With prompting and support, ask and answer questions about key details in a text.

With prompting and support, retell familiar stories, including key details.

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

Ask and answer questions about unknown words in a text.

Recognize common types of texts (e.g., storybooks, poems).

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

With prompting and support, describe the relationship between illustrations and the story.

With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories.

Actively engage in group reading activities with purpose and understanding.

With prompting and support, ask and answer questions about key details in a text.

With prompting and support, identify the main topic and retell key details of a text.

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

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

Identify the front cover, back cover, and title page of a book.

Name the author and illustrator of a text and define the role of each.

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

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

With prompting and support, identify basic similarities in and differences between two texts on the same topic.

Actively engage in group reading activities with purpose and understanding.

Demonstrate understanding of the organization and basic features of print.

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

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

Understand that words are separated by spaces in print.

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

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

Recognize and produce rhyming words.

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

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

Isolate and pronounce the initial, medial vowel, and final sounds in three-phoneme (CVC) words.

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

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

Demonstrate basic knowledge of one-to-one letter-sound correspondences for each consonant.

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

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

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

Read emergent-reader texts with purpose and understanding.

Use drawing, dictating, and writing to compose opinion pieces about a topic or book.

Use drawing, dictating, and writing to compose informative/explanatory texts naming a topic and supplying information.

Use drawing, dictating, and writing to narrate a single event or several loosely linked events.

With guidance and support from adults, respond to questions and suggestions from peers to strengthen writing.

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

Participate in shared research and writing projects (e.g., explore 'how-to' books to write instructions).

With guidance and support from adults, recall information from experiences or gather information to answer a question.

Participate in collaborative conversations with diverse partners about kindergarten topics and texts.

Follow agreed-upon rules for discussions (e.g., listening to others and taking turns speaking).

Continue a conversation through multiple exchanges.

Confirm understanding of a text read aloud or information presented orally by asking and answering questions.

Ask and answer questions in order to seek help, get information, or clarify something not understood.

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

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

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

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

Print many upper- and lowercase letters.

Use frequently occurring nouns and verbs.

Form regular plural nouns orally by adding /s/ or /es/.

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

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

Produce and expand complete sentences in shared language activities.

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

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

Recognize and name end punctuation.

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

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

Determine or clarify the meaning of unknown and multiple-meaning words and phrases.

Identify new meanings for familiar words and apply them accurately.

Use the most frequently occurring inflections and affixes as a clue to the meaning of an unknown word.

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

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

Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites.

Identify real-life connections between words and their use.

Distinguish shades of meaning among verbs describing the same general action by acting out the meanings.

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

Ask and answer questions about key details in a text.

Retell stories, including key details, and demonstrate understanding of their central message or lesson.

Describe characters, settings, and major events in a story, using key details.

Identify words and phrases in stories or poems that suggest feelings or appeal to the senses.

Explain major differences between books that tell stories and books that give information.

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

Use illustrations and details in a story to describe its characters, setting, or events.

Compare and contrast the adventures and experiences of characters in stories.

With prompting and support, read prose and poetry of appropriate complexity for grade 1.

Ask and answer questions about key details in a text.

Identify the main topic and retell key details of a text.

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

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

Know and use various text features to locate key facts or information in a text.

Distinguish between information provided by pictures or other illustrations and information provided by the words.

Use the illustrations and details in a text to describe its key ideas.

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

Identify basic similarities in and differences between two texts on the same topic.

With prompting and support, read informational texts appropriately complex for grade 1.

Demonstrate understanding of the organization and basic features of print.

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

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

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

Orally produce single-syllable words by blending sounds (phonemes), including consonant blends.

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

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

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

Know the spelling-sound correspondences for common consonant digraphs.

Decode regularly spelled one-syllable words.

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

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

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

Read words with inflectional endings.

Recognize and read grade-appropriate irregularly spelled words.

Read with sufficient accuracy and fluency to support comprehension.

Read grade-level text with purpose and understanding.

Read grade-level text orally with accuracy, appropriate rate, and expression.

Use context to confirm or self-correct word recognition and understanding.

Write opinion pieces in which they introduce the topic, state an opinion, and provide a reason.

Write informative/explanatory texts in which they name a topic, supply facts, and provide closure.

Write narratives in which they recount two or more appropriately sequenced events.

With guidance and support, focus on a topic, respond to questions and suggestions, and add details.

With guidance and support, use a variety of digital tools to produce and publish writing.

Participate in shared research and writing projects.

With guidance and support, recall information from experiences or gather information from provided sources.

Participate in collaborative conversations with diverse partners about grade 1 topics and texts.

Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time).

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

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

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

Ask and answer questions about what a speaker says in order to gather additional information.

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

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

Produce complete sentences when appropriate to task and situation.

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

Print all upper- and lowercase letters.

Use common, proper, and possessive nouns.

Use singular and plural nouns with matching verbs in basic sentences.

Use personal, possessive, and indefinite pronouns.

Use verbs to convey a sense of past, present, and future.

Use frequently occurring adjectives.

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

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

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

Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences.

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

Capitalize dates and names of people.

Use end punctuation for sentences.

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

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

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

Determine or clarify the meaning of unknown and multiple-meaning words and phrases.

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

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

Identify frequently occurring root words and their inflectional forms.

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

Sort words into categories to gain a sense of the concepts the categories represent.

Define words by category and by one or more key attributes.

Identify real-life connections between words and their use.

Distinguish shades of meaning among verbs differing in manner and adjectives differing in intensity.

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

Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.

Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral.

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

Describe how words and phrases supply rhythm and meaning in a story, poem, or song.

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

Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud.

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

Compare and contrast two or more versions of the same story by different authors or from different cultures.

By the end of the year, read and comprehend literature in the grades 2-3 text complexity band proficiently, with scaffolding as needed.

Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.

Identify the main topic of a multi-paragraph text as well as the focus of specific paragraphs within the text.

Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.

Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area.

Know and use various text features to locate key facts or information in a text efficiently.

Identify the main purpose of a text, including what the author wants to answer, explain, or describe.

Explain how specific images contribute to and clarify a text.

Describe how reasons support specific points the author makes in a text.

Compare and contrast the most important points presented by two texts on the same topic.

By the end of year, read and comprehend informational texts in the grades 2-3 text complexity band proficiently, with scaffolding as needed.

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

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

Know spelling-sound correspondences for additional common vowel teams.

Decode regularly spelled two-syllable words with long vowels.

Decode words with common prefixes and suffixes.

Identify words with inconsistent but common spelling-sound correspondences.

Recognize and read grade-appropriate irregularly spelled words.

Read with sufficient accuracy and fluency to support comprehension.

Read grade-level text with purpose and understanding.

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

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

Write opinion pieces in which they introduce the topic, state an opinion, supply reasons, use linking words, and provide a concluding statement.

Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement.

Write narratives in which they recount a well-elaborated event, include details, use temporal words, and provide a sense of closure.

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

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

Participate in shared research and writing projects.

Recall information from experiences or gather information from provided sources to answer a question.

Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults.

Follow agreed-upon rules for discussions.

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

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

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

Ask and answer questions about what a speaker says in order to clarify comprehension or deepen understanding.

Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences.

Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences.

Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification.

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

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

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

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

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

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

Produce, expand, and rearrange complete simple and compound sentences.

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

Capitalize holidays, product names, and geographic names.

Use commas in greetings and closings of letters.

Use an apostrophe to form contractions and frequently occurring possessives.

Generalize learned spelling patterns when writing words.

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

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

Compare formal and informal uses of English.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content.

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

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

Use a known root word as a clue to the meaning of an unknown word with the same root.

Use knowledge of the meaning of individual words to predict the meaning of compound words.

Use glossaries and beginning dictionaries to determine or clarify the meaning of words and phrases.

Demonstrate understanding of word relationships and nuances in word meanings.

Identify real-life connections between words and their use.

Distinguish shades of meaning among closely related verbs and closely related adjectives.

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

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

Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed.

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

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

Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza.

Distinguish their own point of view from that of the narrator or those of the characters.

Explain how specific aspects of a text's illustrations contribute to what is conveyed by the words in a story.

Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters.

By the end of the year, read and comprehend literature at the high end of the grades 2-3 text complexity band independently and proficiently.

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

Determine the main idea of a text; recount the key details and explain how they support the main idea.

Describe the relationship between a series of historical events, scientific ideas, or steps in technical procedures, using time, sequence, and cause/effect.

Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.

Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently.

Distinguish their own point of view from that of the author of a text.

Use information gained from illustrations and the words in a text to demonstrate understanding of the text.

Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, sequence).

Compare and contrast the most important points and key details presented in two texts on the same topic.

By the end of the year, read and comprehend informational texts at the high end of the grades 2-3 text complexity band independently.

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

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

Decode words with common Latin suffixes.

Decode multisyllable words.

Read grade-appropriate irregularly spelled words.

Read with sufficient accuracy and fluency to support comprehension.

Read grade-level text with purpose and understanding.

Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

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

Write opinion pieces on topics or texts, supporting a point of view with reasons.

Introduce the topic or text, state an opinion, and create an organizational structure that lists reasons.

Provide reasons that support the opinion.

Use linking words and phrases (e.g., because, therefore, since) to connect opinion and reasons.

Provide a concluding statement or section.

Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

Introduce a topic and group related information together; include illustrations when useful.

Develop the topic with facts, definitions, and details.

Use linking words and phrases (e.g., also, another, and) to connect ideas within categories.

Provide a concluding statement or section.

Write narratives to develop real or imagined experiences using effective technique, descriptive details, and clear event sequences.

Establish a situation and introduce a narrator and/or characters; organize an event sequence.

Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences.

Use temporal words and phrases to signal event order.

Provide a closure.

With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose.

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

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

Conduct short research projects that build knowledge about a topic.

Recall information from experiences or gather information from print and digital sources; take brief notes and sort evidence.

Write routinely over extended time frames and shorter time frames for a range of discipline-specific tasks, purposes, and audiences.

Engage effectively in a range of collaborative discussions with diverse partners, building on others' ideas and expressing their own clearly.

Come to discussions prepared, having read or studied required material; explicitly draw on that preparation.

Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care).

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

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

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

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

Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant details, speaking clearly.

Create engaging audio recordings of stories or poems; add visual displays when appropriate to emphasize facts or details.

Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification.

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

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

Form and use regular and irregular plural nouns.

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

Form and use regular and irregular verbs.

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

Ensure subject-verb and pronoun-antecedent agreement.

Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified.

Use coordinating and subordinating conjunctions.

Produce simple, compound, and complex sentences.

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

Capitalize appropriate words in titles.

Use commas in addresses.

Use commas and quotation marks in dialogue.

Form and use possessives.

Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words.

Use spelling patterns and generalizations (e.g., word families, syllable patterns) in writing words.

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

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

Choose words and phrases for effect.

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

Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content.

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

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

Use a known root word as a clue to the meaning of an unknown word with the same root.

Use glossaries or beginning dictionaries to determine or clarify the precise meaning of key words and phrases.

Demonstrate understanding of word relationships and nuances in word meanings.

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

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

Distinguish shades of meaning among related words that describe states of mind or degrees of certainty.

Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases.

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

Determine a theme of a story, drama, or poem from details in the text; summarize the text.

Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text.

Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters in mythology.

Explain major differences between poems, drama, and prose, and refer to the structural elements of poems and drama.

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

Make connections between the text of a story or drama and a visual or oral presentation of the text.

Compare and contrast the treatment of similar themes and topics and patterns of events in stories, myths, and traditional literature.

By the end of the year, read and comprehend literature in the grades 4-5 text complexity band proficiently.

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

Determine the main idea of a text and explain how it is supported by key details; summarize the text.

Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why.

Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic.

Describe the overall structure of events, ideas, concepts, or information in a text or part of a text.

Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus.

Interpret information presented visually, orally, or quantitatively and explain how it contributes to an understanding of the text.

Explain how an author uses reasons and evidence to support particular points in a text.

Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.

By the end of year, read and comprehend informational texts in the grades 4-5 text complexity band proficiently.

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

Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology to read unfamiliar multisyllabic words.

Read with sufficient accuracy and fluency to support comprehension.

Read grade-level text with purpose and understanding.

Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

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

Write opinion pieces on topics or texts, supporting a point of view with reasons and information.

Introduce a topic or text clearly, state an opinion, and create an organizational structure to support the writer's purpose.

Provide reasons that are supported by facts and details.

Link opinion and reasons using words and phrases (e.g., for instance, in addition, consequently, specifically).

Provide a concluding statement or section related to the opinion presented.

Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

Introduce a topic clearly and group related information in paragraphs and sections; include formatting and multimedia when useful.

Develop the topic with facts, definitions, concrete details, quotations, or other information and examples.

Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).

Use precise language and domain-specific vocabulary to inform about or explain the topic.

Provide a concluding statement or section related to the information or explanation presented.

Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence.

Use dialogue and description to develop experiences and events or show the responses of characters to situations.

Use a variety of transitional words and phrases to manage the sequence of events.

Use concrete words and phrases and sensory details to convey experiences and events precisely.

Provide a conclusion that follows from the narrated experiences or events.

Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.

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

With some guidance and support from adults, use technology to produce and publish writing and interact with others.

Conduct short research projects that build knowledge through investigation of different aspects of a topic.

Recall relevant information from experiences or gather information from print and digital sources; take notes and categorize information.

Draw evidence from literary or informational texts to support analysis, reflection, and research.

Apply grade 4 Reading standards to literature.

Apply grade 4 Reading standards to informational texts.

Write routinely over extended time frames and shorter time frames for a range of tasks, purposes, and audiences.

Engage effectively in a range of collaborative discussions with diverse partners, building on others' ideas.

Come to discussions prepared, having read or studied required material; draw on that preparation to explore ideas.

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

Pose and respond to specific questions to clarify or follow up on information, and make comments that link to others.

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

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

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

Report on a topic or text, tell a story, or recount an experience in an organized manner with appropriate facts.

Add audio recordings and visual displays to presentations when appropriate to enhance main ideas or themes.

Differentiate between contexts that call for formal English and situations where informal discourse is appropriate.

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

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

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

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

Order adjectives within sentences according to conventional patterns.

Form and use prepositional phrases.

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

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

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

Use correct capitalization.

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

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

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

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

Choose words and phrases to convey ideas precisely.

Choose punctuation for effect.

Differentiate between contexts that call for formal English and situations where informal discourse is appropriate.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases choosing flexibly from a range of strategies.

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

Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word.

Consult reference materials to find the pronunciation and determine or clarify the precise meaning of key words and phrases.

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

Explain the meaning of simple similes and metaphors in context.

Recognize and explain common idioms, adages, and proverbs.

Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar meanings (synonyms).

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases.

Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine a theme of a story, drama, or poem from details in the text, including how characters respond to challenges; summarize the text.

Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text.

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

Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem.

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

Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text.

Compare and contrast stories in the same genre on their approaches to similar themes and topics.

By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4-5 text complexity band.

Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.

Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text.

Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text.

Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.

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

Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent.

Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question or solve a problem efficiently.

Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s).

Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably.

By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4-5 band.

Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology to read accurately unfamiliar multisyllabic words.

Read grade-level text with purpose and understanding.

Read grade-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.

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

Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped.

Provide logically ordered reasons that are supported by facts and details.

Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically).

Provide a concluding statement or section related to the opinion presented.

Introduce a topic clearly, provide a general observation and focus, and group related information logically.

Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.

Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).

Use precise language and domain-specific vocabulary to inform about or explain the topic.

Provide a concluding statement or section related to the information or explanation presented.

Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.

Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations.

Use a variety of transitional words, phrases, and clauses to manage the sequence of events.

Use concrete words and phrases and sensory details to convey experiences and events precisely.

Provide a conclusion that follows from the narrated experiences or events.

Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.

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

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

Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic.

Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes.

Apply grade 5 Reading standards to literature (e.g., 'Compare and contrast two or more characters, settings, or events').

Apply grade 5 Reading standards to informational texts (e.g., 'Explain how an author uses reasons and evidence to support particular points').

Write routinely over extended time frames and shorter time frames for a range of discipline-specific tasks, purposes, and audiences.

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

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

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

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

Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

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

Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details.

Include multimedia components and visual displays in presentations when appropriate to enhance the development of main ideas or themes.

Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation.

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

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

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

Recognize and correct inappropriate shifts in verb tense.

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

Use punctuation to separate items in a series.

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

Use a comma to set off the words yes and no, to set off a tag question, and to indicate direct address.

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

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

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

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

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

Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word.

Consult reference materials, both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words.

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

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

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

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases.

Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text.

Describe how a particular story's or drama's plot unfolds in a series of episodes and how characters respond or change.

Determine the meaning of words and phrases, including figurative and connotative meanings; analyze the impact of word choice.

Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure and contributes to the theme or plot.

Explain how an author develops the point of view of the narrator or speaker in a text.

Compare and contrast the experience of reading a text to listening to or viewing an audio, video, or live version.

Compare and contrast texts in different forms or genres in terms of their approaches to similar themes and topics.

By the end of the year, read and comprehend literature in the grades 6-8 text complexity band proficiently.

Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text.

Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text.

Determine the meaning of words and phrases, including figurative, connotative, and technical meanings.

Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure and contributes to ideas.

Determine an author's point of view or purpose in a text and explain how it is conveyed in the text.

Integrate information presented in different media or formats to develop a coherent understanding of a topic or issue.

Trace and evaluate the argument and specific claims in a text, distinguishing supported claims from those that are not.

Compare and contrast one author's presentation of events with that of another (e.g., a memoir and a biography).

By the end of the year, read and comprehend literary nonfiction in the grades 6-8 text complexity band proficiently.

Write arguments to support claims with clear reasons and relevant evidence.

Introduce claim(s) and organize the reasons and evidence clearly.

Support claim(s) with clear reasons and relevant evidence, using credible sources.

Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons.

Establish and maintain a formal style.

Provide a concluding statement or section that follows from the argument presented.

Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information.

Introduce a topic; organize ideas using strategies such as definition, classification, and comparison; include formatting.

Develop the topic with relevant facts, definitions, concrete details, quotations, or other information.

Use appropriate transitions to clarify the relationships among ideas and concepts.

Use precise language and domain-specific vocabulary to inform about or explain the topic.

Establish and maintain a formal style.

Provide a concluding statement or section that follows from the information or explanation presented.

Write narratives to develop real or imagined experiences or events using effective technique and descriptive details.

Engage and orient the reader by establishing a context and introducing a narrator and/or characters.

Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts.

Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences.

Provide a conclusion that follows from the narrated experiences or events.

Produce clear and coherent writing in which the development, organization, and style are appropriate to task.

With guidance, develop and strengthen writing as needed by planning, revising, editing, or rewriting.

Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.

Conduct short research projects to answer a question, drawing on several sources.

Gather relevant information from multiple sources; assess credibility; quote or paraphrase while avoiding plagiarism.

Draw evidence from literary or informational texts to support analysis, reflection, and research.

Apply grade 6 Reading standards to literature.

Apply grade 6 Reading standards to literary nonfiction.

Write routinely over extended and shorter time frames for a range of discipline-specific tasks.

Engage effectively in a range of collaborative discussions with diverse partners on grade 6 topics.

Come to discussions prepared, having read or studied required material; explicitly draw on that preparation.

Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles.

Pose and respond to specific questions with elaboration and detail by making comments that contribute.

Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection.

Interpret information presented in diverse media and formats and explain how it contributes to a topic.

Delineate a speaker's argument and specific claims, distinguishing supported claims from those that are not.

Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details.

Include multimedia components and visual displays in presentations to clarify information.

Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when appropriate.

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

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

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

Recognize and correct inappropriate shifts in pronoun number and person.

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

Recognize variations from standard English in their own and others' writing and speaking.

Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling.

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

Spell correctly.

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

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

Maintain consistency in style and tone.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 content.

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

Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word.

Consult reference materials to find the pronunciation of a word or determine its precise meaning.

Verify the preliminary determination of the meaning of a word or phrase.

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

Interpret figures of speech (e.g., personification) in context.

Use the relationship between particular words to better understand each of the words.

Distinguish among the connotations of words with similar denotations.

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases.

Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.

Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot).

Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions.

Analyze how a drama's or poem's form or structure (e.g., soliloquy, sonnet) contributes to its meaning.

Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.

Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium.

Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors use history.

By the end of the year, read and comprehend literature in the grades 6-8 text complexity band proficiently, with scaffolding as needed at the high end of the range.

Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text.

Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events).

Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of word choice.

Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas.

Determine an author's point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others.

Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium's portrayal of the subject.

Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient.

Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or interpretations.

By the end of the year, read and comprehend literary nonfiction in the grades 6-8 text complexity band proficiently, with scaffolding as needed.

Write arguments to support claims with clear reasons and relevant evidence.

Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically.

Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.

Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence.

Establish and maintain a formal style.

Provide a concluding statement or section that follows from and supports the argument presented.

Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.

Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, and comparison.

Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.

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

Use precise language and domain-specific vocabulary to inform about or explain the topic.

Establish and maintain a formal style.

Provide a concluding statement or section that follows from and supports the information or explanation presented.

Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence.

Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.

Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.

Provide a conclusion that follows from and reflects on the narrated experiences or events.

Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

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

Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others.

Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research.

Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source.

Draw evidence from literary or informational texts to support analysis, reflection, and research.

Apply grade 7 Reading standards to literature.

Apply grade 7 Reading standards to literary nonfiction.

Write routinely over extended time frames and shorter time frames for a range of discipline-specific tasks, purposes, and audiences.

Engage effectively in a range of collaborative discussions with diverse partners on grade 7 topics, texts, and issues, building on others' ideas.

Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence.

Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed.

Pose questions that elicit elaboration and respond to others' questions and comments with relevant observations and ideas.

Acknowledge new information expressed by others and, when warranted, modify their own views.

Analyze the main ideas and supporting details presented in diverse media and formats and explain how the ideas clarify a topic, text, or issue.

Delineate a speaker's argument and specific claims, evaluating the soundness of the reasoning and the relevance and sufficiency of the evidence.

Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts, details, and examples.

Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points.

Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.

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

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

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

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

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

Use a comma to separate coordinate adjectives.

Spell correctly.

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

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

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 7 reading and content.

Use context (e.g., the overall meaning of a sentence or paragraph) as a clue to the meaning of a word or phrase.

Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word.

Consult general and specialized reference materials, both print and digital, to find the pronunciation of a word or determine its precise meaning.

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).

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

Interpret figures of speech (e.g., literary, biblical, and mythological allusions) in context.

Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words.

Distinguish among the connotations of words with similar denotations (e.g., refined, respectful, polite, diplomatic, condescending).

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases.

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

Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.

Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.

Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices.

Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style.

Analyze how differences in the points of view of the characters and the audience or reader create such effects as suspense or humor.

Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script.

Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works.

By the end of the year, read and comprehend literature in the grades 6-8 text complexity band proficiently, with scaffolding as needed.

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

Determine a central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.

Analyze how a text makes connections among and distinctions between individuals, ideas, or events.

Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.

Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept.

Determine an author's point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints.

Evaluate the advantages and disadvantages of using different mediums to present a particular topic or idea.

Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient.

Analyze a case in which two or more texts provide conflicting information on the same topic and identify where the texts disagree.

By the end of the year, read and comprehend literary nonfiction in the grades 6-8 text complexity band proficiently.

Write arguments to support claims with clear reasons and relevant evidence.

Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.

Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.

Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.

Establish and maintain a formal style.

Provide a concluding statement or section that follows from and supports the argument presented.

Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection and analysis of relevant content.

Introduce a topic clearly; organize ideas, concepts, and information into broader categories; include formatting, graphics, and multimedia when useful.

Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.

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

Use precise language and domain-specific vocabulary to inform about or explain the topic.

Establish and maintain a formal style.

Provide a concluding statement or section that follows from and supports the information or explanation presented.

Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

Engage and orient the reader by establishing a context and point of view; organize an event sequence that unfolds naturally and logically.

Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters.

Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.

Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.

Provide a conclusion that follows from and reflects on the narrated experiences or events.

Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

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

Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently.

Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

Gather relevant information from multiple print and digital sources; assess the credibility and accuracy of each source; and quote or paraphrase the data.

Draw evidence from literary or informational texts to support analysis, reflection, and research.

Apply grade 8 Reading standards to literature.

Apply grade 8 Reading standards to literary nonfiction.

Write routinely over extended time frames and shorter time frames for a range of discipline-specific tasks, purposes, and audiences.

Engage effectively in a range of collaborative discussions with diverse partners on grade 8 topics, texts, and issues.

Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence.

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

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

Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented.

Analyze the purpose of information presented in diverse media and formats and evaluate the motives behind its presentation.

Delineate a speaker's argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence.

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

Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest.

Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.

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

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

Form and use verbs in the active and passive voice.

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

Recognize and correct inappropriate shifts in verb voice and mood.

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

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

Use an ellipsis to indicate an omission.

Spell correctly.

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

Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects.

Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content.

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.

Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word.

Consult general and specialized reference materials to find the pronunciation of a word or determine or clarify its precise meaning.

Verify the preliminary determination of the meaning of a word or phrase.

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

Interpret figures of speech (e.g. verbal irony, puns) in context.

Use the relationship between particular words to better understand each of the words.

Distinguish among the connotations (associations) of words with similar denotations (definitions).

Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases.

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a theme or central idea of a text and analyze in detail its development over the course of the text; provide an objective summary.

Analyze how complex characters develop over the course of a text, interact with other characters, and advance the plot or develop the theme.

Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of word choices.

Analyze how an author's choices concerning how to structure a text, order events within it, and manipulate time create such effects as mystery, tension, or surprise.

Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature.

Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment.

Analyze how an author draws on and transforms source material in a specific work.

By the end of grade 10, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 9-10 text complexity band independently.

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.

Determine a central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.

Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made and the connections that are drawn.

Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.

Analyze in detail how an author's ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text.

Determine an author's point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.

Analyze various accounts of a subject told in different mediums, determining which details are emphasized in each account.

Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient.

Analyze seminal U.S. documents of historical and literary significance, including how they address related themes and concepts.

By the end of grade 10, read and comprehend literary nonfiction at the high end of the grades 9-10 text complexity band independently and proficiently.

Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships.

Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both.

Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons.

Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

Provide a concluding statement or section that follows from and supports the argument presented.

Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions.

Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information.

Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas.

Use precise language and domain-specific vocabulary to manage the complexity of the topic.

Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline.

Provide a concluding statement or section that follows from and supports the information or explanation presented.

Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view.

Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.

Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

Use technology, including the Internet, to produce, publish, and update individual or shared writing products.

Conduct short as well as more sustained research projects to answer a question or solve a problem.

Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source.

Apply grades 9-10 Reading standards to literature (e.g., 'Analyze how an author draws on and transforms source material').

Apply grades 9-10 Reading standards to literary nonfiction (e.g., 'Delineate and evaluate the argument and specific claims').

Write routinely over extended time frames and shorter time frames for a range of tasks, purposes, and audiences.

Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation.

Work with peers to set rules for collegial discussions and decision-making, clear goals and deadlines, and individual roles as needed.

Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas.

Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views.

Integrate multiple sources of information presented in diverse media or formats evaluating the credibility and accuracy of each source.

Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence.

Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning.

Make strategic use of digital media in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.

Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.

Use parallel structure.

Use various types of phrases and clauses to convey specific meanings and add variety and interest to writing or presentations.

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

Use a colon to introduce a list or quotation.

Spell correctly.

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

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

Identify and correctly use patterns of word changes that indicate different meanings or parts of speech.

Consult general and specialized reference materials to find the pronunciation of a word or determine its precise meaning.

Verify the preliminary determination of the meaning of a word or phrase.

Interpret figures of speech in context and analyze their role in the text.

Analyze nuances in the meaning of words with similar denotations.

Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening.

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn, including where the text leaves matters uncertain.

Determine two or more themes or central ideas of a text and analyze their development over the course of the text; provide an objective summary.

Analyze the impact of the author's choices regarding how to develop and relate elements of a story or drama.

Determine the meaning of words and phrases as they are used in the text; analyze the impact of specific word choices on meaning and tone.

Analyze how an author's choices concerning how to structure specific parts of a text contribute to its overall structure and meaning as well as its aesthetic impact.

Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant.

Analyze multiple interpretations of a story, drama, or poem, evaluating how each version interprets the source text.

Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature.

By the end of grade 12, read and comprehend literature at the high end of the grades 11-CCR text complexity band independently and proficiently.

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn, including where the text leaves matters uncertain.

Determine two or more central ideas of a text and analyze their development over the course of the text; provide an objective summary.

Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text.

Determine the meaning of words and phrases as they are used in a text; analyze how an author uses and refines the meaning of a key term or terms.

Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument.

Determine an author's point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power.

Integrate and evaluate multiple sources of information presented in different media or formats in order to address a question or solve a problem.

Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning.

Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance for their themes and purposes.

By the end of grade 12, read and comprehend literary nonfiction at the high end of the grades 11-CCR text complexity band independently and proficiently.

Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), and create an organization that logically sequences claim(s).

Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each.

Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify relationships.

Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline.

Provide a concluding statement or section that follows from and supports the argument presented.

Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it.

Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, or other information.

Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify relationships.

Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic.

Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline.

Provide a concluding statement or section that follows from and supports the information or explanation presented.

Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view.

Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone.

Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback.

Conduct short as well as more sustained research projects to answer a question or solve a problem.

Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations.

Apply grades 11-12 Reading standards to literature (e.g., 'Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works').

Apply grades 11-12 Reading standards to literary nonfiction (e.g., 'Delineate and evaluate the reasoning in seminal U.S. texts').

Write routinely over extended time frames and shorter time frames for a range of tasks, purposes, and audiences.

Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation.

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

Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a full range of positions on a topic.

Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue.

Integrate multiple sources of information presented in diverse formats and media in order to make informed decisions and solve problems.

Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, and tone.

Present information, findings, and supporting evidence, conveying a clear and distinct perspective.

Make strategic use of digital media in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.

Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when indicated or appropriate.

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

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

Observe hyphenation conventions.

Spell correctly.

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

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

Identify and correctly use patterns of word changes that indicate different meanings or parts of speech.

Consult general and specialized reference materials to find the pronunciation of a word or determine its precise meaning.

Verify the preliminary determination of the meaning of a word or phrase.

Interpret figures of speech in context and analyze their role in the text.

Analyze nuances in the meaning of words with similar denotations.

Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening.

Generate questions to investigate situations within the classroom.

Collect or consider data through organizing objects or drawing pictures to represent and communicate observations.

Analyze data sets by noticing and describing patterns in data-rich situations.

Interpret and communicate results through structured answers with teacher guidance.

Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

Directly compare two objects with a measurable attribute in common to see which object has more or less of the attribute.

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

Count to 100 by ones and by tens.

Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20.

When counting objects, say the number names in the standard order, pairing each object with one and only one number name.

Understand that the last number name said represents the number of objects counted, regardless of arrangement or order.

Understand that each successive number name refers to a quantity that is one larger.

Count to answer 'how many?' questions about as many as 20 objects; given a number from 1–20, count out that many objects.

Identify whether the number of objects in one group is greater than, less than, or equal to the number in another group.

Compare two numbers between 1 and 10 presented as written numerals.

Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out, or equations.

Efficiently, flexibly, and accurately solve addition and subtraction word problems, and add and subtract within 10.

Decompose numbers less than or equal to 10 into pairs in more than one way and record each decomposition.

For any number from 1 to 9, find the number that makes 10 when added to the given number.

Efficiently, flexibly, and accurately add and subtract within 5.

Compose and decompose numbers from 11 to 19 into ten ones and some further ones.

Describe objects in the environment using names of shapes and describe relative positions using terms like above and below.

Correctly name shapes regardless of their orientations or overall size.

Identify shapes as two-dimensional (lying in a plane, 'flat') or three-dimensional ('solid').

Analyze and compare two- and three-dimensional shapes using informal language to describe attributes like sides and corners.

Model shapes in the world by building shapes from components and/or drawing shapes.

Use 2-dimensional shapes to compose a variety of larger shapes.

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.

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.

Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.

Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on, making ten, and decomposing numbers.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

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.

Understand that the two digits of a two-digit number represent amounts of tens and ones.

10 can be thought of as a bundle of ten ones — called a "ten."

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

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).

Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

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 models or drawings.

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences).

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object end to end.

Tell and write time in hours and half-hours using analog and digital clocks.

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points.

Distinguish between defining attributes versus non-defining attributes; build and draw shapes to possess defining attributes.

Compose two-dimensional shapes or three-dimensional shapes to create a composite shape, and compose new shapes from the composite shape.

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters.

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.

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Determine whether a group of objects (up to 20) has an odd or even number of members; write an equation to express an even number as a sum of two equal addends.

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.

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.

100 can be thought of as a bundle of ten tens — called a 'hundred.'

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).

Count within 1000; skip-count by 5s, 10s, and 100s.

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add up to four two-digit numbers using strategies based on place value and properties of operations.

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.

Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

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.

Estimate lengths using units of inches, feet, centimeters, and meters.

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points, and represent whole-number sums and differences within 100 on a number line diagram.

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Generate measurement data by measuring lengths of several objects to the nearest whole unit. Show the measurements by making a line plot.

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple problems using information presented in a bar graph.

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

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.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

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.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Apply properties of operations as strategies to multiply and divide. Examples: Commutative, Associative, and Distributive properties.

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity.

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Use place value understanding to round whole numbers to the nearest 10 or 100.

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.

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts.

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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.

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0.

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent.

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Compare two fractions with the same numerator or the same denominator by reasoning about their size.

Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot.

Recognize area as an attribute of plane figures and understand concepts of area measurement.

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.

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.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Relate area to the operations of multiplication and addition.

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as multiplying the side lengths.

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems.

Use tiling to show in a concrete case that the area of a rectangle with side lengths a and (b + c) is the sum of a × b and a × c.

Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas.

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length.

Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category.

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiply or divide to efficiently, flexibly, and accurately solve real world word problems involving multiplicative comparison.

Efficiently, flexibly, and accurately solve multistep real world word problems posed with whole numbers using the four operations.

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.

Generate a number or shape pattern that follows a given rule. Identify and explain apparent features of the pattern.

Understand that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Read, write, and compare multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Use place value understanding of multi-digit whole numbers to generate estimates to any place less than or equal to 1,000,000.

Efficiently, flexibly, and accurately add and subtract multi-digit whole numbers using the standard algorithm.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.

Demonstrate understanding of why a fraction is equivalent to another fraction by using visual fraction models.

Compare two fractions with different numerators and different denominators by creating common denominators or numerators.

Efficiently, flexibly, and accurately compose and decompose fractions with a numerator greater than 1 into unit fractions.

Flexibly apply and extend previous understandings of multiplication to multiply a fraction by a whole number using visual models.

Explore and explain using models that a fraction with a denominator of 10 is equivalent to a fraction with denominator of 100.

Use decimal notation for fractions with denominators 10 or 100.

Compare two decimals to hundredths by reasoning about their size. Record results with symbols >, =, <.

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses, and money.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition and subtraction.

Recognize angles as geometric shapes formed wherever two rays share a common endpoint. Understand concepts of angle measurement.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Recognize angle measure as additive. Solve addition and subtraction problems to find unknown angles on a diagram.

Draw points, lines, line segments, rays, angles, and perpendicular and parallel lines. Identify these in two-dimensional figures.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded into matching parts.

Generate questions of interest to the students that elicit data, generate ideas based on the questions, and refine the question as necessary.

Determine strategies for collecting and considering data in a variety of ways including with the use of technology.

Critically analyze data visualizations, including tables, bar graphs, line plots, or spreadsheets to support a claim.

Interpret and communicate results, describing difference between groups, with teacher guidance.

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.

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.

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.

Read, write, and compare decimals to thousandths.

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Use place value understanding to round decimals to any place.

Fluently multiply multi-digit whole numbers using the standard algorithm.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value and properties of operations.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value and properties of operations.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

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 fractions or mixed numbers.

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares, and show that the area is the same as would be found by multiplying the side lengths.

Interpret multiplication as scaling (resizing).

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.

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; and explaining why multiplying by a fraction less than 1 results in a smaller product.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

Interpret division of a whole number by a unit fraction, and compute such quotients.

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.

Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems.

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 to solve problems involving information in line plots.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

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.

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.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying edge lengths.

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths.

Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts.

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the origin arranged to coincide with the 0 on each line.

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in context.

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classify two-dimensional figures in a hierarchy based on properties.

Efficiently, flexibly, and accurately divide multi-digit numbers using strategies or algorithms.

Efficiently, flexibly, and accurately add, subtract, multiply, and divide multi-digit decimals using strategies or algorithms for each operation.

Explain how positive and negative numbers are used together to describe quantities having opposite directions or values; use to represent quantities in real-world contexts.

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes to place any rational number on the line and in the plane.

Understand opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs on a coordinate plane.

Understand ordering and absolute value of positive and negative rational numbers.

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write, interpret, and explain order for rational numbers on a number line in real-world contexts.

Interpret absolute value as the distance a number is from zero on a number line.

Distinguish comparisons of absolute value from statements about order.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

Interpret and efficiently, flexibly, and accurately determine quotients of fractions, and solve word problems involving division of fractions by fractions.

Find the greatest common factor of two whole numbers ≤ 100 and the least common multiple of two whole numbers ≤ 12.

Explain the concept of a ratio and efficiently, flexibly, and accurately use ratio language to describe a ratio relationship between two quantities.

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

Efficiently, flexibly, and accurately demonstrate understanding of ratio and rate reasoning by solving real-world and mathematical problems.

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values, and plot pairs on the coordinate plane.

Solve unit rate problems including those involving unit pricing and constant speed.

Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Efficiently, flexibly, and accurately write and evaluate numerical expressions involving whole-number exponents.

Read, and evaluate expressions efficiently, flexibly, and accurately in which letters stand for numbers.

Write expressions that record operations with numbers and with letters standing for numbers.

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient).

Evaluate expressions at specific values of their variables, including those that arise from formulas used in real-world problems.

Apply the properties of operations (including the distributive property) efficiently, flexibly, and accurately to generate equivalent expressions.

Identify whether two expressions are equivalent (including expressions with one or more variables).

Understand solving an equation or inequality as a process of answering a question: which values from a specified set make it true?

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q.

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.

Use variables to represent two quantities in a real-world problem that change in relationship to one another.

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles.

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes.

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side.

Represent three-dimensional figures using nets made up of rectangles and triangles and use the nets to find the surface area.

Formulate and recognize statistical investigative questions that are of interest to students to collect data from modern sources.

Collect and record data with technology to identify and describe the characteristics of data sets.

Analyze data visualizations and describe measures of center and variability of quantitative data using appropriate displays.

Use statistical evidence from analyses to answer the statistical investigative question and communicate results.

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and shape.

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Summarize numerical data sets in relation to their context.

Report the number of observations.

Describe the nature of the attribute under investigation, including how it was measured and its units of measurement.

Calculate measures of center (mean/median) and variability (IQR/MAD) and identify striking deviations (outliers).

Communicate choice for selecting a given measure of center and variability related to the shape of the data distribution.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Recognize and represent proportional relationships between quantities.

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.

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Represent proportional relationships by equations.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, including (0, 0) and (1, r).

Use proportional relationships to solve multistep ratio and percent problems.

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent on a number line diagram.

Describe situations in which opposite quantities combine to make 0.

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.

Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).

Apply properties of operations as strategies to add and subtract rational numbers.

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations.

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers is a rational number.

Apply properties of operations as strategies to multiply and divide rational numbers.

Convert a rational number to a decimal using long division; know that the decimal form terminates in 0s or eventually repeats.

Solve real-world and mathematical problems involving the four operations with rational numbers.

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Understand that rewriting an expression in different forms in a problem context can shed light on the problem.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.

Use variables to represent quantities and construct simple equations and inequalities to solve problems.

Solve word problems leading to equations of the form px + q = r and p(x + q) = r.

Solve word problems leading to inequalities of the form px + q > r or px + q < r.

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas.

Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides.

Describe the two-dimensional figures that result from slicing three-dimensional figures.

Know the formulas for the area and circumference of a circle and use them to solve problems.

Use facts about supplementary, complementary, vertical, and adjacent angles to write and solve simple equations for an unknown angle.

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects.

Understand that statistics can be used to gain information about a population by examining a representative sample.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities.

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

Approximate the probability of a chance event by collecting data and observing its long-run relative frequency.

Develop a probability model and use it to find probabilities of events.

Develop a uniform probability model by assigning equal probability to all outcomes.

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Understand that the probability of a compound event is the fraction of outcomes in the sample space for which the event occurs.

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.

Design and use a simulation to generate frequencies for compound events.

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 expansion repeats eventually.

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.

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number.

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities.

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.

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line; derive the equation y = mx and y = mx + b.

Solve linear equations in one variable.

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Analyze and solve pairs of simultaneous linear equations.

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs.

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Solve real-world and mathematical problems leading to two linear equations in two variables.

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.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

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.

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function.

Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function.

Verify experimentally the properties of rotations, reflections, and translations.

Lines are taken to lines, and line segments to line segments of the same length.

Angles are taken to angles of the same measure.

Parallel lines are taken to parallel lines.

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.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, and the angles created when parallel lines are cut by a transversal.

Explain a proof of the Pythagorean Theorem and its converse.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.

Know that straight lines are widely used to model relationships between two quantitative variables. Informally fit a straight line to a scatter plot.

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

Formulate multivariable statistical investigative questions and determine how data can be collected and provide an answer, consider causality and prediction.

Understand the issues of bias and confounding variables when collecting data and their impact on interpretation. Understand practices for collecting and handling data.

Create and analyze data sets using technology to clean, sort, or filter data. Summarize and describe relationships using data displays.

Acknowledge missing data values and understand bias. Examine competing explanations for trends. Respond to competing arguments, considering correlation versus causation.

Represent data with plots on the real number line (dot plots, histograms, and box plots).

Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data.

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Compute (using technology) and interpret the correlation coefficient of a linear fit.

Distinguish between correlation and causation.

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

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.

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Evaluate reports based on data.

Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events.

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities.

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B.

Construct and interpret two-way frequency tables of data. Use the table as a sample space to decide if events are independent.

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer.

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.

(+) 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.

(+) Use permutations and combinations to compute probabilities of compound events and solve problems.

(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space.

(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated.

(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically.

(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing).

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values.

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Explain why the sum or product of two rational numbers is rational; that the sum of a rational and irrational is irrational.

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units and scales.

Define appropriate quantities for the purpose of descriptive modeling.

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real.

Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

(+) Represent complex numbers on the complex plane in rectangular and polar form.

(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane.

(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint as the average.

Solve quadratic equations with real coefficients that have complex solutions.

(+) Extend polynomial identities to the complex numbers.

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments.

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

(+) Solve problems involving velocity and other quantities that can be represented by vectors.

(+) Add and subtract vectors.

(+) Multiply a vector by a scalar.

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

(+) Add, subtract, and multiply matrices of appropriate dimensions.

(+) Understand that matrix multiplication for square matrices is not commutative, but still satisfies associative and distributive properties.

(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to 0 and 1 in the real numbers.

(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector.

(+) Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Graph linear, exponential, and quadratic functions from symbolic forms and identify key features including intercepts and end behavior.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Write a function that describes a relationship between two quantities, including linear and exponential relationships.

Interpret expressions that represent a quantity in terms of its context within linear, exponential, and quadratic functions.

Use the structure of an expression to identify ways to rewrite it.

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

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.

Understand that polynomials form a system analogous to the integers, namely, they are closed under addition, subtraction, and multiplication.

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).

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph.

Prove polynomial identities and use them to describe numerical relationships.

(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n.

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x).

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division.

Create equations and inequalities in one variable and use them to solve problems. Include linear and quadratic functions.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve quadratic equations in one variable using inspection, square roots, completing the square, and the quadratic formula.

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.

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

(+) Represent a system of linear equations as a single matrix equation in a vector variable.

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations.

Understand that a function from one set to another set assigns to each element of the domain exactly one element of the range.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

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.

Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Distinguish between situations that can be modeled with linear functions and with exponential functions.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or as a polynomial function.

For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e.

Interpret the parameters in a linear or exponential function in terms of a context.

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers.

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6.

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

(+) Understand that restricting a trigonometric function to a specific domain allows its inverse to be constructed.

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology.

Prove the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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.

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions.

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.

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.

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Prove theorems about lines and angles.

Prove theorems about triangles.

Prove theorems about parallelograms.

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Verify experimentally the properties of dilations given by a center and a scale factor.

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar.

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems about triangles.

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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.

Explain and use the relationship between the sine and cosine of complementary angles.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

(+) 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.

(+) Prove the Laws of Sines and Cosines and use them to solve problems.

(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

Prove that all circles are similar.

Identify and describe relationships among inscribed angles, radii, and chords.

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

(+) Construct a tangent line from a point outside a given circle to the circle.

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.

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.

Derive the equation of a parabola given a focus and directrix.

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Use coordinates to prove simple geometric theorems algebraically.

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

(+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

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).

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).

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).

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality).

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.

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.

Make observations to determine the effect of sunlight on Earth’s surface.

Use tools and materials to design and build a structure that will reduce the warming effect of sunlight on an area.

Use observations to describe patterns of what plants and animals (including humans) need to survive.

Use and share observations of local weather conditions to describe patterns over time.

Construct an argument supported by evidence for how plants and animals (including humans) can change the environment to meet their needs.

Use a model to represent the relationship between the needs of different plants or animals (including humans) and the places they live.

Ask questions to obtain information about the purpose of weather forecasting to prepare for, and respond to, severe weather.

Communicate solutions that will reduce the impact of humans on the land, water, air, and/or other living things in the local environment.

Ask questions, make observations, and gather information about a situation people want to change to define a simple problem that can be solved through a new tool.

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.

Analyze data from tests of two objects designed to solve the same problem to compare the strengths and weaknesses of how each performs.

Plan and conduct investigations to provide evidence that vibrating materials can make sound and that sound can make materials vibrate.

Make observations to construct an evidence-based account that objects can be seen only when illuminated.

Plan and conduct an investigation to determine the effect of placing objects made with different materials in the path of a beam of light.

Use tools and materials to design and build a device that uses light or sound to solve the problem of communicating over a distance.

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.

Read texts and use media to determine patterns in behavior of parents and offspring that help offspring survive.

Make observations to construct an evidence-based account that young plants and animals are like, but not exactly like, their parents.

Use observations of the sun, moon, and stars to describe patterns that can be predicted.

Make observations at different times of year to relate the amount of daylight to the time of year.

Ask questions, make observations, and gather information about a situation people want to change to define a simple problem.

Develop a simple sketch, drawing, or physical model to illustrate how the shape of an object helps it function as needed.

Analyze data from tests of two objects designed to solve the same problem to compare the strengths and weaknesses of how each performs.

Plan and conduct an investigation to describe and classify different kinds of materials by their observable properties.

Analyze data obtained from testing different materials to determine which materials have the properties that are best suited for an intended purpose.

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.

Construct an argument with evidence that some changes caused by heating or cooling can be reversed and some cannot.

Plan and conduct an investigation to determine if plants need sunlight and water to grow.

Develop a simple model that mimics the function of an animal in dispersing seeds or pollinating plants.

Make observations of plants and animals to compare the diversity of life in different habitats.

Use information from several sources to provide evidence that Earth events can occur quickly or slowly.

Compare multiple solutions designed to slow or prevent wind or water from changing the shape of the land.

Develop a model to represent the shapes and kinds of land and bodies of water in an area.

Obtain information to identify where water is found on Earth and that it can be solid or liquid.

Ask questions, make observations, and gather information about a situation people want to change to define a simple problem that can be solved through a new tool.

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.

Analyze data from tests of two objects designed to solve the same problem to compare the strengths and weaknesses of how each performs.

Plan and conduct an investigation to provide evidence of the effects of balanced and unbalanced forces on the motion of an object.

Make observations and/or measurements of an object’s motion to provide evidence that a pattern can be used to predict future motion.

Ask questions to determine cause and effect relationships of electric or magnetic interactions between two objects not in contact with each other.

Define a simple design problem that can be solved by applying scientific ideas about magnets.

Develop models to describe that organisms have unique and diverse life cycles but all have in common birth, growth, reproduction, and death.

Construct an argument that some animals form groups that help members survive.

Analyze and interpret data to provide evidence that plants and animals have traits inherited from parents and that variation exists in a group.

Use evidence to support the explanation that traits can be influenced by the environment.

Analyze and interpret data from fossils to provide evidence of the organisms and the environments in which they lived long ago.

Use evidence to construct an explanation for how variations in characteristics among individuals may provide advantages in surviving and reproducing.

Construct an argument with evidence that in a particular habitat some organisms can survive well, some survive less well, and some cannot survive.

Make a claim about the merit of a solution to a problem caused when the environment changes and the types of plants and animals may change.

Represent data in tables and graphical displays to describe typical weather conditions expected during a particular season.

Obtain and combine information to describe climates in different regions of the world.

Make a claim about the merit of a design solution that reduces the impacts of a weather-related hazard.

Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.

Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints.

Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects that can be improved.

Use evidence to construct an explanation relating the speed of an object to the energy of that object.

Make observations to provide evidence that energy can be transferred from place to place by sound, light, heat, and electric currents.

Ask questions and predict outcomes about the changes in energy that occur when objects collide.

Apply scientific ideas to design, test, and refine a device that converts energy from one form to another.

Develop a model of waves to describe patterns in terms of amplitude and wavelength and that waves can cause objects to move.

Develop a model to describe that light reflecting from objects and entering the eye allows objects to be seen.

Generate and compare multiple solutions that use patterns to transfer information.

Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction.

Use a model to describe that animals receive different types of information through their senses, process the information in their brain, and respond in different ways.

Identify evidence from patterns in rock formations and fossils in rock layers to support an explanation for changes in a landscape over time.

Make observations and/or measurements to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation.

Analyze and interpret data from maps to describe patterns of Earth’s features.

Obtain and combine information to describe that energy and fuels are derived from natural resources and their uses affect the environment.

Generate and compare multiple solutions to reduce the impacts of natural Earth processes on humans.

Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.

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.

Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects of a model that can be improved.

Develop a model to describe that matter is made of particles too small to be seen.

Measure and graph quantities to provide evidence that regardless of the type of change, the total weight of matter is conserved.

Make observations and measurements to identify materials based on their properties.

Conduct an investigation to determine whether the mixing of two or more substances results in new substances.

Support an argument that the gravitational force exerted by Earth on objects is directed down.

Use models to describe that energy in animals’ food (used for body repair, growth, motion, and warmth) was once energy from the sun.

Support an argument that plants get the materials they need for growth chiefly from air and water.

Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment.

Support an argument that differences in the apparent brightness of the sun compared to other stars is due to their relative distances.

Represent data in graphical displays to reveal patterns of daily changes in shadows, day and night, and seasonal appearance of stars.

Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact.

Describe and graph the amounts and percentages of water and fresh water in various reservoirs to provide evidence about water distribution.

Obtain and combine information about ways individual communities use science ideas to protect the Earth’s resources and environment.

Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints.

Generate and compare multiple possible solutions to a problem based on how well each is likely to meet criteria and constraints.

Plan and carry out fair tests in which variables are controlled and failure points are considered to identify improvements.

Develop models to describe the atomic composition of simple molecules and extended structures.

Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred.

Gather and make sense of information to describe that synthetic materials come from natural resources and impact society.

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.

Conduct an investigation to provide evidence that living things are made of cells; either one cell or many different numbers and types of cells.

Develop and use a model to describe the function of a cell as a whole and ways parts of cells contribute to the function.

Use argument supported by evidence for how the body is a system of interacting subsystems composed of groups of cells.

Use argument based on empirical evidence and scientific reasoning to support an explanation for how animal behaviors and plant structures affect reproductive success.

Construct a scientific explanation based on evidence for how environmental and genetic factors influence the growth of organisms.

Gather and make sense of information to describe that sensory receptors respond to stimuli by sending messages to the brain for immediate behavior or memory storage.

Develop a model to describe the cycling of water through Earth's systems driven by energy from the sun and the force of gravity.

Collect data to provide evidence for how the motions and complex interactions of air masses result in changes in weather conditions.

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.

Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment.

Ask questions to clarify evidence of the factors that have caused the rise in global temperatures over the past century.

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles.

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each.

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.

Develop models to describe the atomic composition of simple molecules and extended structures.

Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred.

Gather and make sense of information to describe that synthetic materials come from natural resources and impact society.

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.

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.

Undertake a design project to construct, test, and modify a device that either releases or absorbs thermal energy by chemical processes.

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.

Develop a model to describe how food is rearranged through chemical reactions forming new molecules that support growth and/or release energy.

Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem.

Construct an explanation that predicts patterns of interactions among organisms across multiple ecosystems.

Develop a model to describe the cycling of matter and flow of energy among living and nonliving parts of an ecosystem.

Construct an argument supported by empirical evidence that changes to physical or biological components of an ecosystem affect populations.

Evaluate competing design solutions for maintaining biodiversity and ecosystem services.

Develop a model to describe the cycling of Earth's materials and the flow of energy that drives this process.

Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales.

Analyze and interpret data on the distribution of fossils and rocks, continental shapes, and seafloor structures to provide evidence of past plate motions.

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.

Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their effects.

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution.

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each.

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.

Apply Newton’s Third Law to design a solution to a problem involving the motion of two colliding objects.

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.

Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects.

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.

Apply scientific principles to design, construct, and test a device that either minimizes or maximizes thermal energy transfer.

Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.

Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials.

Integrate qualitative scientific and technical information to support the claim that digitized signals are a more reliable way to encode and transmit information than analog signals.

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.

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.

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.

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.

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.

Gather and synthesize information about the technologies that have changed the way humans influence the inheritance of desired traits in organisms.

Use mathematical representations to support explanations of how natural selection may lead to increases and decreases of specific traits in populations over time.

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.

Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system.

Analyze and interpret data to determine scale properties of objects in the solar system.

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.

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

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.

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.

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.

Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms and trends in the periodic table.

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.

Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends upon the changes in total bond energy.

Apply scientific principles and evidence to provide an explanation about the effects of changing temperature or concentration on the rate at which a reaction occurs.

Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium.

Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.

Develop models to illustrate changes in the nucleus of the atom and the energy released during fission, fusion, and radioactive decay.

Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among net force, mass, and acceleration.

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.

Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.

Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict gravitational and electrostatic forces between objects.

Plan and conduct an investigation to provide evidence that an electric current can produce a magnetic field and vice versa.

Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials.

Create a computational model to calculate the change in the energy of one component in a system when energy flows are known.

Develop and use a model to illustrate that energy at the macroscopic scale is a combination of particle motion and relative position.

Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.

Plan and conduct an investigation to provide evidence that thermal energy transfer results in a more uniform energy distribution (second law of thermodynamics).

Develop and use a model of two objects interacting through electric or magnetic fields to illustrate forces and changes in energy.

Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media.

Evaluate questions about the advantages of using digital transmission and storage of information.

Evaluate claims, evidence, and reasoning that electromagnetic radiation can be described either by a wave model or a particle model.

Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter.

Communicate technical information about how technological devices use wave behavior and interactions with matter to transmit and capture information and energy.

Construct an explanation based on evidence for how the structure of DNA determines the structure of proteins which carry out essential life functions.

Develop and use a model to illustrate the hierarchical organization of interacting systems that provide specific functions within multicellular organisms.

Plan and conduct an investigation to provide evidence that feedback mechanisms maintain homeostasis.

Use a model to illustrate the role of cellular division (mitosis) and differentiation in producing and maintaining complex organisms.

Use a model to illustrate how photosynthesis transforms light energy into stored chemical energy.

Construct and revise an explanation for how carbon, hydrogen, and oxygen from sugar molecules combine with other elements to form large carbon-based molecules.

Use a model to illustrate that cellular respiration is a chemical process whereby bonds are broken and new compounds formed, resulting in energy transfer.

Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales.

Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems.

Construct and revise an explanation based on evidence for the cycling of matter and flow of energy in aerobic and anaerobic conditions.

Use mathematical representations to support claims for the cycling of matter and flow of energy among organisms in an ecosystem.

Develop a model to illustrate the role of photosynthesis and cellular respiration in the cycling of carbon among Earth's spheres.

Evaluate claims, evidence, and reasoning that complex interactions in ecosystems maintain stability, but changing conditions may result in a new ecosystem.

Design, evaluate, and refine a solution for reducing the impacts of human activities on the environment and biodiversity.

Evaluate the evidence for the role of group behavior on individual and species’ chances to survive and reproduce.

Ask questions to clarify relationships about the role of DNA and chromosomes in coding instructions for characteristic traits passed from parents to offspring.

Make and defend a claim based on evidence that inheritable genetic variations result from meiosis, replication errors, and/or environmental mutations.

Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.

Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence.

Construct an explanation based on evidence that evolution results from species potential, genetic variation, resource competition, and natural selection.

Apply concepts of statistics and probability to support explanations that organisms with advantageous traits tend to increase in proportion.

Construct an explanation based on evidence for how natural selection leads to adaptation of populations.

Evaluate evidence supporting claims that changes in environmental conditions may result in species increase, new species, or extinction.

Create or revise a simulation to test a solution to mitigate adverse impacts of human activity on biodiversity.

Develop a model based on evidence to illustrate the life span of the sun and the role of nuclear fusion in releasing energy.

Construct an explanation of the Big Bang theory based on astronomical evidence of light spectra, motion of galaxies, and matter composition.

Communicate scientific ideas about the way stars, over their life cycle, produce elements.

Use mathematical or computational representations to predict the motion of orbiting objects in the solar system.

Evaluate evidence of the movements of continental and oceanic crust and plate tectonics to explain the ages of crustal rocks.

Apply scientific reasoning and evidence from ancient Earth materials and meteorites to construct an account of Earth’s formation and history.

Develop a model to illustrate how Earth’s internal and surface processes operate at different scales to form continental and ocean-floor features.

Analyze geoscience data to make the claim that one change to Earth’s surface can create feedbacks that cause changes to other Earth systems.

Develop a model based on evidence of Earth’s interior to describe the cycling of matter by thermal convection.

Use a model to describe how variations in the flow of energy into and out of Earth’s systems result in changes in climate.

Plan and conduct an investigation of the properties of water and its effects on Earth materials and surface processes.

Develop a quantitative model to describe the cycling of carbon among the hydrosphere, atmosphere, geosphere, and biosphere.

Construct an argument based on evidence about the simultaneous coevolution of Earth’s systems and life on Earth.

Construct an explanation based on evidence for how natural resources, hazards, and climate change have influenced human activity.

Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.

Create a computational simulation to illustrate relationships among resource management, human population sustainability, and biodiversity.

Evaluate or refine a technological solution that reduces impacts of human activities on natural systems.

Analyze geoscience data and global climate models to make an evidence-based forecast of the current rate of climate change and future impacts.

Use a computational representation to illustrate the relationships among Earth systems and how they are modified by human activity.

Analyze a major global challenge to specify qualitative and quantitative criteria and constraints for solutions that account for societal needs.

Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems.

Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs including cost, safety, and environmental impacts.

Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints.

State and clarify one's point of view.

Evaluate the fairness of one's point of view.

State own viewpoints on fairness and listen to the viewpoints of classmates and teacher.

Retell a sequence of events that have happened over time.

Demonstrate how to ask questions about the classroom and school community.

Share their own viewpoints and give respectful attention to the viewpoints of others.

Use a graphic organizer to explain the beginning, middle, and end of a story.

Recognize a key ideal of justice and fairness within the context of the classroom community.

Explain the purpose of rules in the classroom.

Know the people and the roles that make and carry out rules in the classroom.

Demonstrate how rules provide structure for problem solving within the classroom.

Identify names and locations of tribal nations and bands in your area.

Identify key technologies and natural resources tribal nations and bands in their area valued prior to contact.

Understand key values, relationships, and characteristics tribes in their area had prior to contact.

Be a contributing member of the classroom and school community.

Demonstrate that good citizenship is to follow the established rules of a classroom and school community.

Explain, give examples, and demonstrate ways to show good citizenship in the classroom and school community.

Explain the difference between a need and a want.

Explain why people have to make choices between needs and wants.

Identify consumers and producers.

List and provide examples of goods and services.

Identify public and private providers of goods and services.

Describe goods that are produced in local geographic regions.

Recognize one's classroom and school as distinct environments based on physical characteristics and expectations.

Explain how weather, climate, and other environmental characteristics affect people's lives in a place or region.

Identify natural events or physical features such as air, water, land, or wind.

Describe how environment affects one's own activities.

Describe how the things we use in our lives come from different locations.

Demonstrate that a timeline represents a chronological sequence of events.

Describe the factors that influence an individual student's life.

Explain how their actions may cause change in others.

Demonstrate the importance of listening to other points of view in the classroom and on the playground.