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. (See grade K Language standards 4-6 for additional expectations.) CA

Recognize common types of texts (e.g., storybooks, poems, fantasy, realistic text). CA

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

With prompting and support, describe the relationship between illustrations and the story in which they appear.

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.

Activate prior knowledge related to the information and events in texts. CA

Use illustrations and context to make predictions about text. CA

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 in a text.

With prompting and support, ask and answer questions about unknown words in a text. (See grade K Language standards 4-6 for additional expectations.) CA

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 in presenting the ideas or information in a text.

With prompting and support, describe the relationship between illustrations and the text in which they appear.

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.

Activate prior knowledge related to the information and events in texts. CA

Use illustrations and context to make predictions about text. CA

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 (phonemes) in three-phoneme (CVC) words.

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

Blend two to three phonemes into recognizable words. CA

Know and apply grade-level phonics and word analysis skills in decoding words both in isolation and in text. CA

Demonstrate basic knowledge of one-to-one letter-sound correspondences by producing the primary sounds for each consonant.

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

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

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

Read emergent-reader texts with purpose and understanding.

Use a combination of drawing, dictating, and writing to compose opinion pieces.

Use a combination of drawing, dictating, and writing to compose informative/explanatory texts.

Use a combination of 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 and add details 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.

With guidance and support from adults, recall information from experiences or gather information from provided sources 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 about key details.

Understand and follow one- and two-step oral directions. CA

Ask and answer questions in order to seek help, get information, or clarify something that is 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/ (e.g., dog, dogs; wish, wishes).

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 based on kindergarten reading and content.

Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck).

Use the most frequently occurring inflections and affixes (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word.

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 the categories represent.

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

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

Distinguish shades of meaning among verbs describing the same general action (e.g., walk, march, strut, prance) 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. (See grade 1 Language standards 4-6 for additional expectations.) CA

Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types.

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.

(Not applicable to literature)

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.

Activate prior knowledge related to the information and events in a text. CA

Confirm predictions about what will happen next in a text. CA

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. (See grade 1 Language standards 4-6 for additional expectations.) CA

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

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

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 (e.g., in illustrations, descriptions, or procedures).

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

Activate prior knowledge related to the information and events in a text. CA

Confirm predictions about what will happen next in a text. CA

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 both in isolation and in text. CA

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 in a printed word.

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 on-level text with purpose and understanding.

Read on-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 or name the book, state an opinion, supply a reason, and provide closure.

Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.

Write narratives in which they recount two or more sequenced events, include details, use temporal words, and provide closure.

(Begins in grade 2) CA

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

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 (e.g., explore a number of “how-to” books and use them to write instructions).

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

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

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 or through other media.

Give, restate, and follow simple two-step directions. CA

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

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

Memorize and recite poems, rhymes, and songs with expression. CA

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 (subject, object), possessive, and indefinite pronouns. CA

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. CA

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

(Begins in grade 2)

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 1 reading and content.

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 from adults, 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. (See grade 2 Language standards 4-6 for additional expectations.) CA

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 (e.g., Cinderella stories) 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 multiparagraph 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. (See grade 2 Language standards 4-6.) CA

Know and use various text features (e.g., captions, bold print, subheadings, glossaries, indexes) to locate key facts or information efficiently.

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

Explain how specific images (e.g., a diagram showing how a machine works) 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 both in isolation and in text. CA

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 on-level text with purpose and understanding.

Read on-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 to describe actions and feelings, use temporal words, and provide closure.

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

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 (e.g., read a number of books on a single topic to produce a report).

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

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

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

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

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.

Give and follow three- and four-step oral directions. CA

Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, 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 when appropriate.

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.

Create readable documents with legible print. CA

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 (e.g., cage -> badge; boy -> boil).

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 (e.g., happy/unhappy).

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

Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g., birdhouse, bookshelf).

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

Demonstrate understanding of word relationships and nuances in word meanings.

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

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

Use words and phrases acquired through conversations, reading, and responding to texts, including using adjectives and adverbs to describe.

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 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, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band.

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 language that pertains to time and sequence.

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 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.

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 and proficiently.

Know and apply grade-level phonics and word analysis skills in decoding words both in isolation and in text. CA

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 on-level text with purpose and understanding.

Read on-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 they are writing about, 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, for example) 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 to aiding comprehension.

Develop the topic with facts, definitions, and details.

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

Provide a concluding statement or section.

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

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

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

Use temporal words and phrases to signal event order.

Provide a sense of 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 (using keyboarding skills) as well as to interact and collaborate.

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 on sources and sort evidence into provided categories.

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 to explore ideas under discussion.

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, descriptive details, speaking clearly at an understandable pace.

Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate.

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. CA

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, position-based spellings, 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 words 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, both print and digital, 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 found in mythology. CA

Explain major differences between poems, drama, and prose, and refer to the structural elements of poems and drama when writing or speaking about a text.

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

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 from different cultures.

By the end of the year, read and comprehend literature, including stories, dramas, and poetry, 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, based on specific information in the text.

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

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

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

Interpret information presented visually, orally, or quantitatively and explain how the information 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 accurately unfamiliar multisyllabic words.

Read with sufficient accuracy and fluency to support comprehension.

Read on-level text with purpose and understanding.

Read on-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 in which related ideas are grouped.

Provide reasons that are supported by facts and details.

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

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, illustrations, and multimedia.

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, including the Internet, to produce and publish writing.

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

Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and provide a list of sources.

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 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 and carry out assigned roles.

Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion.

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; speak clearly at an understandable pace.

Plan and deliver a narrative presentation that: recounts a well-elaborated event, includes details, reflects a logical sequence, and provides a conclusion. CA

Add audio recordings and visual displays to presentations when appropriate to enhance the development of 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 (e.g., a small red bag rather than a red small bag).

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).

Write fluidly and legibly in cursive or joined italic. CA

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 based on grade 4 reading and content.

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 the meaning of 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 at the high end of the grades 4-5 text complexity band independently and proficiently.

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 of events, ideas, concepts, 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 quickly.

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 at the high end of the grades 4-5 text complexity band independently.

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 accurately 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 in which ideas are grouped to support the purpose.

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.

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

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.

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 that unfolds naturally.

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

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.

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.

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

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

Apply grade 5 Reading standards to informational texts (e.g., 'Explain how an author uses reasons and 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 to explore ideas.

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, and identify and analyze any logical fallacies. (CA)

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

Plan and deliver an opinion speech that states an opinion, logically sequences evidence, and provides a concluding statement. (CA)

Memorize and recite a poem or section of a speech or historical document using rate, expression, and gestures appropriate to the selection. (CA)

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.

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

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).

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

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.

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

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.

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content.

Use context 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.

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

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 distinct from personal opinions.

Describe how a particular story's or drama's plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution.

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

Analyze how a particular sentence, chapter, scene, or stanza fits into the overall structure of a text and contributes to the development of the theme, setting, 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 story, drama, or poem to listening to or viewing an audio, video, or live version of the text.

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, including stories, dramas, and poems, 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 distinct from personal opinions or judgments.

Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes).

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

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

Analyze the use of text features (e.g., graphics, headers, captions) in popular media. (CA Addition)

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 (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.

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

Compare and contrast one author's presentation of events with that of another (e.g., a memoir written by and a biography on the same person).

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 and demonstrating an understanding of the topic or text.

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 through the selection, organization, and analysis of relevant content.

Introduce a topic or thesis statement; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect. (CA Addition)

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

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, relevant descriptive details, and well-structured event sequences.

Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

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 convey experiences and events.

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, 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 as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills.

Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.

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

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

Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues.

Come to discussions prepared, having read or studied required material; explicitly draw on that preparation by referring to evidence on the topic, text, or issue.

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

Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion.

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

Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study.

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

Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes.

Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information.

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.

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).

Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons. (CA Addition)

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

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 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 or phrase.

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

Consult reference materials (e.g., dictionaries, glossaries, thesauruses) 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., personification) in context.

Use the relationship between particular words (e.g., cause/effect, part/whole, item/category) to better understand each of the words.

Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., stingy, scrimping, economical, unwasteful, thrifty).

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

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.

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, including figurative and connotative meanings; analyze the impact of rhymes and repetitions of sounds.

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.

Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period.

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

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.

Analyze the interactions between individuals, events, and ideas in a text.

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

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

Analyze the use of text features (e.g., graphics, headers, captions) in public documents.

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.

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

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 address 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.

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 selection and analysis of relevant content.

Introduce a topic or thesis statement clearly; organize ideas using strategies like definition or classification; include formatting and graphics.

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 a logical 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; quote or paraphrase the data and conclusions of others while avoiding plagiarism.

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, building on others' ideas and expressing their own clearly.

Come to discussions prepared, having read or researched material; 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.

Delineate a speaker's argument and specific claims, and attitude toward the subject, evaluating the soundness of reasoning and relevance of 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 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 to find the pronunciation of a word or determine its precise meaning or its part of speech.

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., 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.

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

Cite specific textual evidence to support analysis of primary and secondary sources.

Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source.

Identify key steps in a text's description of a process related to history/social studies.

Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies.

Describe how a text presents information (e.g., sequentially, comparatively, causally).

Identify aspects of a text that reveal an author's point of view or purpose.

Integrate visual information with other information in print and digital texts.

Distinguish among fact, opinion, and reasoned judgment in a text.

Analyze the relationship between a primary and secondary source on the same topic.

By the end of grade 8, read and comprehend history/social studies texts in the grades 6-8 text complexity band independently and proficiently.

Cite specific textual evidence to support analysis of science and technical texts.

Determine the central ideas or conclusions of a text; provide an accurate summary of the text.

Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

Determine the meaning of symbols, key terms, and other domain-specific words and phrases used in a scientific or technical context.

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

Analyze the author's purpose in providing an explanation, describing a procedure, or discussing an experiment in a text.

Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually.

Distinguish among facts, reasoned judgments based on research findings, and speculation in a text.

Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text.

By the end of grade 8, read and comprehend science/technical texts in the grades 6-8 text complexity band independently and proficiently.

Write arguments focused on discipline-specific content.

Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.

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, or rewriting.

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

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

Gather relevant information from multiple print and digital sources; quote or paraphrase the data and conclusions of others while avoiding plagiarism.

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

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

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.

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, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone.

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 at the high end of grades 6–8 text complexity band independently and proficiently.

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.

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

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

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 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 at the high end of the grades 6–8 text complexity band independently and 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, including career development documents (e.g., simple business letters and job applications), to examine a topic and convey ideas.

Introduce a topic or thesis statement clearly, previewing what is to follow; organize ideas into broader categories; include formatting and multimedia.

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 and introducing a narrator and/or characters; organize an event sequence.

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, 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.

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

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, building on others’ ideas and expressing their own clearly.

Come to discussions prepared, having read or researched material; 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.

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

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.

Plan and present a narrative that establishes context, presents a logical sequence, uses narrative techniques, and provides a conclusion.

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 and sound valid reasoning.

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 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, part of speech, or etymology.

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 of words with similar denotations.

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

Cite specific textual evidence to support analysis of primary and secondary sources.

Determine the central ideas or information of a primary or secondary source; provide an accurate summary.

Identify key steps in a text’s description of a process related to history/social studies.

Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to history/social studies.

Describe how a text presents information (e.g., sequentially, comparatively, causally).

Identify aspects of a text that reveal an author’s point of view or purpose.

Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.

Distinguish among fact, opinion, and reasoned judgment in a text.

Analyze the relationship between a primary and secondary source on the same topic.

By the end of grade 8, read and comprehend history/social studies texts in the grades 6–8 text complexity band independently.

Cite specific textual evidence to support analysis of science and technical texts.

Determine the central ideas or conclusions of a text; provide an accurate summary of the text.

Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

Determine the meaning of symbols, key terms, and other domain-specific words and phrases in scientific or technical contexts.

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

Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text.

Integrate quantitative or technical information expressed in words with a version expressed visually.

Distinguish among facts, reasoned judgment based on research findings, and speculation in a text.

Compare and contrast information gained from experiments, simulations, or multimedia with that gained from reading a text.

By the end of grade 8, read and comprehend science/technical texts in the grades 6–8 text complexity band independently.

Write arguments focused on discipline-specific content.

Write informative/explanatory texts, including the narration of historical events, scientific procedures, or technical processes.

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

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

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

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

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

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

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

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 word choice impact.

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

Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States.

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

Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme from Ovid).

By the end of grade 9, read and comprehend literature in the grades 9-10 text complexity band proficiently, with scaffolding as needed.

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.

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

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.

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 evidence is sufficient.

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

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

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

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.

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

Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately.

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

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

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

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

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 usefulness.

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

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

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

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

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

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 justify 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 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.

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

Use parallel structure.

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

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

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.

Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style.

Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabian's Manual for Writers).

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9-10 reading and content.

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

Identify and correctly utilize 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.

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

Interpret figures of speech (e.g., euphemism, oxymoron) 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 specific textual evidence to support analysis of primary and secondary sources, attending to features like date and origin.

Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events develop.

Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them.

Determine the meaning of words and phrases as they are used in a text, including vocabulary describing political, social, or economic aspects.

Analyze how a text uses structure to emphasize key points or advance an explanation or analysis.

Compare the point of view of two or more authors for how they treat the same or similar topics, including which details they include.

Integrate quantitative or technical analysis with qualitative analysis in print or digital text.

Assess the extent to which the reasoning and evidence in a text support the author's claims.

Compare and contrast treatments of the same topic in several primary and secondary sources.

By the end of grade 10, read and comprehend history/social studies texts in the grades 9-10 text complexity band independently.

Cite specific textual evidence to support analysis of science and technical texts, attending to precise details of explanations.

Determine the central ideas or conclusions of a text; trace the text's explanation or depiction of a complex process, phenomenon, or concept.

Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific context.

Analyze the structure of the relationships among concepts in a text, including relationships among key terms.

Analyze the author's purpose in providing an explanation, describing a procedure, or discussing an experiment in a text.

Translate quantitative or technical information expressed in words in a text into visual form and translate information expressed visually into words.

Assess the extent to which the reasoning and evidence in a text support the author's claim or a recommendation for solving a problem.

Compare and contrast findings presented in a text to those from other sources, noting when the findings support or contradict previous explanations.

By the end of grade 10, read and comprehend science/technical texts in the grades 9-10 text complexity band independently.

Write arguments focused on discipline-specific content.

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 data and evidence for each while pointing out strengths and limitations.

Use words, phrases, and clauses 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.

Write informative/explanatory texts, including the narration of historical events, scientific procedures, or technical processes.

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

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

Use varied transitions and sentence structures to link the major sections of the text and create cohesion.

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 of the discipline.

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

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.

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

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

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining 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, including how they interact and build on one another; provide an objective summary.

Analyze the impact of the author's choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how characters are introduced).

Determine the meaning of words and phrases, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone. (Include Shakespeare as well as other authors.) CA

Analyze how an author's choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its structure.

Analyze a case in which grasping point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement).

Analyze multiple interpretations of a story, drama, or poem, evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.) CA

Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics. CA

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

Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining 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, including how they interact and build on one another; 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, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term.

Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging.

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, persuasiveness or beauty of the text.

Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words 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 and the premises, purposes, and arguments in works of public advocacy.

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

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

Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

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

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, focusing on addressing what is most significant for a specific purpose and audience.

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

Conduct short as well as more sustained research projects to answer a question or solve a problem; narrow or broaden the inquiry; synthesize multiple sources on the subject.

Gather relevant information from multiple authoritative print and digital sources; assess the strengths and limitations of each source; integrate information selectively to maintain flow and avoid plagiarism.

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

Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

Initiate and participate effectively in a range of collaborative discussions with diverse partners on grades 11–12 topics, texts, and issues, building on others' ideas and expressing their own clearly.

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

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

Present information, findings, and supporting evidence, conveying a clear and distinct perspective; ensure the organization, development, substance, and style are appropriate to purpose and audience.

Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) 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.

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

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

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

Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 11–12 reading and content, choosing flexibly from a range of strategies.

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

Acquire and use accurately general academic and domain-specific words and phrases; demonstrate independence in gathering vocabulary knowledge.

Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights gained from specific details to an understanding of the text as a whole.

Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas.

Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain.

Determine the meaning of words and phrases as they are used in a text, including analyzing how an author uses and refines the meaning of a key term over the course of a text.

Analyze in detail how a complex primary source is structured, including how key sentences, paragraphs, and larger portions of the text contribute to the whole.

Evaluate authors' differing points of view on the same historical event or issue by assessing the authors' claims, reasoning, and evidence.

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

Evaluate an author's premises, claims, and evidence by corroborating or challenging them with other information.

Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources.

By the end of grade 12, read and comprehend history/social studies texts in the grades 11–CCR text complexity band independently and proficiently.

Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account.

Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.

Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.

Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics.

Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas.

Analyze the author's purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved.

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

Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information.

Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information.

By the end of grade 12, read and comprehend science/technical texts in the grades 11–CCR text complexity band independently and proficiently.

Write arguments focused on discipline-specific content.

Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.

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, focusing on addressing what is most significant for a specific purpose and audience.

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

Conduct short as well as more sustained research projects to answer a question or solve a problem; narrow or broaden the inquiry; synthesize multiple sources on the subject.

Gather relevant information from multiple authoritative print and digital sources; assess the strengths and limitations of each source; integrate information selectively to maintain flow.

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

Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks.

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 (with 0 representing a count of no objects).

Understand the relationship between numbers and quantities; connect counting to cardinality.

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

Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

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 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration.

Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

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

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

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation.

For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Fluently add and subtract within 5.

Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation.

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 of”/“less of” the attribute, and describe the difference.

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

Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

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, in different sizes and orientations, using informal language to describe their similarities, differences, parts and other attributes.

Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

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. (Commutative property of addition.)

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 making ten; decomposing a number leading to a ten.

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.

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, using concrete models or drawings and strategies.

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.

Relate time to events (e.g., before/after, yesterday/today/tomorrow). (CA Addition)

Identify the value of coins (e.g., penny, nickel, dime, quarter). (CA Addition)

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 (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size).

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 2s, 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.

Use estimation strategies to make reasonable estimates in problem solving.

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. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).

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 put-together, take-apart, and compare problems using information 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.

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.

Understand division as an unknown-factor problem.

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

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.

Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones.

Fluently add and subtract within 1000 using strategies and algorithms based on place value and properties of operations.

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

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.

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.

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 time.

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.

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.

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.

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world 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.

Solve real world and mathematical problems involving perimeters of polygons.

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, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.

Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems with whole numbers using the four operations, including problems with remainders. Represent problems using equations with a letter for the unknown.

Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine if a number is prime or composite.

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Recognize 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 and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers using >, =, and < symbols.

Use place value understanding to round multi-digit whole numbers to any place.

Fluently 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, using strategies based on place value and properties of operations.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value and properties of operations.

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models. Use this principle to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole.

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Understand a fraction a/b as a multiple of 1/b.

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

Use decimal notation for fractions with denominators 10 or 100.

Compare two decimals to hundredths by reasoning about their size. Record the results of comparisons with the symbols >, =, or <.

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals.

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 (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions using line plots.

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

An angle is measured with reference to a circle with its center at the common endpoint of the rays. An angle that turns through 1/360 of a circle is called a 'one-degree angle'.

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

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 in real-world and mathematical problems.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), 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 the presence or absence of angles of a specified size. Identify right triangles.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures.

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.

Express a whole number in the range 2–50 as a product of its prime factors.

Generate two numerical patterns using two given rules. Identify relationships between corresponding terms and graph ordered pairs on a coordinate plane.

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 its left.

Explain patterns in the number of zeros of the product when multiplying by powers of 10, and patterns in the placement of the decimal point.

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.

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.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value.

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.

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.

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths.

Interpret multiplication as scaling (resizing).

Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the multiplication.

Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number.

Solve real world problems involving multiplication of fractions and mixed numbers.

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 problems.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

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.

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.

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes.

Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms.

Use a pair of perpendicular number lines, called axes, to define a coordinate system.

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane.

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.

Understand the concept of a ratio and 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.

Use ratio and rate reasoning to solve real-world and mathematical problems.

Make tables of equivalent ratios, find missing values, and plot pairs of values 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 percent.

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately.

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

Fluently divide multi-digit numbers using the standard algorithm.

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Find the greatest common factor of two whole numbers ≤ 100 and the least common multiple of two whole numbers ≤ 12.

Understand that every positive whole number > 1 is prime or composite; write composite numbers as products of primes.

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes.

Recognize 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 number line diagram and on a coordinate plane.

Understand ordering and absolute value of rational numbers.

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Understand the absolute value of a rational number as its distance from 0 on the 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.

Write and evaluate numerical expressions involving whole-number exponents.

Write, read, and evaluate expressions 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 from real-world formulas.

Apply the properties of operations to generate equivalent expressions.

Identify when two expressions are equivalent (i.e., when the two expressions name the same number).

Understand solving an equation or inequality as a process of answering a question.

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.

Use variables to represent two quantities that change in relationship to one another.

Find the area of right triangles, other triangles, special quadrilaterals, and polygons.

Find the volume of a right rectangular prism with fractional edge lengths.

Draw polygons in the coordinate plane given coordinates for the vertices.

Represent three-dimensional figures using nets made up of rectangles and triangles.

Recognize a statistical question as one that anticipates variability in the data.

Understand that a set of data has a distribution which can be described by its center, spread, and shape.

Recognize that a measure of center summarizes values with one number, while variation describes spread.

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.

Give quantitative measures of center (median/mean) and variability (IQR/MAD).

Relate the choice of measures of center and variability 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. For example, if total cost t is proportional to the number n of items at price p, the relationship is t = pn.

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to (0, 0) and (1, r).

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups, gratuities, percent increase/decrease.

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent on a horizontal or vertical number line.

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its constituents are oppositely charged.

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). Show that the distance between two numbers is the absolute value.

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 of a rational number 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 and how the quantities in it are related.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically.

Use variables to represent quantities in a real-world or mathematical problem, 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, where p, q, and r are specific rational numbers.

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set.

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing.

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures.

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between them.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem 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 composed of triangles, quadrilaterals, etc.

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations are valid only if representative.

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples to gauge variation.

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers.

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

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 on the chance process that produces it and observing its long-run relative frequency.

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies.

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

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, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

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 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.

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 in the coordinate plane.

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 consisting of an input and the corresponding output.

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 from a description or from two (x, y) values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).

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, about 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. For scatter plots that suggest a linear association, informally fit a straight line.

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.

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.

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas.

Define appropriate quantities for the purpose of descriptive modeling.

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Interpret expressions that represent a quantity in terms of its context.

Interpret parts of an expression, such as terms, factors, and coefficients.

Interpret complicated expressions by viewing one or more of their parts as a single entity.

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.

Factor a quadratic expression to reveal the zeros of the function it defines.

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function.

Use the properties of exponents to transform expressions for exponential functions.

Understand that polynomials form a system analogous to the integers, namely, they are closed under addition, subtraction, and multiplication.

Create equations and inequalities in one variable and use them to solve problems.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities.

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 linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Solve one-step linear equations in one variable.

Solve quadratic equations in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q.

Solve quadratic equations by inspection, square roots, completing the square, quadratic formula, and factoring.

Prove that 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, focusing on pairs of linear equations in two variables.

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

Explain why the x-coordinates of the points where the graphs of y = f(x) and y = g(x) intersect are the solutions of f(x) = g(x).

Graph the solutions to a linear inequality in two variables as a half-plane.

Understand that a function 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.

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 for a function that models a relationship.

Relate the domain of a function to its graph and to the quantitative relationship it describes.

Calculate and interpret the average rate of change of a function over a specified interval.

Graph functions expressed symbolically and show key features of the graph.

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties.

Use factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry.

Compare properties of two functions each represented in a different way.

Write a function that describes a relationship between two quantities.

Determine an explicit expression, a recursive process, or steps for calculation from a context.

Write arithmetic and geometric sequences both recursively and with an explicit formula.

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k).

Distinguish between situations that can be modeled with linear functions and with exponential functions.

Prove that linear functions grow by equal differences and exponential functions grow by equal factors.

Recognize situations in which one quantity changes at a constant rate per unit interval.

Recognize situations in which a quantity grows or decays by a constant percent rate.

Construct linear and exponential functions given a graph, description, or two input-output pairs.

Observe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Interpret the parameters in a linear or exponential function in terms of a context.

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.

Interpret differences in shape, center, and spread in the context of the data sets, accounting for outliers.

Summarize categorical data for two categories in two-way frequency tables.

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Fit a function to the data; use functions fitted to data to solve problems.

Informally assess the fit of a function by plotting and analyzing residuals.

Fit a linear function for a scatter plot that suggests a linear association.

Interpret the slope and the intercept of a linear model in the context of the data.

Compute and interpret the correlation coefficient of a linear fit.

Distinguish between correlation and causation.

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment.

Represent transformations in the plane; describe transformations as functions.

Describe the rotations and reflections that carry a rectangle, parallelogram, trapezoid, or regular polygon onto itself.

Develop definitions of rotations, reflections, and translations in terms of angles, circles, and lines.

Draw the transformed figure using graph paper, tracing paper, or geometry software.

Use geometric descriptions of rigid motions to transform figures and to predict the effect.

Use the definition of congruence in terms of rigid motions to show triangle congruence.

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from 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.

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.

Use the definition of similarity in terms of similarity transformations to decide if figures are similar.

Use the properties of similarity transformations to establish the AA criterion for similarity.

Prove theorems about triangles involving similarity.

Use congruence and similarity criteria for triangles to solve problems and prove relationships.

Understand that side ratios in right triangles are properties of the angles, leading to trigonometric ratios.

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.

Know and use the Pythagorean Theorem and its converse.

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.

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius.

Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

Derive the equation of a parabola given a focus and directrix.

Use coordinates to prove simple geometric theorems algebraically.

Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.

Find the point on a directed line segment that partitions the segment in a given ratio.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Give an informal argument for the formulas for circumference, area, and volume.

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Use geometric shapes, their measures, and their properties to describe objects.

Apply concepts of density based on area and volume in modeling situations.

Apply geometric methods to solve design problems.

Describe events as subsets of a sample space using characteristics of the outcomes.

Understand that two events are independent if the probability of both occurring is the product of their probabilities.

Understand conditional probability and interpret independence.

Construct and interpret two-way frequency tables of data.

Recognize and explain the concepts of conditional probability and independence in everyday language.

Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A.

Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B).

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, and explain why both represent the same number.

(+) 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.

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 vectors by directed line segments.

(+) Find the components of a vector by subtracting the coordinates of an initial point from a terminal point.

(+) Solve problems involving velocity and other quantities that can be represented by vectors.

(+) Add and subtract vectors using end-to-end, component-wise, and parallelogram methods.

(+) 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.

(+) 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 real numbers.

(+) Multiply a vector by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations.

(+) Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Derive the formula for the sum of a finite geometric series, and use the formula to solve problems.

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 using inspection, long division, or synthetic division.

(+) Understand that rational expressions form a system analogous to the rational numbers; add, subtract, multiply, and divide them.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

(+) 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.

Find inverse functions.

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

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.

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 domain on which it is always increasing or always decreasing 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.

(+) 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.

(+) Construct a tangent line from a point outside a given circle to the circle.

(+) 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.

Given a quadratic equation of the form ax^2 + by^2 + cx + dy + e = 0, use the method of completing the square to put the equation into standard form. (CA)

(+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

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 the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

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.

(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

(+) 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.

(+) Analyze decisions and strategies using probability concepts.

Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions.

Students prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions.

Students use graphical calculators to verify and estimate limits.

Students prove and use special limits, such as the limits of (sin(x))/x and (1-cos(x))/x as x tends to 0.

Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.

Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.

Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability.

Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.

Students demonstrate an understanding of the derivative as an instantaneous rate of change.

Students can use the limit definition to find the derivative of a function.

Students understand the relationship between differentiability and continuity.

Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.

Students find the derivatives of and use implicitly defined functions.

Students compute derivatives of higher orders.

Students know and can apply Rolle's theorem, the mean value theorem, and L'Hôpital's rule.

Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.

Students know Newton's method for approximating the zeros of a function.

Students use differentiation to solve optimization (maximum-minimum problems) in a variety of contexts.

Students use differentiation to solve related rate problems in a variety of contexts.

Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals.

Students apply the fundamental theorem of calculus to interpret a definite integral as a change in an antiderivative and to compute definite integrals of standard elementary functions.

Students use definite integrals to solve problems in various contexts, such as finding the area of a region, the volume of a solid, the length of a curve, and the average value of a function.

Students use substitution (change of variables) to compute indefinite and definite integrals.

Students use integration by parts to compute indefinite and definite integrals.

Students use partial fractions to compute indefinite and definite integrals.

Students use improper integrals to solve problems.

Students understand the concept of a differential equation and can solve simple separable differential equations.

Students use differential equations to model various phenomena.

Students understand the concept of a sequence and a series and can determine whether a sequence or a series converges or diverges.

Students understand and can use the integral test, the comparison test, the ratio test, and the root test to determine the convergence or divergence of a series.

Students understand and can use the concept of a power series and can find the radius and interval of convergence of a power series.

Students understand and can use Taylor series and Maclaurin series to represent functions.

Students understand and can use the concept of a vector-valued function and can find the derivative and integral of a vector-valued function.

Students understand and can use the concept of a polar coordinate system and can find the area of a region in polar coordinates.

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.

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 in darkness 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 survive and grow.

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 each.

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 or improved object.

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 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 of the problem.

Plan and carry out fair tests in which variables are controlled and failure points are considered to identify aspects that can be improved.