Listening and Describing

Theatre:

1. Terminology
2. Production

Visual Arts:

1. Artist's Purpose
2. Elements of Art and Principles of Design
3. Media, Tools, Techniques, and Processes
B. Creation, Performance, and Expression

Dance:

1. Communication
2. Sequencing
3. Solving Challenges
4. Technical Aspects

Music:

1. Style/Genre
2. Composition

Theatre:

1. Movement
2. Character
3. Improvisation

Visual Arts:

1. Media Skills
2. Composition Skills
3. Making Meaning
4. Exhibition
C. Creative Problem-Solving
1. Application of Creative Process
D. Aesthetics and Criticism
1. Aesthetics and Criticism
E. Visual and Performing Arts Connections
1. The Arts and History and World Cultures
2. The Arts and Other Disciplines
3. Goal-Setting
4. Impact of the Arts on Lifestyle and Career
5. Interpersonal Skills
A. Disciplinary Literacy

Dance:

Students show literacy in the discipline through understanding and demonstrating concepts, skills, terminology, and processes.

A1 Terminology

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify space, time, and energy concepts.

a. Identify elements of space: high/low, forward/backward, near/far , and personal space, and wide/narrow and stretched/curled/twisted shape(s).

b. Identify elements of time: steady and fast/slow beat.

c. Identify elements of energy: hard/soft, light/strong, and resting/moving.

Students identify and describe the dance concepts of space, time, energy, and composition form.

a. Identify and describe elements of space: straight/curved/ zig-zag/ spiral pathways, and positive/negative space.

b. Identify and describe elements of time: steady beat and tempo changes.

c. Identify and describe sustained/abrupt energy.

d. Identify and describe patterns of composition form.

Students identify and describe the dance terms of time, composition, and style/tradition.

a. Identify and describe time: complex meters.

b. Identify and describe composition : phrasing.

c. Identify and describestyle/tradition: specific dances students learn from different cultures and/or their own.

Students apply accumulated knowledge of dance composition, dynamics, and terminology to describe and perform dances with greater complexity and variation

A2 Space

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students demonstrate space concepts including high/low, forward/backward, near/far, and personal space and wide/narrow, and stretched/curled/twisted shape(s). Students use space concepts to solve movement challenges including straight/curved/zig-zag/spiral pathways and positive/negative space. Students apply space concepts in a repeatable movement phrase. Students apply space concepts in an original repeatable, choreographed piece.

A3 Time

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students replicate tempo change using body movement. Students identify and replicate a steady beat in varied tempos using body movement. Students move to complex rhythm patterns and syncopation. Students identify and move to rhythms of various genres.

A4 Energy

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students recognize and demonstrate hard/soft, light/strong, and resting/moving movements to show differences in energy qualities. Students recognize and demonstrate sustained and abrupt movements to show differences in energy qualities. Students explain and incorporate bound/free, tension/relaxation, indirect/direct movements to show differences in energy qualities. Students incorporate energy qualities into a choreographed piece as a solo, small group, or ensemble.

A5 Locomotor and Non-Locomotor Movement

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify and demonstrate locomotor and non-locomotor/axial skills.

a. Identify the difference between a locomotor and non-locomotor/axial skill.

b. Demonstrate locomotor patterns using change in direction, level, and pathway.

c. Demonstrate non-locomotor/axial skills.

Students demonstrate expressive combinations of locomotor and non-locomotor/axial skills.

a. Demonstrate combinations of locomotor patterns, with changes in direction, level, and path.

b. Demonstrate a combination of locomotor and non-locomotor/

axial skills into a pattern that may change direction, level, energy, or pathway.

c. Demonstrate combinations of non-locomotor/axial skills.

Students combine and demonstrate the technical skills of skeletal alignment, strength, agility, and coordination. Students integrate and demonstrate the technical skills of skeletal alignment, body-part isolation, strength, flexibility, agility, and coordination.

A6 Compositional Forms

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students replicate, with a partner, the dance composition forms of copying, mirroring, leading, and following. Students replicate a dance movement. Students replicate a dance phrase. Students replicate dance composition forms and themes, including narrative, canon, call and response, ab, aba, rondo, retrograde, palindrome, and theme and variation.
A. Disciplinary Literacy - Music: Students show literacy in the discipline by understanding and demonstrating concepts, skills, terminology, and processes.

A1 Music Difficulty

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students accurately perform a short musical selection, both instrumentally and vocally, while modeling proper posture and technique, alone or with others. Students accurately perform music in easy keys, meters, and rhythms with limited ranges, both instrumentally and vocally, while modeling proper posture and technique, alone or with others. Students accurately perform music that includes changes of tempo, key, and meter in modest ranges with moderate technical demands, modeling proper posture and technique, alone or with others. Students perform music that requires well-developed technical skills, attention to phrasing and interpretation, and the ability to perform various meters and rhythms in a variety of keys while modeling proper posture and technique, alone or with others.

A2 Notation and Terminology

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify and read musical notation, symbols, and terminology of dynamics.

a. Read whole and half notes in 4/4 meter signatures.

b. Identify symbols and traditional terms referring to dynamics.

Students identify and read musical notation, symbols, and terminology of dynamics.

a. Read whole, half, dotted half, quarter, and eighth notes and rests in 2/4, 3/4, and 4/4 meter signatures.

b. Identify symbols and traditional terms referring to dynamics, tempo, and articulation.

Students apply accumulated knowledge of musical notation, symbols, and terminology to a music performance.

a. Read whole, half, quarter, eighth, sixteenth, and dotted notes and rests in 2/4, 3/4, 4/4, 6/8, and 3/8 meter signatures.

b. Read simple melodies in both the treble and bass clefs.

c. Apply notation symbols for pitch, rhythm, dynamics, tempo, articulation, and expression.

Students apply accumulated knowledge of musical notation, symbols, and terminology to perform music with greater complexity and variation including sudden dynamic contrasts.

A3 Listening and Describing

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students listen to and identify elements of music including meter and simple form and attributes including loud/soft, fast/slow, high/low, and long/short beat and steady/strong beat. Students listen to and describe simple examples of the elements of music including pitch, rhythm, tempo, dynamics, form, timbre, meter, phrases, style, and major/minor harmony. Students listen to and compare elements of music, including pitch, rhythm, tempo, dynamics, form, timbre, texture, harmony, style, and compound meter. Students listen to, analyze, and evaluate music using their understanding of pitch, rhythm, tempo, dynamics, form, timbre, texture, harmony, style, and compound meter.
A. Disciplinary Literacy - Theatre : Students show literacy in the art discipline by understanding and demonstrating concepts, skills, terminology, and processes.

A1 Terminology

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify the "who, what, where, when, and why" of a dramatic performance they have participated in or seen. Students describe theatre terms including stage directions, rehearsal, plot, gesture, director, motivation, conflict, improvisation, and b locking. Students identify and explain theatre terms and concepts including stage business, ad-libbing, conflict, action/reaction, focus, and stage directions. Students identify and define the parts of the stage, and identify and describe the crisis, resolution, and theme of the play.

A2 Production

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students select or make props, costumes, set pieces, and/or puppets, and practice using them appropriately. Students select and make props, costumes, set pieces, and/or puppets, and present a rehearsed scene. Students describe and participate in a performance from pre-show through strike.

a. Identify and explain the roles of production staff.

b. Design and select props, costumes and stage pieces, and use them appropriately and safely.

c. Build scenic elements or props to fit production design.

d. Experiment with lighting, sound, and costume in scene development.

e. Direct or stage-manage a scene.

f. Describe basic technical needs for a theatre production, including lights, sound, props, makeup, and costumes.

Students fulfill at least one technical role from pre-show through strike.

a. Apply technical knowledge and skills to collaboratively and safely create and use theatre props, costumes, makeup, and stage pieces.

b. Direct or stage-manage a scene or full production.

c. Develop specific light and sound cues and use them in scene development.

d. Participate in the audition process.

A. Disciplinary Literacy - Visual Arts : Students show literacy in the art discipline by understanding and demonstrating concepts, skills, terminology, and processes.

A1 Artist's Purpose

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students recognize a variety of purposes for making art, including telling a story, communicating emotion, or beautifying functional objects. Students explain purposes for making art in different times and places, and the relationship to cultural traditions, personal expression, and communication of beliefs. Students explain and compare different purposes of artists and their artwork, in the context of time and place. Students research and explain how art and artists reflect and influence culture and periods of time.

A2 Elements of Art and Principles of Design

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify features of composition.

a. Identify Elements of Art: color, form, line, shape, space, texture, and value.

b. Identify Principles of Design including pattern and balance.

Students describe features of composition.

a. Describe Elements of Art: color, form, line, shape, space, texture, and value.

b. Describe Principles of Design including balance, contrast, emphasis, movement, and pattern.

Students compare features of composition both within an art work and among art works.

a. Compare Elements of Art: color, form, line, shape,space, texture, and value.

b. Compare Principles of Design including balance, contrast, emphasis, movement, pattern, rhythm, and unity.

Students evaluate all the features of composition.

a. Evaluate Elements of Art: color, form, line, shape, space, texture, and value.

b. Evaluate Principles of Design including balance, contrast, emphasis, movement, pattern, rhythm, and unity.

A3 Media, Tools, Techniques, and Processes

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students name art media and associated tools, for multiple art forms and genres. Students describe a variety of media and associated tools, techniques, and processes, for multiple art forms and genres. Students explain the effects of media and their associated tools, techniques, and processes, using elements, principles and expressive qualities in art forms and genres. Students compare the effects of media and their associated tools, techniques, and processes, using elements, principles, and expressive qualities in art forms and genres.
B. Creation, Performance, and Expression - Dance: Students create, perform, and express ideas through the art discipline.

B1 Communication

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
No performance indicator.

Although no performance indicators are stated students are expected to have instructional experiences that help them to express themselves through movement

Students use movement to express a basic idea and share it with their peers. Students use movement to express and communicate a story, a piece of music, an artwork, or an emotion. Students create an original piece of choreography using the elements of dance.

a. Improvise new movements.

b. Manipulate learned movements.

B2 Sequencing

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students develop a short dance sequence with a beginning, middle, and end. Students develop a dance phrase with a beginning, middle, and end, accurately repeating and varying it. Students create and develop dance sequences.

a. Create and develop dance sequences based on personal ideas or concepts from other sources.

b. Reproduce a more complex or pre-existing choreographed movement sequence as a solo or in a small group.

Students create both solo and ensemble dance works accurately producing an original or pre-existing complex movement sequence with rhythmic acuity.

B3 Solving Challenges

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students solve a variety of movement challenges alone or in a group. Students solve movement challenges involving one or more movement concepts alone or with a partner. Students use improvisation to discover and invent movement sequences and solve movement challenges with one or more partners. Students solve increasingly complex movement challenges involving several dance concepts with one or more partners.

B4 Technical Aspects

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify possible props or costumes to enhance a short dance phrase. Students select props or costumes to enhance a dance phrase and explain the choice. Students identify and select light, costume, or sound changes to enhance a dance phrase. Students include and explain costume, light, and sound changes in a piece of choreography.
B. Creation, Performance, and Expression - Music: Students create, perform, and express through the art discipline.

B1 Style/Genre

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students create or perform short musical selections of various styles and genres accurately applying selected knowledge and skills of: proper posture and technique; notation; symbols; and terminology of dynamics. Students create or perform music of various styles and genres in easy keys, meters, and rhythms with limited ranges accurately applying the knowledge and skills of: proper posture and technique; notation; symbols; and terminology of dynamics. Students perform music of various styles and genres that includes changes of tempo, key, and meter in modest ranges with moderate technical demands accurately applying the accumulated knowledge and skills of: proper posture and technique; musical notation; symbols; and terminology. Students perform music of various styles and genres that requires well-developed technical skills, attention to phrasing and interpretation and various meters and rhythms in a variety of keys, accurately applying the accumulated knowledge and skills of: proper posture and technique; musical notation; symbols; and terminology.

B2 Composition

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students use knowledge and skills of standard and non-standard notation, symbols, and terminology of dynamics. Students create their own compositions by applying the knowledge and skills of notation, symbols, and terminology of dynamics. Students compare musical ideas expressed in their own compositions or the compositions of others. Students analyze and evaluate musical ideas expressed in their own compositions or the compositions of others.
B. Creation, Performance, and Expression - Theatre: Students create, perform, and express through the art discipline.

B1 Movement

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students participate in skits, puppet shows, theatre games, and/or show and tell using movement skills. Students demonstrate blocking in a play by carrying out their assigned stage movements. Students apply gesture, movement, and stage business in the portrayal of a role. Students refine gesture and stage business in the portrayal of a role.

B2 Character

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students demonstrate a character by participating in skits, puppet shows, and/or theatre games. Students demonstrate the ideas, moods, and/or feelings of a character and demonstrate proper posture and breathing techniques to project voice through the use of script and improvisation based on stories. Students demonstrate development of a character's attitude and point of view by adjusting voice timing and tone/level and using nonverbal techniques. Students demonstrate development of a character's attitude and point of view using voice timing, voice tone/level, and physicality to communicate ideas, moods, intentions, and/or feelings.

B3 Improvisation

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students improvise through theatre games by using plot, setting, and characters. Students improvise through theatre games by using voice, motivation, and body part isolations. Students improvise through theatre games by using blocking, relationships, props, and movement. Students improvise through theatre games or productions to address unforeseen circumstances.
B. Creation, Performance, and Expression - Visual Arts: Students create, express, and communicate through the art discipline.

B1 Media Skills

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students use basic media, tools and techniques to create original art works. Students use a variety of media, tools, techniques, and processes to create original art works. Students choose suitable media, tools, techniques, and processes to create original art works. Students choose multiple suitable media, tools, techniques, and processes to create a variety of original art works.

B2 Composition Skills

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students use Elements Of Art and Principles Of Design to create original art works. Students use Elements of Art and Principles of Design to create original art works including paintings, three-dimensional objects, drawings from imagination and real life, and a variety of other media and visual art forms. Students use Elements of Art and Principles of Design to create original art works that demonstrate different styles in paintings, three-dimensional objects, drawings from imagination and real life, and a variety of other media and visual art forms. Students use Elements of Art and Principles of Design to create original art works that demonstrate development of personal style in a variety of media and visual art forms.

B3 Making Meaning

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students create art works that communicate ideas and feelings and demonstrate skill in the use of media, tools, and techniques. Students create art works that communicate ideas, feelings, and meanings and demonstrate skill in the use of media, tools, techniques, and processes. Students create art works that communicate an individual point of view.

a. Demonstrate skills in the use of media, tools, techniques, and processes.

b. Demonstrate knowledge of visual art concepts.

c. Communicate a variety of ideas, feelings, and meanings.

Students create a body of original art work.

a. Demonstrate sophisticated use of media, tools, techniques, and processes.

b. Demonstrate knowledge of visual art concepts.

c. Communicate a variety of ideas, feelings, and meanings.

B4 Exhibition

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
No performance indicator.

Although no performance indicators are stated, students may participate in the preparation of art for display and all students are expected to have instructional experiences that help them to understand how art is prepared for display and why different choices related to preparation may be made.

Students help with the selection and preparation of art works for display in the classroom, school, or other community location. Students select and prepare art works for display in the classroom, school, or other community location, and articulate an artistic justification for their selection. Students select, prepare, and help with exhibiting their works in the classroom, school, or other community location, and articulate an artistic justification for their selection.
C. Creative Problem Solving: Students approach artistic problem-solving using multiple solutions and the creative process.

C1 Application of Creative Process

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify and demonstrate creative problem-solving skills.

a. Improvise to solve problems in the performing arts.

b. Imagine and share possible solutions to apply to challenges in creating art.

Students describe and apply steps of creative problem-solving.

a. Identify problem.

b. Define problem.

c. Generate a variety of solutions.

d. Implement solution(s).

e. Evaluate solution(s).

Students describe and apply creative-thinking skills that are part of the creative problem-solving process.

a. Fluency

b. Flexibility

c. Elaboration

d. Originality

e. Analysis

Students apply and analyze creative problem-solving and creative-thinking skills to improve or vary their own work and/or the work of others.
D. Aesthetics and Criticism: Students describe analyze, interpret, and evaluate art (dance, music, theatre, and visual arts).

D1 Aesthetics and Criticism

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students observe, listen to, describe and ask questions about art forms.

a. Describe the art form by applying grade span appropriate arts concepts, terminology, skills, and processes as referenced in Standard A: Disciplinary Literacy.

Students describe and compare art forms.

a. Describe and compare art forms by applying grade span appropriate arts concepts, terminology, skills, and processes as referenced in Standard A: Disciplinary Literacy.

Students compare and analyze art forms.

a. Compare and analyze art forms by applying grade span appropriate concepts, vocabulary, skills, and processes as referenced in Standard A: Disciplinary Literacy.

Students analyze and evaluate art forms.

a. Describe, analyze, interpret, and evaluate art forms by applying grade span appropriate arts concepts, vocabulary, skills, and processes as referenced in Standard A: Disciplinary Literacy.

b. Ask questions about the art form to further understand how the artist

created/performed the work of art.

c. Recognize a variety of purposes for making/performing art works, including telling a story and communicating emotions and ideas.

b. Ask questions about an art form to further understand the concepts, skills, and processes used to create/perform the work of art.

c. Explain purposes for making art in different times and places, including cultural traditions, personal expression, and communication of beliefs.

b. Compare the quality and effectiveness of art works using multiple criteria from observations, print and/or non-print resources

.

c. Compare the effectiveness of selected media, techniques, and processes in communicating ideas.

d. Explain and compare different purposes of artists and art work in the context of time and place.

b. Analyze and evaluate varied interpretations of works of art using evidence from observations and a variety of print and/or non-print sources

.

c. Demonstrate an understanding of the difference between a personal opinion and an informed judgment.

d. Research and explain how art and artists reflect and shape their time and culture.

E. Visual and Performing Arts Connections: Students understand the relationship among the arts, history and world culture; and they make connections among the arts and to other disciplines, to goal-setting, and to interpersonal interaction.

E1 The Arts and History and World Cultures

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify family or community symbols and celebrations in the visual/performing arts from different world cultures. Students explain that the visual/performing arts help people understand history and/or world cultures. Students compare products of the visual/performing arts to understand history and/or world cultures. Students analyze the characteristics and purposes of products of the visual/performing arts to understand history and/or world cultures.

E2 The Arts and Other Disciplines

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify connections between and among the arts and other disciplines. Students describe characteristics shared between and among the arts and other disciplines. Students explain skills and concepts that are similar across disciplines. Students analyze skills and concepts that are similar across disciplines.

E3 Goal-Setting

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify choices that lead to success in the arts. Students identify and demonstrate choices that will lead to success in the arts including time management, interpersonal interactions, skill development, and goal-setting. Students set goals related to time management, interpersonal interactions, or skill development that will lead to success in the arts. Students make short-term and long-term goals based on rigorous criteria and related to time management, interpersonal interactions, or skill development that will lead to success in the arts.

E4 Impact of the Arts on Lifestyle and Career

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify the arts in life experiences.

a. Identify the activities and careers of a visual or performing artist.

b. Describe common arts activities.

c. Describe the way the arts can make people feel.

Students describe the contribution of the arts on lifestyle and career choices.

a. Identify the various roles of, and requirements to become, artists.

b. Describe the benefit of participation in the arts on a healthy lifestyle including the use of leisure time.

Students explain the impact of artistic and career choices on self, others, and the natural and man-made environment. Students explain how their knowledge of the arts relates to school-to-school and school-to-work transitions and other career and life decisions including the recognition that the arts are a means of renewal and recreation.

E5 Interpersonal Skills

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify positive interpersonal skills that impact the quality of their art and participation in the arts.

a. Getting along with others

b. Respecting differences

c. Working as a team/ensemble

d. Managing conflict

e. Accepting/giving/using constructive feedback

f. Accepting responsibility for personal behavior

g. Demonstrating ethical behavior

h. Following established rules/etiquette for observing/listening to art

i. Demonstrating safe behavior

Students identify and demonstrate the positive interpersonal skills necessary to get along with others and participate in the arts.

a. Getting along with others

b. Respecting differences

c. Working as a team/ensemble

d. Managing conflict

e. Accepting/giving/using constructive feedback

f. Accepting responsibility for personal behavior

g. Demonstrating ethical behavior

h. Following established rules/etiquette for observing/listening to art

i. Demonstrating safe behavior

Students demonstrate positive interpersonal skills and analyze how interpersonal skills affect participation in the arts.

a. Getting along with others

b. Respecting differences

c. Working as a team/ensemble

d. Managing conflict

e. Accepting/giving/using constructive feedback

f. Accepting responsibility for personal behavior

g. Demonstrating ethical behavior

h. Following established rules/etiquette for observing/listening to art

i. Demonstrating safe behavior

Students demonstrate positive interpersonal skills and reflect on the impact of interpersonal skills on personal success in the arts.

a. Getting along with others

b. Respecting differences

c. Working as a team/ensemble

d. Managing conflict

e. Accepting/giving/using constructive feedback

f. Accepting responsibility for personal behavior.

g. Demonstrating ethical behavior

h. Following established rules/etiquette for observing/listening to art

i. Demonstrating safe behavior

WORLD LANGUAGES

Language and communication are at the heart of the human experience whether communication occurs face-to-face, in writing, or through the arts and media. Graduates of Maine's publicly supported schools must have the linguistic and cultural skills to communicate successfully in a pluralistic society at home and abroad. The need to understand and communicate with other peoples of the world is more urgent today because of the forces of globalization. All students are expected to develop the level of proficiency defined in the standards and performance indicators at the 9-Diploma grade span in at least one language other than English. To succeed, all students must study language and culture in an integrated fashion beginning in the early elementary grades and extending through their school experience. A PreK-Diploma structure in all schools is foundational to the State vision for world languages.

The major organizing principle in today's world language classrooms is communication. While knowledge of vocabulary and the linguistic system remain essential tools for communication, learning to use a second language in meaningful and appropriate ways is the ultimate goal of world language instruction. In any mode of communication, there are particular links between language usage and knowledge of the associated culture(s). In the study of classical languages such as Latin or ancient Greek, proficiency will emphasize the ability to understand the written language over oral communication and will recognize the linguistic and historical importance of the language and the people who spoke it.

Differentiation and Commonality Among World Languages - The World Languages Standards outline both common and unique descriptors for modern and classical languages. Distinctions between modern and classical languages are identified only where necessary to acknowledge significant differences in communication modes and resources. References in the performance indicators and descriptors of modern languages are inclusive of American Sign Language (ASL) except where otherwise noted.

Multiple Entry Points - Throughout the World Languages Standards, the sequence of performance indicators is based on a PreK-Diploma course of study of mainly cognate languages (languages that contain words from two languages that are similar in spelling and meaning or sound and meaning). Some students may elect to participate in the study of more than one world language. In these instances, it is important to recognize that the PreK-Diploma grade span represents a continuum of learning. Students who begin a language later in the Pre-K-Diploma sequence of study and students who study a non-cognate language may not be able to reach the highest level performance indicators (9-Diploma) without additional language experiences - instructional or immersion - or a heritage language background. Students beginning additional world languages at grade 9 or above should not be held accountable for performance indicators at this level. Rather, curriculum, instruction, and assessment will need to be aligned to the grade span expectations that reflect the students' level of proficiency and advance from that point to the standards and performance indicators defined in subsequent grade spans.

Instruction and Support in the Target Language - All performance indicators for modern languages, with the exception of one (A4), are to be accomplished in the target language (the non-English language being studied by the student). Students engaged in a sequential PreK-Diploma modern language program are expected to develop the knowledge and skills necessary to communicate basic understandings for all performance indicators using target language at a level appropriate to the grade span. Proficiency in the study of classical languages, such as Latin or ancient Greek, emphasizes the ability to understand written language over oral communication although oral communication remains a component. Accordingly, performance indicators A2, A4, B1, B2, B3, C1, C2, and D1 may be accomplished in the target language or English.

Level of Discourse - Standard A outlines grade span proficiencies at grades PreK-2, 3-5, 6-8, and 9-Diploma for communication skills. The document assumes that as students learn the knowledge and skills outlined in Standards B, C, and D, they will do so by developing and using communication skills learned in Standard A, as appropriate to their grade span. By the end of the grade span, students should be able to demonstrate their proficiency of the standards and performance indicators related to Standards B, C, and D using communication skills learned in Standard A, as appropriate for the end of that grade span.

OUTLINE OF WORLD LANGUAGES STANDARDS AND PERFORMANCE INDICATOR LABELS

A. Communication
1. Interpersonal
2. Interpretive
3. Presentational
4. Language Comparisons
B. Cultures
1. Practices and Perspectives
2. Products and Perspectives
3. Comparisons with Own Culture
C. Connections
1. Knowledge of Other Learning Results Content Areas
2. Distinctive Viewpoints
D. Communities
1. Communities
A. Communication: Students communicate in the target language. A1 Interpersonal

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students engage in simple interactions to provide and obtain information using single words or learned phrases.

Modern and Classical

a. Use culturally-appropriate and age-appropriate courtesy expressions.

b. Participate in brief guided exchanges related to likes and dislikes.

c. Make age-appropriate introductions of classmates, family members, and friends.

d. Ask and answer simple learned questions.

Students engage in simple conversations to provide and obtain information using learned phrases and simple sentences.

Modern and Classical

a. Recognize and use appropriate forms of address and courtesy expressions in a variety of situations.

b. Ask and answer simple questions regarding familiar activities.

c. Give and respond to simple oral/signed directions and commands and make routine requests in the classroom.

Modern only

d. Participate in brief guided conversations related to needs, interests, likes, dislikes, and states of being.

e. Express basic agreement and disagreement.

Students engage in simple conversations to provide and obtain information and to express feelings and emotions by creating simple sentences and/or strings of sentences. Students of modern languages use pronunciation and intonation patterns or use appropriate non-manual markers (ASL), which are comprehensible to speakers accustomed to interacting with language learners.

Modern and Classical

a. Ask and answer a variety of questions on familiar topics, orally or in sign language, and in writing.

Modern only

b. Participate in conversations on a variety of everyday topics to meet personal needs.

c. Give and respond to directions and commands, orally or in sign language, and in writing.

Classical only

d. Exchange information in writing about familiar topics.

Students express their own thoughts and opinions about familiar topics and elicit the thoughts and opinions of others by using strings of sentences and/or short paragraphs. Students of modern languages use pronunciation and intonation patterns or use appropriate non-manual markers (ASL), which would be comprehensible to a native speaker accustomed to interacting with language learners.

Modern only

a. Interact in a variety of social situations including formal and informal personal exchanges and/or phone inquiries.

b. Provide and exchange detailed information on familiar topics, orally or in sign language, and in writing.

c. Describe and explain states of being, orally or in sign language, and in writing.

d. Express agreement and disagreement, orally or in sign language, and in writing, supporting opinions with simple reasoning.

Classical only

e. Exchange information in writing on identified topics.

A2 Interpretive

For classical languages only, the 6-8 and 9-Diploma indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students comprehend and respond to simple spoken/signed language in a classroom setting.

Modern and Classical

a. Respond to simple oral/signed directions, commands, and routine requests in the classroom.

b. Identify people and objects based on oral/signed descriptions.

Students comprehend and respond to simple spoken/signed and written language in familiar contexts.

Modern only

a. Comprehend isolated

words, phrases, and simple sentences in familiar print materials.

b. Respond to simple written directions.

c. Respond to oral/signed directions, commands, and routine requests.

d. Identify people and objects based on oral/signed and written descriptions.

Classical only

e. Identify people and objects based on written descriptions.

f. Demonstrate comprehension of simple texts by identifying people and objects.

Students comprehend brief conversations, narratives, and recorded material in familiar contexts.

Modern only

a. Identify main ideas, topics, and details from simple oral/signed and written texts.

Classical only

b. Identify main ideas, topics, and details from simple written texts.

Students comprehend conversations, narratives, and recorded material in familiar contexts that are longer and/or more complex than those in the 6-8 grade span.

Modern and Classical

a. Identify main ideas, topics, and specific information in a variety of authentic written/signed materials.

Modern only

b. Identify main ideas, topics, and specific information in authentic films.

c. Identify main ideas, topics, and specific information in a variety of authentic oral/signed materials.

Classical only

d. Interpret the author's use of literary devices evident in prose and poetry.

A3 Presentational

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students use memorized words or phrases and visuals in short oral/signed presentations.

Modern and Classical a. Provide simple descriptions of people, places, and objects.

Students use phrases and simple sentences in rehearsed oral /signed and written presentations on familiar topics.

Modern and Classical

a. Write/sign familiar words and phrases, and short messages, descriptions, or simple poems.

Modern only

b. Provide simple oral/signed and written descriptions of people, places, and objects.

c. Present simple short plays/skits and/or simple short written texts.

Classical only

d. Read aloud from an adapted text.

Students use simple sentences and strings of simple sentences to produce short oral/signed and written presentations based on familiar topics and including a level of accuracy in form and pronunciation that could be understood by speakers accustomed to interacting with language learners.

Modern only

a. Write/sign messages using a prescribed, culturally-appropriate format.

b. Produce and present simple creative works orally or in sign language, and in writing.

c. Convey personal preferences or information pertaining to everyday life orally or in sign language, and in writing.

Classical only

d. Create written products based on a given topic.

e. Read aloud from adapted texts with appropriate intonation and pronunciation.

Students express their own thoughts to describe and narrate in oral/signed and written presentations using strings of sentences and/or short paragraphs and with sufficient accuracy in form and pronunciation that couldbe understood by native speakers accustomed to interacting with language learners.

Modern and Classical

a. Read authentic passages aloud with appropriate pronunciation, phrasing, and intonation.

Modern only

b. Relate a story about a personal experience or event orally or in sign language.

c. Paraphrase and/or summarize texts orally or in sign language, and in writing using a presentational format.

d. Write/sign brief narrative compositions and expository/informational compositions.

e. Give oral/signed presentations on familiar subjects related to a culture(s) in which the target language is spoken.

Classical only

f. Paraphrase and/or summarize texts orally or in writing in a presentational format using the target language or English.

A4 Language Comparisons

For both modern and classical languages, indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
No performance indicator.

Although no performance indicators are stated, students are expected to have instructional experiences related to similarities and differences between the target language and English.

Students recognize a variety of similarities and differences between the target language and English.

Modern and Classical

a. Recognize word borrowings and cognates among languages.

b. Recognize differences in the writing systems among languages.*

c. Recognize some idiomatic expressions of the target language.

Students compare the target language with English in order to better understand language systems.

Modern and Classical

a. Compare basic grammatical structures and syntax between languages.

b. Compare idiomatic expressions between languages.

c. Compare pronunciation systems between languages. *

d. Recognize that there are regional and/or historical variations in spoken/signed language.

e. Explain connections between languages through the identification of cognates.

Students use their understanding of the nature of language to enhance their communication in the target language.

Modern and Classical

a. Compare a variety of grammatical structures and syntax between languages.

b. Identify examples of vocabulary, in both languages, that do not translate directly from one language to another.

c. Use idiomatic expressions and/or proverbs in the target language.

d. Identify examples of vocabulary (in English and the target language) that convey different meanings in different contexts.

* These descriptors are not appropriate for instruction in ASL.

B. Cultures: Students demonstrate an understanding of a culture(s) in which the target language is spoken.

B1 Practices and Perspectives

For classical languages only, indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify and imitate basic culturally-appropriate practices of a culture(s) in which the target language is spoken.

Modern and Classical

a. Use culturally-appropriate courtesy expressions and demonstrate greeting and leave -taking.

b. Recognize cultural differences including dress, mealtime practices, gestures, and/or celebrations.

Students identify and demonstrate basic culturally-appropriate practices of daily life within a culture(s) in which the target language is spoken.

Modern and Classical

a. Use culturally-appropriate polite requests and courtesy expressions, and demonstrate greeting and leave -taking behaviors in a variety of age-appropriate social situations.

b. Recognize age-appropriate similarities and differences related to practices of a culture(s) in which the target language is spoken.

Students describe practices of a culture(s) and perspectives of a culture(s) in which the target language is spoken.

Modern and Classical

a. Describe examples of common beliefs of a culture(s) in which the target language is spoken.

b. Describe common attitudes of a culture(s) in which the target language is spoken.

c. Describe common similarities and differences related to practices of a culture(s) in which the target language is spoken.

Students identify and explain how perspectives of a culture(s) are related to cultural practices of a culture(s) in which the target language is spoken.

Modern and Classical

a. Identify and explain the reason behind significant practices of a culture(s) in which the target language is spoken.

b. Describe stereotypes associated with perspectives of a culture(s) in which the target language is spoken.

c. Identify differences in cultural practices among peoples that speak the same language.

B2 Products and Perspectives

For classical languages only, indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
No performance indicator.

Although no performance indicators are stated, students are expected to have instructional experiences related to products of a culture(s) in which the target language is spoken.

Students identify common products of a culture(s) in which the target language is spoken. Students identify and explain the significance of objects used in daily life, works of art, or historical artifacts that reflect the perspectives of a culture(s) in which the target language is spoken. Students explain how political structures, historical artifacts, literature, and/or visual and performing arts reflect the perspectives of a culture(s) in which the target language is spoken.

B3 Comparisons with Own Culture

For classical languages only, indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
No performance indicator.

Although no performance indicators are stated, students are expected to have instructional experiences related to comparison of the target culture with the culture in which the student lives.

Students compare some common culturally-appropriate products and practices of daily life of a culture(s) in which the target language is spoken to the culture in which the student lives.

Modern and Classical

a. Compare daily acti vities of their own lives to those of individuals in a culture(s) in which the target language is spoken.

b. Compare foods, celebrations, dress, and/or dwellings of a culture(s) in which the target language is spoken with those of the culture in which the student lives.

Students recognize and compare perspectives related to products and practices of a culture(s) in which the target language is spoken to the cultural perspectives of the culture in which the student lives.

Modern and Classical

a. Compare verbal and nonverbal communication in a culture(s) in which the target language is spoken to communication in the culture in which the student lives.

b. Recognize contributions of a culture(s) in which the target language is spoken to life in the United States including foods, celebrations, dress, and/or architecture.

Students explain how products, practices, and perspectives of a culture(s) in which the target language is spoken contribute to the culture in which the student lives.

Modern and Classical

a. Identify and compare influential figures from the two cultures.

b. Explain the reasons for a variety of similarities and differences between the culture in which the student lives and the culture(s) in which the target language is spoken.

Modern only

c. Use the target language in a manner that would be considered appropriate by native speakers and explain what makes it appropriate communication.

C. Connections: Students expand their knowledge by connecting their study of a world language(s) with other content areas.

C1 Knowledge of Other Learning Results Content Areas

For classical languages only, indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students identify basic language connections to other Learning Results content areas.

Modern and Classical

a. Identify ways of counting.

b. Identify common ways of greeting people.

Students identify connections between other Learning Results content areas and the target language and associated culture(s).

Modern and Classical

a. Identify common expressions and traditions.

b. Identify examples of the visual/performing arts.

c. Identify products important to the livelihood of the people.

d. Identify the earth's major geographical features.

Students apply information acquired in other Learning Results content areas to further their knowledge and skills in the target language.

Modern and Classical

a. Use the wr iting process learned in English Language Arts when writing for the target language class. *

b. Apply research skills to further knowledge in the target language.

c. Apply knowledge from other Learning Results content areas including literature, social studies, science and technology, and/or the visual and performing arts to tasks in the world language classroom.

Students use the target language to enhance their knowledge of other Learning Results content areas.

Modern and Classical

a. Provide examples of grammatical knowledge acquired in the target language that are used to achieve a better understanding of grammatical structures in English.

b. Provide examples of information gathered through target language resources that are applied in other Learning Results content areas.

* These descriptors are not appropriate for instruction in ASL.

C2 Distinctive Viewpoints

For classical languages only, indicators may be accomplished in the target language or English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
No performance indicator.

Although no performance indicators are stated, students are expected to have instructional experiences related to a variety of print and non-print materials created in a language other than English.

Students recognize some distinctive viewpoints available only through sources from the target language.

Modern and Classical

a. Identify examples of simple narrative selections from a culture(s) in which the target language is spoken.

Classical only

b. Identify information about the Roman/Greek world by reading passages with culturally authentic settings.

Students locate authentic resources, available only through sources in the target language, and identify ideas about a culture(s) in which the target language is spoken.

Modern and Classical

a. Locate media or other authentic sources from the target language and a culture(s) in which the target language is spoken and identify a perspective and/or practice of a culture(s) different from the students' own viewpoints and/or beha viors.

Students locate authentic resources and describe ideas about the target language and associated culture(s) that are available only through sources in the target language.

Modern and Classical

a. Interpret short prose, poetry, or plays in the target language that reflect the culture(s) in which the target language is spoken and make connections to the viewpoints of the culture associated with the target language(s).

b. Locate selected magazines, newspapers, authentic entertainment media and electronic media in the target language and use these media as the basis for describing the viewpoints of the culture associated with the target language(s).

c. Locate selected magazines, newspapers, authentic entertainment media and electronic media in the target language and describe viewpoints of a culture(s) in which the target language is spoken.

D. Communities: Students encounter and use the target language both in and beyond the classroom for personal enjoyment and lifelong learning.

D1 Communities

For classical languages only, performance indicators may be accomplished in the target language or in English.

Performance Indicators & Descriptors
Pre-K-2 3-5 6-8 9-Diploma
Students include family, friends, or peers in activities using the target language. Students demonstrate understanding and use of the target language and their knowledge of a culture(s) in which the language is spoken through community involvement.

Modern and Classical

a. Demonstrate use of oral/signed and/or written forms of the target language with family, friends, or peers.

b. Participate in activities using the target language which can benefit the school or broader community.

c. Ask questions and share knowledge about aspects of a culture(s) in which the target language is spoken to demonstrate an interest in the target language and an associated culture(s).

d. Access online resources or resources available in the community to understand aspects of a culture(s) in which the target language is spoken.

Students demonstrate an understanding and use their knowledge of the target language to communicate with target language speakers, obtain information on familiar topics, and gain understanding of another culture(s).

Modern and Classical

a. Participate in and summarize

school/community events related to the target language or associated culture(s).

b. Identify community and online resources that can be used to gain information about the target language or associated culture(s).

c. Communicate with students in the target language.

d. Describe language skills and cultural insights gained through real or virtual travel.

Students demonstrate an understanding and use their knowledge of the target language to communicate with target language speakers and to understand the importance of culture and language in the 21st century.

Modern and Classical

a. Interact with people, either in the community or online, who use the target language in their professions

b. Independently access a variety of target language sources for one's own entertainment or enrichment.

c. Explain how personal, educational, and career opportunities are expanded and enhanced by knowledge of the target language and associated culture(s).

Modern only

d. Communicate with target language speakers using the target language.

Notes

EFFECTIVE DATE:
October 22, 2007
June 23, 2019 - filing 2019-086
7/18/2020 - filing 2020-139 (Final adoption, major substantive)

STATUTORY AUTHORITY: 20-A MRS §6211

The following state regulations pages link to this page.



State regulations are updated quarterly; we currently have two versions available. Below is a comparison between our most recent version and the prior quarterly release. More comparison features will be added as we have more versions to compare.