window._standardsHTML = "<select class=\"standards-ela\" multiple style=\"display:none;\"><option value=\"K.RL.1\">K.RL.1: With prompting and support, ask and answer questions about key details in a text.<\/option><option value=\"K.RL.2\">K.RL.2: With prompting and support, retell familiar stories, including key details.<\/option><option value=\"K.RL.3\">K.RL.3: With prompting and support, identify characters, settings, and major events in a story.<\/option><option value=\"K.RL.4\">K.RL.4: Ask and answer questions about unknown words in a text.<\/option><option value=\"K.RL.5\">K.RL.5: Recognize common types of texts (e.g., storybooks, poems).<\/option><option value=\"K.RL.6\">K.RL.6: With prompting and support, name the author and illustrator of a story and define the role of each in telling the story.<\/option><option value=\"K.RL.7\">K.RL.7: With prompting and support, describe the relationship between illustrations and the story in which they appear (e.g., what moment in a story an illustration depicts).<\/option><option value=\"K.RL.8\">K.RL.8: (Not applicable to literature)<\/option><option value=\"K.RL.9\">K.RL.9: With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories.<\/option><option value=\"K.RL.10\">K.RL.10: Actively engage in group reading activities with purpose and understanding.<\/option><option value=\"1.RL.1\">1.RL.1: Ask and answer questions about key details in a text.<\/option><option value=\"1.RL.2\">1.RL.2: Retell stories, including key details, and demonstrate understanding of their central message or lesson.<\/option><option value=\"1.RL.3\">1.RL.3: Describe characters, settings, and major events in a story, using key details.<\/option><option value=\"1.RL.4\">1.RL.4: Identify words and phrases in stories or poems that suggest feelings or appeal to the senses.<\/option><option value=\"1.RL.5\">1.RL.5: Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types.<\/option><option value=\"1.RL.6\">1.RL.6: Identify who is telling the story at various points in a text.<\/option><option value=\"1.RL.7\">1.RL.7: Use illustrations and details in a story to describe its characters, setting, or events.<\/option><option value=\"1.RL.8\">1.RL.8: (Not applicable to literature)<\/option><option value=\"1.RL.9\">1.RL.9: Compare and contrast the adventures and experiences of characters in stories.<\/option><option value=\"1.RL.10\">1.RL.10: With prompting and support, read prose and poetry of appropriate complexity for grade 1.<\/option><option value=\"2.RL.1\">2.RL.1: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.<\/option><option value=\"2.RL.2\">2.RL.2: Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral.<\/option><option value=\"2.RL.3\">2.RL.3: Describe how characters in a story respond to major events and challenges.<\/option><option value=\"2.RL.4\">2.RL.4: Describe how words and phrases (e.g., regular beats, alliteration, rhymes, repeated lines) supply rhythm and meaning in a story, poem, or song.<\/option><option value=\"2.RL.5\">2.RL.5: Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action.<\/option><option value=\"2.RL.6\">2.RL.6: Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud.<\/option><option value=\"2.RL.7\">2.RL.7: Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot.<\/option><option value=\"2.RL.8\">2.RL.8: (Not applicable to literature)<\/option><option value=\"2.RL.9\">2.RL.9: Compare and contrast two or more versions of the same story (e.g., Cinderella stories) by different authors or from different cultures.<\/option><option value=\"2.RL.10\">2.RL.10: By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2\u20133 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"3.RL.1\">3.RL.1: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.<\/option><option value=\"3.RL.2\">3.RL.2: Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text.<\/option><option value=\"3.RL.3\">3.RL.3: Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events.<\/option><option value=\"3.RL.4\">3.RL.4: Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language.<\/option><option value=\"3.RL.5\">3.RL.5: Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections.<\/option><option value=\"3.RL.6\">3.RL.6: Distinguish their own point of view from that of the narrator or those of the characters.<\/option><option value=\"3.RL.7\">3.RL.7: Explain how specific aspects of a text\u2019s illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting).<\/option><option value=\"3.RL.8\">3.RL.8: (Not applicable to literature)<\/option><option value=\"3.RL.9\">3.RL.9: Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series).<\/option><option value=\"3.RL.10\">3.RL.10: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2\u20133 text complexity band independently and proficiently.<\/option><option value=\"4.RL.1\">4.RL.1: Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.<\/option><option value=\"4.RL.2\">4.RL.2: Determine a theme of a story, drama, or poem from details in the text; summarize the text.<\/option><option value=\"4.RL.3\">4.RL.3: Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character\u2019s thoughts, words, or actions).<\/option><option value=\"4.RL.4\">4.RL.4: Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean).<\/option><option value=\"4.RL.5\">4.RL.5: Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text.<\/option><option value=\"4.RL.6\">4.RL.6: Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations.<\/option><option value=\"4.RL.7\">4.RL.7: Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text.<\/option><option value=\"4.RL.8\">4.RL.8: (Not applicable to literature)<\/option><option value=\"4.RL.9\">4.RL.9: Compare and contrast the treatment of similar themes and topics (e.g., opposition of good and evil) and patterns of events (e.g., the quest) in stories, myths, and traditional literature from different cultures.<\/option><option value=\"4.RL.10\">4.RL.10: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4\u20135 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"5.RL.1\">5.RL.1: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.<\/option><option value=\"5.RL.2\">5.RL.2: Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text.<\/option><option value=\"5.RL.3\">5.RL.3: Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact).<\/option><option value=\"5.RL.4\">5.RL.4: Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes.<\/option><option value=\"5.RL.5\">5.RL.5: Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem.<\/option><option value=\"5.RL.6\">5.RL.6: Describe how a narrator\u2019s or speaker\u2019s point of view influences how events are described.<\/option><option value=\"5.RL.7\">5.RL.7: Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel, multimedia presentation of fiction, folktale, myth, poem).<\/option><option value=\"5.RL.8\">5.RL.8: (Not applicable to literature)<\/option><option value=\"5.RL.9\">5.RL.9: Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics.<\/option><option value=\"5.RL.10\">5.RL.10: By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4\u20135 text complexity band independently and proficiently.<\/option><option value=\"K.RI.1\">K.RI.1: With prompting and support, ask and answer questions about key details in a text.<\/option><option value=\"K.RI.2\">K.RI.2: With prompting and support, identify the main topic and retell key details of a text.<\/option><option value=\"K.RI.3\">K.RI.3: With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text.<\/option><option value=\"K.RI.4\">K.RI.4: With prompting and support, ask and answer questions about unknown words in a text.<\/option><option value=\"K.RI.5\">K.RI.5: Identify the front cover, back cover, and title page of a book.<\/option><option value=\"K.RI.6\">K.RI.6: Name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text.<\/option><option value=\"K.RI.7\">K.RI.7: With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts).<\/option><option value=\"K.RI.8\">K.RI.8: With prompting and support, identify the reasons an author gives to support points in a text.<\/option><option value=\"K.RI.9\">K.RI.9: With prompting and support, identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures).<\/option><option value=\"K.RI.10\">K.RI.10: Actively engage in group reading activities with purpose and understanding.<\/option><option value=\"1.RI.1\">1.RI.1: Ask and answer questions about key details in a text.<\/option><option value=\"1.RI.2\">1.RI.2: Identify the main topic and retell key details of a text.<\/option><option value=\"1.RI.3\">1.RI.3: Describe the connection between two individuals, events, ideas, or pieces of information in a text.<\/option><option value=\"1.RI.4\">1.RI.4: Ask and answer questions to help determine or clarify the meaning of words and phrases in a text.<\/option><option value=\"1.RI.5\">1.RI.5: Know and use various text features (e.g., headings, tables of contents, glossaries, electronic menus, icons) to locate key facts or information in a text.<\/option><option value=\"1.RI.6\">1.RI.6: Distinguish between information provided by pictures or other illustrations and information provided by the words in a text.<\/option><option value=\"1.RI.7\">1.RI.7: Use the illustrations and details in a text to describe its key ideas.<\/option><option value=\"1.RI.8\">1.RI.8: Identify the reasons an author gives to support points in a text.<\/option><option value=\"1.RI.9\">1.RI.9: Identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures).<\/option><option value=\"1.RI.10\">1.RI.10: With prompting and support, read informational texts appropriately complex for grade 1.<\/option><option value=\"2.RI.1\">2.RI.1: Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text.<\/option><option value=\"2.RI.2\">2.RI.2: Identify the main topic of a multiparagraph text as well as the focus of specific paragraphs within the text.<\/option><option value=\"2.RI.3\">2.RI.3: Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.<\/option><option value=\"2.RI.4\">2.RI.4: Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area.<\/option><option value=\"2.RI.5\">2.RI.5: Know and use various text features (e.g., captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently.<\/option><option value=\"2.RI.6\">2.RI.6: Identify the main purpose of a text, including what the author wants to answer, explain, or describe.<\/option><option value=\"2.RI.7\">2.RI.7: Explain how specific images (e.g., a diagram showing how a machine works) contribute to and clarify a text.<\/option><option value=\"2.RI.8\">2.RI.8: Describe how reasons support specific points the author makes in a text.<\/option><option value=\"2.RI.9\">2.RI.9: Compare and contrast the most important points presented by two texts on the same topic.<\/option><option value=\"2.RI.10\">2.RI.10: By the end of year, read and comprehend informational texts, including history\/social studies, science, and technical texts, in the grades 2\u20133 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"3.RI.1\">3.RI.1: Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.<\/option><option value=\"3.RI.2\">3.RI.2: Determine the main idea of a text; recount the key details and explain how they support the main idea.<\/option><option value=\"3.RI.3\">3.RI.3: Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause\/effect.<\/option><option value=\"3.RI.4\">3.RI.4: Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area.<\/option><option value=\"3.RI.5\">3.RI.5: Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently.<\/option><option value=\"3.RI.6\">3.RI.6: Distinguish their own point of view from that of the author of a text.<\/option><option value=\"3.RI.7\">3.RI.7: Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur).<\/option><option value=\"3.RI.8\">3.RI.8: Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause\/effect, first\/second\/third in a sequence).<\/option><option value=\"3.RI.9\">3.RI.9: Compare and contrast the most important points and key details presented in two texts on the same topic.<\/option><option value=\"3.RI.10\">3.RI.10: By the end of the year, read and comprehend informational texts, including history\/social studies, science, and technical texts, at the high end of the grades 2\u20133 text complexity band independently and proficiently.<\/option><option value=\"4.RI.1\">4.RI.1: Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text.<\/option><option value=\"4.RI.2\">4.RI.2: Determine the main idea of a text and explain how it is supported by key details; summarize the text.<\/option><option value=\"4.RI.3\">4.RI.3: Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text.<\/option><option value=\"4.RI.4\">4.RI.4: Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area.<\/option><option value=\"4.RI.5\">4.RI.5: Describe the overall structure (e.g., chronology, comparison, cause\/effect, problem\/solution) of events, ideas, concepts, or information in a text or part of a text.<\/option><option value=\"4.RI.6\">4.RI.6: Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided.<\/option><option value=\"4.RI.7\">4.RI.7: Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.<\/option><option value=\"4.RI.8\">4.RI.8: Explain how an author uses reasons and evidence to support particular points in a text.<\/option><option value=\"4.RI.9\">4.RI.9: Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.<\/option><option value=\"4.RI.10\">4.RI.10: By the end of year, read and comprehend informational texts, including history\/social studies, science, and technical texts, in the grades 4\u20135 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"5.RI.1\">5.RI.1: Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.<\/option><option value=\"5.RI.2\">5.RI.2: Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text.<\/option><option value=\"5.RI.3\">5.RI.3: Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text.<\/option><option value=\"5.RI.4\">5.RI.4: Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.<\/option><option value=\"5.RI.5\">5.RI.5: Compare and contrast the overall structure (e.g., chronology, comparison, cause\/effect, problem\/solution) of events, ideas, concepts, or information in two or more texts.<\/option><option value=\"5.RI.6\">5.RI.6: Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent.<\/option><option value=\"5.RI.7\">5.RI.7: Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently.<\/option><option value=\"5.RI.8\">5.RI.8: Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s).<\/option><option value=\"5.RI.9\">5.RI.9: Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably.<\/option><option value=\"5.RI.10\">5.RI.10: By the end of the year, read and comprehend informational texts, including history\/social studies, science, and technical texts, at the high end of the grades 4\u20135 text complexity band independently and proficiently.<\/option><option value=\"K.RF.1\">K.RF.1: Demonstrate understanding of the organization and basic features of print.<\/option><option value=\"K.RF.1.a\">K.RF.1.a: Follow words from left to right, top to bottom, and page by page.<\/option><option value=\"K.RF.1.b\">K.RF.1.b: Recognize that spoken words are represented in written language by specific sequences of letters.<\/option><option value=\"K.RF.1.c\">K.RF.1.c: Understand that words are separated by spaces in print.<\/option><option value=\"K.RF.1.d\">K.RF.1.d: Recognize and name all upper- and lowercase letters of the alphabet.<\/option><option value=\"K.RF.2\">K.RF.2: Demonstrate understanding of spoken words, syllables, and sounds (phonemes).<\/option><option value=\"K.RF.2.a\">K.RF.2.a: Recognize and produce rhyming words.<\/option><option value=\"K.RF.2.b\">K.RF.2.b: Count, pronounce, blend, and segment syllables in spoken words.<\/option><option value=\"K.RF.2.c\">K.RF.2.c: Blend and segment onsets and rimes of single-syllable spoken words.<\/option><option value=\"K.RF.2.d\">K.RF.2.d: Isolate and pronounce the initial, medial vowel, and final sounds (phonemes) in three-phoneme (consonent-vowel-consonent, or CVC) words.* (This does not include CVCs ending with \/l\/, \/r\/, or \/x\/.)<\/option><option value=\"K.RF.2.e\">K.RF.2.e: Add or substitute individual sounds (phonemes) in simple, one-syllable words to make new words.<\/option><option value=\"K.RF.3\">K.RF.3: Know and apply grade-level phonics and word analysis skills in decoding words.<\/option><option value=\"K.RF.3.a\">K.RF.3.a: Demonstrate basic knowledge of one-to-one letter-sound correspondences by producing the primary or many of the most frequent sound for each consonant.<\/option><option value=\"K.RF.3.b\">K.RF.3.b: Associate the long and short sounds with common spellings (graphemes) for the five major vowels.<\/option><option value=\"K.RF.3.c\">K.RF.3.c: Read common high-frequency words by sight (e.g., the, of, to, you, she, my, is, are, do, does).<\/option><option value=\"K.RF.3.d\">K.RF.3.d: Distinguish between similarly spelled words by identifying the sounds of the letters that differ.<\/option><option value=\"K.RF.4\">K.RF.4: Read emergent-reader texts with purpose and understanding.<\/option><option value=\"1.RF.1\">1.RF.1: Demonstrate understanding of the organization and basic features of print.<\/option><option value=\"1.RF.1.a\">1.RF.1.a: Recognize the distinguishing features of a sentence (e.g., first word, capitalization, ending punctuation).<\/option><option value=\"1.RF.2\">1.RF.2: Demonstrate understanding of spoken words, syllables, and sounds (phonemes).<\/option><option value=\"1.RF.2.a\">1.RF.2.a: Distinguish long from short vowel sounds in spoken single-syllable words.<\/option><option value=\"1.RF.2.b\">1.RF.2.b: Orally produce single-syllable words by blending sounds (phonemes), including consonant blends.<\/option><option value=\"1.RF.2.c\">1.RF.2.c: Isolate and pronounce initial, medial vowel, and final sounds (phonemes) in spoken single-syllable words.<\/option><option value=\"1.RF.2.d\">1.RF.2.d: Segment spoken single-syllable words into their complete sequence of individual sounds (phonemes).<\/option><option value=\"1.RF.3\">1.RF.3: Know and apply grade-level phonics and word analysis skills in decoding words.<\/option><option value=\"1.RF.3.a\">1.RF.3.a: Know the spelling-sound correspondences for common consonant digraphs.<\/option><option value=\"1.RF.3.b\">1.RF.3.b: Decode regularly spelled one-syllable words.<\/option><option value=\"1.RF.3.c\">1.RF.3.c: Know final -e and common vowel team conventions for representing long vowel sounds.<\/option><option value=\"1.RF.3.d\">1.RF.3.d: Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word.<\/option><option value=\"1.RF.3.e\">1.RF.3.e: Decode two-syllable words following basic patterns by breaking the words into syllables.<\/option><option value=\"1.RF.3.f\">1.RF.3.f: Read words with inflectional endings.<\/option><option value=\"1.RF.3.g\">1.RF.3.g: Recognize and read grade-appropriate irregularly spelled words.<\/option><option value=\"1.RF.4\">1.RF.4: Read with sufficient accuracy and fluency to support comprehension.<\/option><option value=\"1.RF.4.a\">1.RF.4.a: Read on-level text with purpose and understanding.<\/option><option value=\"1.RF.4.b\">1.RF.4.b: Read on-level text orally with accuracy, appropriate rate, and expression on successive readings.<\/option><option value=\"1.RF.4.c\">1.RF.4.c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.<\/option><option value=\"2.RF.3\">2.RF.3: Know and apply grade-level phonics and word analysis skills in decoding words.<\/option><option value=\"2.RF.3.a\">2.RF.3.a: Distinguish long and short vowels when reading regularly spelled one-syllable words.<\/option><option value=\"2.RF.3.b\">2.RF.3.b: Know spelling-sound correspondences for additional common vowel teams.<\/option><option value=\"2.RF.3.c\">2.RF.3.c: Decode regularly spelled two-syllable words with long vowels.<\/option><option value=\"2.RF.3.d\">2.RF.3.d: Decode words with common prefixes and suffixes.<\/option><option value=\"2.RF.3.e\">2.RF.3.e: Identify words with inconsistent but common spelling-sound correspondences.<\/option><option value=\"2.RF.3.f\">2.RF.3.f: Recognize and read grade-appropriate irregularly spelled words.<\/option><option value=\"2.RF.4\">2.RF.4: Read with sufficient accuracy and fluency to support comprehension.<\/option><option value=\"2.RF.4.a\">2.RF.4.a: Read on-level text with purpose and understanding.<\/option><option value=\"2.RF.4.b\">2.RF.4.b: Read on-level text orally with accuracy, appropriate rate, and expression on successive readings.<\/option><option value=\"2.RF.4.c\">2.RF.4.c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.<\/option><option value=\"3.RF.3\">3.RF.3: Know and apply grade-level phonics and word analysis skills in decoding words.<\/option><option value=\"3.RF.3.a\">3.RF.3.a: Identify and know the meaning of the most common prefixes and derivational suffixes.<\/option><option value=\"3.RF.3.b\">3.RF.3.b: Decode words with common Latin suffixes.<\/option><option value=\"3.RF.3.c\">3.RF.3.c: Decode multisyllable words.<\/option><option value=\"3.RF.3.d\">3.RF.3.d: Read grade-appropriate irregularly spelled words.<\/option><option value=\"3.RF.4\">3.RF.4: Read with sufficient accuracy and fluency to support comprehension.<\/option><option value=\"3.RF.4.a\">3.RF.4.a: Read on-level text with purpose and understanding.<\/option><option value=\"3.RF.4.b\">3.RF.4.b: Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings<\/option><option value=\"3.RF.4.c\">3.RF.4.c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.<\/option><option value=\"4.RF.3\">4.RF.3: Know and apply grade-level phonics and word analysis skills in decoding words.<\/option><option value=\"4.RF.3.a\">4.RF.3.a: Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.<\/option><option value=\"4.RF.4\">4.RF.4: Read with sufficient accuracy and fluency to support comprehension.<\/option><option value=\"4.RF.4.a\">4.RF.4.a: Read on-level text with purpose and understanding.<\/option><option value=\"4.RF.4.b\">4.RF.4.b: Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.<\/option><option value=\"4.RF.4.c\">4.RF.4.c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.<\/option><option value=\"5.RF.3\">5.RF.3: Know and apply grade-level phonics and word analysis skills in decoding words.<\/option><option value=\"5.RF.3.a\">5.RF.3.a: Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context.<\/option><option value=\"5.RF.4\">5.RF.4: Read with sufficient accuracy and fluency to support comprehension.<\/option><option value=\"5.RF.4.a\">5.RF.4.a: Read on-level text with purpose and understanding.<\/option><option value=\"5.RF.4.b\">5.RF.4.b: Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.<\/option><option value=\"5.RF.4.c\">5.RF.4.c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.<\/option><option value=\"K.W.1\">K.W.1: Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is...).<\/option><option value=\"K.W.2\">K.W.2: Use a combination of drawing, dictating, and writing to compose informative\/explanatory texts in which they name what they are writing about and supply some information about the topic.<\/option><option value=\"K.W.3\">K.W.3: Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.<\/option><option value=\"K.W.4\">K.W.4: (Begins in grade 3)<\/option><option value=\"K.W.5\">K.W.5: With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed.<\/option><option value=\"K.W.6\">K.W.6: With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including in collaboration with peers.<\/option><option value=\"K.W.7\">K.W.7: Participate in shared research and writing projects (e.g., explore a number of books by a favorite author and express opinions about them).<\/option><option value=\"K.W.8\">K.W.8: With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question.<\/option><option value=\"K.W.9\">K.W.9: (Begins in grade 4)<\/option><option value=\"K.W.10\">K.W.10: (Begins in grade 3)<\/option><option value=\"1.W.1\">1.W.1: Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure.<\/option><option value=\"1.W.2\">1.W.2: Write informative\/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure.<\/option><option value=\"1.W.3\">1.W.3: Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure.<\/option><option value=\"1.W.4\">1.W.4: (Begins in grade 3)<\/option><option value=\"1.W.5\">1.W.5: With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed.<\/option><option value=\"1.W.6\">1.W.6: With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers.<\/option><option value=\"1.W.7\">1.W.7: Participate in shared research and writing projects (e.g., explore a number of \u201chow-to\u201d books on a given topic and use them to write a sequence of instructions).<\/option><option value=\"1.W.8\">1.W.8: With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question.<\/option><option value=\"1.W.9\">1.W.9: (Begins in grade 4)<\/option><option value=\"1.W.10\">1.W.10: (Begins in grade 3)<\/option><option value=\"2.W.1\">2.W.1: Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section.<\/option><option value=\"2.W.2\">2.W.2: Write informative\/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section.<\/option><option value=\"2.W.3\">2.W.3: Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.<\/option><option value=\"2.W.4\">2.W.4: (Begins in grade 3)<\/option><option value=\"2.W.5\">2.W.5: With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing.<\/option><option value=\"2.W.6\">2.W.6: With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers.<\/option><option value=\"2.W.7\">2.W.7: Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations).<\/option><option value=\"2.W.8\">2.W.8: Recall information from experiences or gather information from provided sources to answer a question.<\/option><option value=\"2.W.9\">2.W.9: (Begins in grade 4)<\/option><option value=\"2.W.10\">2.W.10: (Begins in grade 3)<\/option><option value=\"3.W.1\">3.W.1: Write opinion pieces on topics or texts, supporting a point of view with reasons.<\/option><option value=\"3.W.1.a\">3.W.1.a: Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons.<\/option><option value=\"3.W.1.b\">3.W.1.b: Provide reasons that support the opinion.<\/option><option value=\"3.W.1.c\">3.W.1.c: Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons.<\/option><option value=\"3.W.1.d\">3.W.1.d: Provide a concluding statement or section.<\/option><option value=\"3.W.2\">3.W.2: Write informative\/explanatory texts to examine a topic and convey ideas and information clearly.<\/option><option value=\"3.W.2.a\">3.W.2.a: Introduce a topic and group related information together; include illustrations when useful to aiding comprehension.<\/option><option value=\"3.W.2.b\">3.W.2.b: Develop the topic with facts, definitions, and details.<\/option><option value=\"3.W.2.c\">3.W.2.c: Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information.<\/option><option value=\"3.W.2.d\">3.W.2.d: Provide a concluding statement or section.<\/option><option value=\"3.W.3\">3.W.3: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.<\/option><option value=\"3.W.3.a\">3.W.3.a: Establish a situation and introduce a narrator and\/or characters; organize an event sequence that unfolds naturally.<\/option><option value=\"3.W.3.b\">3.W.3.b: Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations.<\/option><option value=\"3.W.3.c\">3.W.3.c: Use temporal words and phrases to signal event order.<\/option><option value=\"3.W.3.d\">3.W.3.d: Provide a sense of closure.<\/option><option value=\"3.W.4\">3.W.4: With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"3.W.5\">3.W.5: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.<\/option><option value=\"3.W.6\">3.W.6: With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others.<\/option><option value=\"3.W.7\">3.W.7: Conduct short research projects that build knowledge about a topic.<\/option><option value=\"3.W.8\">3.W.8: Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.<\/option><option value=\"3.W.9\">3.W.9: (Begins in grade 4)<\/option><option value=\"3.W.10\">3.W.10: 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 discipline-specific tasks, purposes, and audiences.<\/option><option value=\"4.W.1\">4.W.1: Write opinion pieces on topics or texts, supporting a point of view with reasons and information.<\/option><option value=\"4.W.1.a\">4.W.1.a: Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer\u2019s purpose.<\/option><option value=\"4.W.1.b\">4.W.1.b: Provide reasons that are supported by facts and details.<\/option><option value=\"4.W.1.c\">4.W.1.c: Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition).<\/option><option value=\"4.W.1.d\">4.W.1.d: Provide a concluding statement or section related to the opinion presented.<\/option><option value=\"4.W.2\">4.W.2: Write informative\/explanatory texts to examine a topic and convey ideas and information clearly.<\/option><option value=\"4.W.2.a\">4.W.2.a: Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.<\/option><option value=\"4.W.2.b\">4.W.2.b: Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.<\/option><option value=\"4.W.2.c\">4.W.2.c: Link ideas within categories of information using words and phrases (e.g., another, for example, also, because).<\/option><option value=\"4.W.2.d\">4.W.2.d: d.Use precise language and domain-specific vocabulary to inform about or explain the topic.<\/option><option value=\"4.W.2.e\">4.W.2.e: Provide a concluding statement or section related to the information or explanation presented.<\/option><option value=\"4.W.3\">4.W.3: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.<\/option><option value=\"4.W.3.a\">4.W.3.a: Orient the reader by establishing a situation and introducing a narrator and\/or characters; organize an event sequence that unfolds naturally.<\/option><option value=\"4.W.3.b\">4.W.3.b: Use dialogue and description to develop experiences and events or show the responses of characters to situations.<\/option><option value=\"4.W.3.c\">4.W.3.c: Use a variety of transitional words and phrases to manage the sequence of events.<\/option><option value=\"4.W.3.d\">4.W.3.d: Use concrete words and phrases and sensory details to convey experiences and events precisely.<\/option><option value=\"4.W.3.e\">4.W.3.e: Provide a conclusion that follows from the narrated experiences or events.<\/option><option value=\"4.W.4\">4.W.4: Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"4.W.5\">4.W.5: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.<\/option><option value=\"4.W.6\">4.W.6: With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.<\/option><option value=\"4.W.7\">4.W.7: Conduct short research projects that build knowledge through investigation of different aspects of a topic.<\/option><option value=\"4.W.8\">4.W.8: Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources.<\/option><option value=\"4.W.9\">4.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"4.W.9.a\">4.W.9.a: Apply grade 4 Reading standards to literature (e.g., \u201cDescribe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character\u2019s thoughts, words, or actions].\u201d).<\/option><option value=\"4.W.9.b\">4.W.9.b: Apply grade 4 Reading standards to informational texts (e.g., \u201cExplain how an author uses reasons and evidence to support particular points in a text\u201d).<\/option><option value=\"4.W.10\">4.W.10: 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 discipline-specific tasks, purposes, and audiences.<\/option><option value=\"5.W.1\">5.W.1: Write opinion pieces on topics or texts, supporting a point of view with reasons and information.<\/option><option value=\"5.W.1.a\">5.W.1.a: Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer\u2019s purpose.<\/option><option value=\"5.W.1.b\">5.W.1.b: Provide logically ordered reasons that are supported by facts and details.<\/option><option value=\"5.W.1.c\">5.W.1.c: Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically).<\/option><option value=\"5.W.1.d\">5.W.1.d: Provide a concluding statement or section related to the opinion presented.<\/option><option value=\"5.W.2\">5.W.2: Write informative\/explanatory texts to examine a topic and convey ideas and information clearly.<\/option><option value=\"5.W.2.a\">5.W.2.a: Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.<\/option><option value=\"5.W.2.b\">5.W.2.b: Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.<\/option><option value=\"5.W.2.c\">5.W.2.c: Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).<\/option><option value=\"5.W.2.d\">5.W.2.d: Use precise language and domain-specific vocabulary to inform about or explain the topic.<\/option><option value=\"5.W.2.e\">5.W.2.e: Provide a concluding statement or section related to the information or explanation presented.<\/option><option value=\"5.W.3\">5.W.3: Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.<\/option><option value=\"5.W.3.a\">5.W.3.a: Orient the reader by establishing a situation and introducing a narrator and\/or characters; organize an event sequence that unfolds naturally.<\/option><option value=\"5.W.3.b\">5.W.3.b: Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations.<\/option><option value=\"5.W.3.c\">5.W.3.c: Use a variety of transitional words, phrases, and clauses to manage the sequence of events.<\/option><option value=\"5.W.3.d\">5.W.3.d: Use concrete words and phrases and sensory details to convey experiences and events precisely.<\/option><option value=\"5.W.3.e\">5.W.3.e: Provide a conclusion that follows from the narrated experiences or events.<\/option><option value=\"5.W.4\">5.W.4: Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"5.W.5\">5.W.5: With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.<\/option><option value=\"5.W.6\">5.W.6: With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of two pages in a single sitting.<\/option><option value=\"5.W.7\">5.W.7: Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic.<\/option><option value=\"5.W.8\">5.W.8: Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources.<\/option><option value=\"5.W.9\">5.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"5.W.9.a\">5.W.9.a: Apply grade 5 Reading standards to literature (e.g., \u201cCompare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]\u201d).<\/option><option value=\"5.W.9.b\">5.W.9.b: Apply grade 5 Reading standards to informational texts (e.g., \u201cExplain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]\u201d).<\/option><option value=\"5.W.10\">5.W.10: 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 discipline-specific tasks, purposes, and audiences.<\/option><option value=\"K.SL.1\">K.SL.1: Participate in collaborative conversations with diverse partners about kindergarten topics and texts with peers and adults in small and larger groups.<\/option><option value=\"K.SL.2\">K.SL.2: Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details and requesting clarification if something is not understood.<\/option><option value=\"K.SL.3\">K.SL.3: Ask and answer questions in order to seek help, get information, or clarify something that is not understood.<\/option><option value=\"K.SL.4\">K.SL.4: Describe familiar people, places, things, and events and, with prompting and support, provide additional detail.<\/option><option value=\"K.SL.5\">K.SL.5: Add drawings or other visual displays to descriptions as desired to provide additional detail.<\/option><option value=\"K.SL.6\">K.SL.6: Speak audibly and express thoughts, feelings, and ideas clearly.<\/option><option value=\"1.SL.1\">1.SL.1: Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups.<\/option><option value=\"1.SL.1.a\">1.SL.1.a: Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion).<\/option><option value=\"1.SL.1.b\">1.SL.1.b: Build on others\u2019 talk in conversations by responding to the comments of others through multiple exchanges.<\/option><option value=\"1.SL.1.c\">1.SL.1.c: Ask questions to clear up any confusion about the topics and texts under discussion.<\/option><option value=\"1.SL.2\">1.SL.2: Ask and answer questions about key details in a text read aloud or information presented orally or through other media.<\/option><option value=\"1.SL.3\">1.SL.3: Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood.<\/option><option value=\"1.SL.4\">1.SL.4: Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly.<\/option><option value=\"1.SL.5\">1.SL.5: Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings.<\/option><option value=\"1.SL.6\">1.SL.6: Produce complete sentences when appropriate to task and situation.<\/option><option value=\"2.SL.1\">2.SL.1: Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups.<\/option><option value=\"2.SL.1.a\">2.SL.1.a: Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).<\/option><option value=\"2.SL.1.b\">2.SL.1.b: Build on others\u2019 talk in conversations by linking their comments to the remarks of others.<\/option><option value=\"2.SL.1.c\">2.SL.1.c: Ask for clarification and further explanation as needed about the topics and texts under discussion.<\/option><option value=\"2.SL.2\">2.SL.2: Recount or describe key ideas or details from a text read aloud or information presented orally or through other media.<\/option><option value=\"2.SL.3\">2.SL.3: Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue.<\/option><option value=\"2.SL.4\">2.SL.4: Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences.<\/option><option value=\"2.SL.5\">2.SL.5: Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings.<\/option><option value=\"2.SL.6\">2.SL.6: Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification.<\/option><option value=\"3.SL.1\">3.SL.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others\u2019 ideas and expressing their own clearly.<\/option><option value=\"3.SL.1.a\">3.SL.1.a: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.<\/option><option value=\"3.SL.1.b\">3.SL.1.b: Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion).<\/option><option value=\"3.SL.1.c\">3.SL.1.c: Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others.<\/option><option value=\"3.SL.1.d\">3.SL.1.d: Explain their own ideas and understanding in light of the discussion.<\/option><option value=\"3.SL.2\">3.SL.2: Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.<\/option><option value=\"3.SL.3\">3.SL.3: Ask and answer questions about information from a speaker, offering appropriate elaboration and detail.<\/option><option value=\"3.SL.4\">3.SL.4: 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.<\/option><option value=\"3.SL.5\">3.SL.5: Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details.<\/option><option value=\"3.SL.6\">3.SL.6: Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification.<\/option><option value=\"4.SL.1\">4.SL.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others\u2019 ideas and expressing their own clearly.<\/option><option value=\"4.SL.1.a\">4.SL.1.a: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.<\/option><option value=\"4.SL.1.b\">4.SL.1.b: Follow agreed-upon rules for discussions and carry out assigned roles.<\/option><option value=\"4.SL.1.c\">4.SL.1.c: Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others.<\/option><option value=\"4.SL.1.d\">4.SL.1.d: Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.<\/option><option value=\"4.SL.2\">4.SL.2: Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.<\/option><option value=\"4.SL.3\">4.SL.3: Identify the reasons and evidence a speaker provides to support particular points.<\/option><option value=\"4.SL.4\">4.SL.4: Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.<\/option><option value=\"4.SL.5\">4.SL.5: Add audio recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes.<\/option><option value=\"4.SL.6\">4.SL.6: Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion); use formal English when appropriate to task and situation.<\/option><option value=\"5.SL.1\">5.SL.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others\u2019 ideas and expressing their own clearly.<\/option><option value=\"5.SL.1.a\">5.SL.1.a: Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.<\/option><option value=\"5.SL.1.b\">5.SL.1.b: Follow agreed-upon rules for discussions and carry out assigned roles.<\/option><option value=\"5.SL.1.c\">5.SL.1.c: Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.<\/option><option value=\"5.SL.1.d\">5.SL.1.d: Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.<\/option><option value=\"5.SL.2\">5.SL.2: Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.<\/option><option value=\"5.SL.3\">5.SL.3: Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence.<\/option><option value=\"5.SL.4\">5.SL.4: Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.<\/option><option value=\"5.SL.5\">5.SL.5: Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes.<\/option><option value=\"5.SL.6\">5.SL.6: Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation.<\/option><option value=\"K.L.1\">K.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"K.L.1.a\">K.L.1.a: Print many upper- and lowercase letters.<\/option><option value=\"K.L.1.b\">K.L.1.b: Use frequently occurring nouns and verbs.<\/option><option value=\"K.L.1.c\">K.L.1.c: Form regular plural nouns orally by adding \/s\/ or \/es\/ (e.g., dog, dogs; wish, wishes).<\/option><option value=\"K.L.1.d\">K.L.1.d: Understand and use question words (interrogatives) (e.g., who, what, where, when, why, how).<\/option><option value=\"K.L.1.e\">K.L.1.e: Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with).<\/option><option value=\"K.L.1.f\">K.L.1.f: Produce and expand complete sentences in shared language activities.<\/option><option value=\"K.L.2\">K.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"K.L.2.a\">K.L.2.a: Capitalize the first word in a sentence and the pronoun I.<\/option><option value=\"K.L.2.b\">K.L.2.b: Recognize and name end punctuation.<\/option><option value=\"K.L.2.c\">K.L.2.c: Write a letter or letters for most consonant and short-vowel sounds (phonemes).<\/option><option value=\"K.L.2.d\">K.L.2.d: Spell simple words phonetically, drawing on knowledge of sound-letter relationships.<\/option><option value=\"K.L.3\">K.L.3: (Begins in grade 2)<\/option><option value=\"K.L.4\">K.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on kindergarten reading and content.<\/option><option value=\"K.L.4.a\">K.L.4.a: Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck).<\/option><option value=\"K.L.4.b\">K.L.4.b: Use the most frequently occurring inflections and affixes (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word.<\/option><option value=\"K.L.5\">K.L.5: With guidance and support from adults, explore word relationships and nuances in word meanings.<\/option><option value=\"K.L.5.a\">K.L.5.a: Sort common objects into categories (e.g., shapes, foods) to gain a sense of the concepts the categories represent.<\/option><option value=\"K.L.5.b\">K.L.5.b: Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites (antonyms).<\/option><option value=\"K.L.5.c\">K.L.5.c: Identify real-life connections between words and their use (e.g., note places at school that are colorful).<\/option><option value=\"K.L.5.d\">K.L.5.d: Distinguish shades of meaning among verbs describing the same general action (e.g., walk, march, strut, prance) by acting out the meanings.<\/option><option value=\"K.L.6\">K.L.6: Use words and phrases acquired through conversations, reading and being read to, and responding to texts.<\/option><option value=\"1.L.1\">1.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"1.L.1.a\">1.L.1.a: Print all upper- and lowercase letters.<\/option><option value=\"1.L.1.b\">1.L.1.b: Use common, proper, and possessive nouns.<\/option><option value=\"1.L.1.c\">1.L.1.c: Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop).<\/option><option value=\"1.L.1.d\">1.L.1.d: Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their, anyone, everything).<\/option><option value=\"1.L.1.e\">1.L.1.e: Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home).<\/option><option value=\"1.L.1.f\">1.L.1.f: Use frequently occurring adjectives.<\/option><option value=\"1.L.1.g\">1.L.1.g: Use frequently occurring conjunctions (e.g., and, but, or, so, because).<\/option><option value=\"1.L.1.h\">1.L.1.h: Use determiners (e.g., articles, demonstratives).<\/option><option value=\"1.L.1.i\">1.L.1.i: Use frequently occurring prepositions (e.g., during, beyond, toward).<\/option><option value=\"1.L.1.j\">1.L.1.j: Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts.<\/option><option value=\"1.L.2\">1.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"1.L.2.a\">1.L.2.a: Capitalize dates and names of people.<\/option><option value=\"1.L.2.b\">1.L.2.b: Use end punctuation for sentences.<\/option><option value=\"1.L.2.c\">1.L.2.c: Use commas in dates and to separate single words in a series.<\/option><option value=\"1.L.2.d\">1.L.2.d: Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words.<\/option><option value=\"1.L.2.e\">1.L.2.e: Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions.<\/option><option value=\"1.L.3\">1.L.3: (Begins in grade 2)<\/option><option value=\"1.L.4\">1.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies.<\/option><option value=\"1.L.4.a\">1.L.4.a: Use sentence-level context as a clue to the meaning of a word or phrase.<\/option><option value=\"1.L.4.b\">1.L.4.b: Use frequently occurring affixes as a clue to the meaning of a word.<\/option><option value=\"1.L.4.c\">1.L.4.c: Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking).<\/option><option value=\"1.L.5\">1.L.5: With guidance and support from adults, demonstrate understanding of figurative language, word relationships and nuances in word meanings.<\/option><option value=\"1.L.5.a\">1.L.5.a: Sort words into categories (e.g., colors, clothing) to gain a sense of the concepts the categories represent.<\/option><option value=\"1.L.5.b\">1.L.5.b: Define words by category and by one or more key attributes (e.g., a duck is a bird that swims; a tiger is a large cat with stripes).<\/option><option value=\"1.L.5.c\">1.L.5.c: Identify real-life connections between words and their use (e.g., note places at home that are cozy).<\/option><option value=\"1.L.5.d\">1.L.5.d: Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings.<\/option><option value=\"1.L.6\">1.L.6: Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., because).<\/option><option value=\"2.L.1\">2.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"2.L.1.a\">2.L.1.a: Use collective nouns (e.g.,\u00a0group).<\/option><option value=\"2.L.1.b\">2.L.1.b: Form and use frequently occurring irregular plural nouns (e.g.,\u00a0feet, children, teeth, mice, fish).<\/option><option value=\"2.L.1.c\">2.L.1.c: Use reflexive pronouns (e.g.,\u00a0myself, ourselves).<\/option><option value=\"2.L.1.d\">2.L.1.d: Form and use the past tense of frequently occurring irregular verbs (e.g.,\u00a0sat, hid, told).<\/option><option value=\"2.L.1.e\">2.L.1.e: Use adjectives and adverbs, and choose between them depending on what is to be modified.<\/option><option value=\"2.L.1.f\">2.L.1.f: Produce, expand, and rearrange complete simple and compound sentences (e.g.,\u00a0The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy).<\/option><option value=\"2.L.2\">2.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"2.L.2.a\">2.L.2.a: Capitalize holidays, product names, and geographic names.<\/option><option value=\"2.L.2.b\">2.L.2.b: Use commas in greetings and closings of letters.<\/option><option value=\"2.L.2.c\">2.L.2.c: Use an apostrophe to form contractions and frequently occurring possessives.<\/option><option value=\"2.L.2.d\">2.L.2.d: Generalize learned spelling patterns when writing words (e.g.,\u00a0cage \u2192 badge; boy \u2192 boil).<\/option><option value=\"2.L.2.e\">2.L.2.e: Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.<\/option><option value=\"2.L.3\">2.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"2.L.3.a\">2.L.3.a: Compare formal and informal uses of English.<\/option><option value=\"2.L.4\">2.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 2 reading and content, choosing flexibly from an array of strategies.<\/option><option value=\"2.L.4.a\">2.L.4.a: Use sentence-level context as a clue to the meaning of a word or phrase.<\/option><option value=\"2.L.4.b\">2.L.4.b: Determine the meaning of the new word formed when a known prefix is added to a known word (e.g.,\u00a0happy\/unhappy, tell\/retell).<\/option><option value=\"2.L.4.c\">2.L.4.c: Use a known root word as a clue to the meaning of an unknown word with the same root (e.g.,\u00a0addition, additional).<\/option><option value=\"2.L.4.d\">2.L.4.d: Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g.,\u00a0birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark).<\/option><option value=\"2.L.4.e\">2.L.4.e: Use glossaries and beginning dictionaries, both print and digital, to determine or clarify the meaning of words and phrases.<\/option><option value=\"2.L.5\">2.L.5: Demonstrate understanding of figurative language, word relationships and nuances in word meanings.<\/option><option value=\"2.L.5.a\">2.L.5.a: Identify real-life connections between words and their use (e.g.,\u00a0describe foods that are spicy or juicy).<\/option><option value=\"2.L.5.b\">2.L.5.b: Distinguish shades of meaning among closely related verbs (e.g.,\u00a0toss, throw, hurl) and closely related adjectives (e.g.,\u00a0thin, slender, skinny, scrawny).<\/option><option value=\"2.L.6\">2.L.6: Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g.,\u00a0When other kids are happy that makes me happy).<\/option><option value=\"3.L.1\">3.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"3.L.1.a\">3.L.1.a: Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences.<\/option><option value=\"3.L.1.b\">3.L.1.b: Form and use regular and irregular plural nouns.<\/option><option value=\"3.L.1.c\">3.L.1.c: Use abstract nouns (e.g., childhood).<\/option><option value=\"3.L.1.d\">3.L.1.d: Form and use regular and irregular verbs.<\/option><option value=\"3.L.1.e\">3.L.1.e: Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses.<\/option><option value=\"3.L.1.f\">3.L.1.f: Ensure subject-verb and pronoun-antecedent agreement.*<\/option><option value=\"3.L.1.g\">3.L.1.g: Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified.<\/option><option value=\"3.L.1.h\">3.L.1.h: Use coordinating and subordinating conjunctions.<\/option><option value=\"3.L.1.i\">3.L.1.i: Produce simple, compound, and complex sentences.<\/option><option value=\"3.L.2\">3.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"3.L.2.a\">3.L.2.a: Capitalize appropriate words in titles.<\/option><option value=\"3.L.2.b\">3.L.2.b: Use commas in addresses.<\/option><option value=\"3.L.2.c\">3.L.2.c: Use commas and quotation marks in dialogue.<\/option><option value=\"3.L.2.d\">3.L.2.d: Form and use possessives.<\/option><option value=\"3.L.2.e\">3.L.2.e: Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness).<\/option><option value=\"3.L.2.f\">3.L.2.f: Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words.<\/option><option value=\"3.L.2.g\">3.L.2.g: Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.<\/option><option value=\"3.L.3\">3.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"3.L.3.a\">3.L.3.a: Choose words and phrases for effect.*<\/option><option value=\"3.L.3.b\">3.L.3.b: Recognize and observe differences between the conventions of spoken and written standard English.<\/option><option value=\"3.L.4\">3.L.4: Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"3.L.4.a\">3.L.4.a: Use sentence-level context as a clue to the meaning of a word or phrase.<\/option><option value=\"3.L.4.b\">3.L.4.b: Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable\/disagreeable, comfortable\/uncomfortable, care\/careless, heat\/preheat).<\/option><option value=\"3.L.4.c\">3.L.4.c: Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion).<\/option><option value=\"3.L.4.d\">3.L.4.d: Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases.<\/option><option value=\"3.L.5\">3.L.5: Demonstrate understanding of figurative language, word relationships and nuances in word meanings.<\/option><option value=\"3.L.5.a\">3.L.5.a: Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps).<\/option><option value=\"3.L.5.b\">3.L.5.b: Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful).<\/option><option value=\"3.L.5.c\">3.L.5.c: Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered).<\/option><option value=\"3.L.6\">3.L.6: Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).<\/option><option value=\"4.L.1\">4.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"4.L.1.a\">4.L.1.a: Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why).<\/option><option value=\"4.L.1.b\">4.L.1.b: Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses.<\/option><option value=\"4.L.1.c\">4.L.1.c: Use modal auxiliaries (e.g., can, may, must) to convey various conditions.<\/option><option value=\"4.L.1.d\">4.L.1.d: Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag).<\/option><option value=\"4.L.1.e\">4.L.1.e: Form and use prepositional phrases.<\/option><option value=\"4.L.1.f\">4.L.1.f: Produce complete sentences, recognizing and correcting inappropriate fragments and run-ons.*<\/option><option value=\"4.L.1.g\">4.L.1.g: Correctly use frequently confused words (e.g., to, too, two; there, their).*<\/option><option value=\"4.L.2\">4.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"4.L.2.a\">4.L.2.a: Use correct capitalization.<\/option><option value=\"4.L.2.b\">4.L.2.b: Use commas and quotation marks to mark direct speech and quotations from a text.<\/option><option value=\"4.L.2.c\">4.L.2.c: Use a comma before a coordinating conjunction in a compound sentence.<\/option><option value=\"4.L.2.d\">4.L.2.d: Spell grade-appropriate words correctly, consulting references as needed.<\/option><option value=\"4.L.3\">4.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"4.L.3.a\">4.L.3.a: Choose words and phrases to convey ideas precisely.*<\/option><option value=\"4.L.3.b\">4.L.3.b: Choose punctuation for effect.*<\/option><option value=\"4.L.3.c\">4.L.3.c: Differentiate between contexts that call for formal English (e.g., presenting ideas) and situations where informal discourse is appropriate (e.g., small-group discussion).<\/option><option value=\"4.L.4\">4.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 4 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"4.L.4.a\">4.L.4.a: Use context (e.g., definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase.<\/option><option value=\"4.L.4.b\">4.L.4.b: Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph).<\/option><option value=\"4.L.4.c\">4.L.4.c: Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.<\/option><option value=\"4.L.5\">4.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"4.L.5.a\">4.L.5.a: Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context.<\/option><option value=\"4.L.5.b\">4.L.5.b: Recognize and explain the meaning of common idioms, adages, and proverbs.<\/option><option value=\"4.L.5.c\">4.L.5.c: Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms).<\/option><option value=\"4.L.6\">4.L.6: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation).<\/option><option value=\"5.L.1\">5.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"5.L.2\">5.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"5.L.3\">5.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"5.L.3.a\">5.L.3.a: Expand, combine, and reduce sentences for meaning, reader\/listener interest, and style.<\/option><option value=\"5.L.3.b\">5.L.3.b: Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems.<\/option><option value=\"5.L.4\">5.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 5 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"5.L.4.a\">5.L.4.a: Use context (e.g., cause\/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase.<\/option><option value=\"5.L.4.b\">5.L.4.b: Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis).<\/option><option value=\"5.L.4.c\">5.L.4.c: Consult reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases.<\/option><option value=\"5.L.5\">5.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"5.L.5.a\">5.L.5.a: Interpret figurative language, including similes and metaphors, in context.<\/option><option value=\"5.L.5.b\">5.L.5.b: Recognize and explain the meaning of common idioms, adages, and proverbs.<\/option><option value=\"5.L.5.c\">5.L.5.c: Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words.<\/option><option value=\"5.L.6\">5.L.6: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition).<\/option><option value=\"6.RL.1\">6.RL.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"6.RL.2\">6.RL.2: 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 or judgments.<\/option><option value=\"6.RL.3\">6.RL.3: Describe how a particular story\u2019s or drama\u2019s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution.<\/option><option value=\"6.RL.4\">6.RL.4: 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.<\/option><option value=\"6.RL.5\">6.RL.5: 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.<\/option><option value=\"6.RL.6\">6.RL.6: Explain how an author develops the point of view of the narrator or speaker in a text.<\/option><option value=\"6.RL.7\">6.RL.7: 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, including contrasting what they \u201csee\u201d and \u201chear\u201d when reading the text to what they perceive when they listen or watch.<\/option><option value=\"6.RL.8\">6.RL.8: (Not applicable to literature)<\/option><option value=\"6.RL.9\">6.RL.9: Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics.<\/option><option value=\"6.RL.10\">6.RL.10: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6\u20138 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"7.RL.1\">7.RL.1: Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"7.RL.2\">7.RL.2: Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text.<\/option><option value=\"7.RL.3\">7.RL.3: Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot).<\/option><option value=\"7.RL.4\">7.RL.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of rhymes and other repetitions of sounds (e.g., alliteration) on a specific verse or stanza of a poem or section of a story or drama.<\/option><option value=\"7.RL.5\">7.RL.5: Analyze how a drama\u2019s or poem\u2019s form or structure (e.g., soliloquy, sonnet) contributes to its meaning.<\/option><option value=\"7.RL.6\">7.RL.6: Analyze how an author develops and contrasts the points of view of different characters or narrators in a text.<\/option><option value=\"7.RL.7\">7.RL.7: Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film).<\/option><option value=\"7.RL.8\">7.RL.8: (Not applicable to literature)<\/option><option value=\"7.RL.9\">7.RL.9: Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history.<\/option><option value=\"7.RL.10\">7.RL.10: By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6\u20138 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"8.RL.1\">8.RL.1: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"8.RL.2\">8.RL.2: Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text.<\/option><option value=\"8.RL.3\">8.RL.3: 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.<\/option><option value=\"8.RL.4\">8.RL.4: Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.<\/option><option value=\"8.RL.5\">8.RL.5: 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.<\/option><option value=\"8.RL.6\">8.RL.6: nalyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor.<\/option><option value=\"8.RL.7\">8.RL.7: 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, evaluating the choices made by the director or actors.<\/option><option value=\"8.RL.8\">8.RL.8: (Not applicable to literature)<\/option><option value=\"8.RL.9\">8.RL.9: Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new.<\/option><option value=\"8.RL.10\">8.RL.10: By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6\u20138 text complexity band independently and proficiently.<\/option><option value=\"9-10.RL.1\">9-10.RL.1: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"9-10.RL.2\">9-10.RL.2: Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.<\/option><option value=\"9-10.RL.3\">9-10.RL.3: Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme.<\/option><option value=\"9-10.RL.4\">9-10.RL.4: Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone).<\/option><option value=\"9-10.RL.5\">9-10.RL.5: Analyze how an author\u2019s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise.<\/option><option value=\"9-10.RL.6\">9-10.RL.6: Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature.<\/option><option value=\"9-10.RL.7\">9-10.RL.7: Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden\u2019s \u201cMus\u00e9e des Beaux Arts\u201d and Breughel\u2019s Landscape with the Fall of Icarus).<\/option><option value=\"9-10.RL.8\">9-10.RL.8: (Not applicable to literature)<\/option><option value=\"9-10.RL.9\">9-10.RL.9: Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare).<\/option><option value=\"9-10.RL.10\">9-10.RL.10: By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9\u201310 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"11-12.RL.1\">11-12.RL.1: 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.<\/option><option value=\"11-12.RL.2\">11-12.RL.2: 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 to produce a complex account; provide an objective summary of the text.<\/option><option value=\"11-12.RL.3\">11-12.RL.3: Analyze the impact of the author\u2019s 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 the characters are introduced and developed).<\/option><option value=\"11-12.RL.4\">11-12.RL.4: Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.)<\/option><option value=\"11-12.RL.5\">11-12.RL.5: Analyze how an author\u2019s 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 overall structure and meaning as well as its aesthetic impact.<\/option><option value=\"11-12.RL.6\">11-12.RL.6: Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement).<\/option><option value=\"11-12.RL.7\">11-12.RL.7: Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.)<\/option><option value=\"11-12.RL.8\">11-12.RL.8: (Not applicable to literature)<\/option><option value=\"11-12.RL.9\">11-12.RL.9: 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.<\/option><option value=\"11-12.RL.10\">11-12.RL.10: By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11\u2013CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"6.RI.1\">6.RI.1: Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"6.RI.2\">6.RI.2: 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.<\/option><option value=\"6.RI.3\">6.RI.3: Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes).<\/option><option value=\"6.RI.4\">6.RI.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings.<\/option><option value=\"6.RI.5\">6.RI.5: 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.<\/option><option value=\"6.RI.6\">6.RI.6: Determine an author\u2019s point of view or purpose in a text and explain how it is conveyed in the text.<\/option><option value=\"6.RI.7\">6.RI.7: 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.<\/option><option value=\"6.RI.8\">6.RI.8: 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.<\/option><option value=\"6.RI.9\">6.RI.9: Compare and contrast one author\u2019s presentation of events with that of another (e.g., a memoir written by and a biography on the same person).<\/option><option value=\"6.RI.10\">6.RI.10: By the end of the year, read and comprehend literary nonfiction in the grades 6\u20138 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"7.RI.1\">7.RI.1: Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"7.RI.2\">7.RI.2: Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text.<\/option><option value=\"7.RI.3\">7.RI.3: Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events).<\/option><option value=\"7.RI.4\">7.RI.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone.<\/option><option value=\"7.RI.5\">7.RI.5: Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas.<\/option><option value=\"7.RI.6\">7.RI.6: Determine an author\u2019s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others.<\/option><option value=\"7.RI.7\">7.RI.7: Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium\u2019s portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words).<\/option><option value=\"7.RI.8\">7.RI.8: Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims.<\/option><option value=\"7.RI.9\">7.RI.9: Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts.<\/option><option value=\"7.RI.10\">7.RI.10: By the end of the year, read and comprehend literary nonfiction in the grades 6\u20138 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"8.RI.1\">8.RI.1: Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"8.RI.2\">8.RI.2: Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text.<\/option><option value=\"8.RI.3\">8.RI.3: Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories).<\/option><option value=\"8.RI.4\">8.RI.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts.<\/option><option value=\"8.RI.5\">8.RI.5: 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.<\/option><option value=\"8.RI.6\">8.RI.6: Determine an author\u2019s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints.<\/option><option value=\"8.RI.7\">8.RI.7: Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea.<\/option><option value=\"8.RI.8\">8.RI.8: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced.<\/option><option value=\"8.RI.9\">8.RI.9: Analyze a case in which two or more texts provide conflicting information on the same topic and identify where the texts disagree on matters of fact or interpretation.<\/option><option value=\"8.RI.10\">8.RI.10: By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6\u20138 text complexity band independently and proficiently.<\/option><option value=\"9-10.RI.1\">9-10.RI.1: Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.<\/option><option value=\"9-10.RI.2\">9-10.RI.2: Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text.<\/option><option value=\"9-10.RI.3\">9-10.RI.3: Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.<\/option><option value=\"9-10.RI.4\">9-10.RI.4: Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper).<\/option><option value=\"9-10.RI.5\">9-10.RI.5: Analyze in detail how an author\u2019s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter).<\/option><option value=\"9-10.RI.6\">9-10.RI.6: Determine an author\u2019s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose.<\/option><option value=\"9-10.RI.7\">9-10.RI.7: Analyze various accounts of a subject told in different mediums (e.g., a person\u2019s life story in both print and multimedia), determining which details are emphasized in each account.<\/option><option value=\"9-10.RI.8\">9-10.RI.8: Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning.<\/option><option value=\"9-10.RI.9\">9-10.RI.9: Analyze seminal U.S. documents of historical and literary significance (e.g., Washington\u2019s Farewell Address, the Gettysburg Address, Roosevelt\u2019s Four Freedoms speech, King\u2019s \u201cLetter from Birmingham Jail\u201d), including how they address related themes and concepts.<\/option><option value=\"9-10.RI.10\">9-10.RI.10: By the end of grade 9, read and comprehend literary nonfiction in the grades 9\u201310 text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"11-12.RI.1\">11-12.RI.1: 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.<\/option><option value=\"11-12.RI.2\">11-12.RI.2: 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 to provide a complex analysis; provide an objective summary of the text.<\/option><option value=\"11-12.RI.3\">11-12.RI.3: 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.<\/option><option value=\"11-12.RI.4\">11-12.RI.4: 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 or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10).<\/option><option value=\"11-12.RI.5\">11-12.RI.5: 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.<\/option><option value=\"11-12.RI.6\">11-12.RI.6: Determine an author\u2019s 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.<\/option><option value=\"11-12.RI.7\">11-12.RI.7: 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.<\/option><option value=\"11-12.RI.8\">11-12.RI.8: Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses).<\/option><option value=\"11-12.RI.9\">11-12.RI.9: Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln\u2019s Second Inaugural Address) for their themes, purposes, and rhetorical features.<\/option><option value=\"11-12.RI.10\">11-12.RI.10: By the end of grade 11, read and comprehend literary nonfiction in the grades 11\u2013CCR text complexity band proficiently, with scaffolding as needed at the high end of the range.<\/option><option value=\"6.W.1\">6.W.1: Write arguments to support claims with clear reasons and relevant evidence.<\/option><option value=\"6.W.1.a\">6.W.1.a: Introduce claim(s) and organize the reasons and evidence clearly.<\/option><option value=\"6.W.1.b\">6.W.1.b: Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text.<\/option><option value=\"6.W.1.c\">6.W.1.c: Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons.<\/option><option value=\"6.W.1.d\">6.W.1.d: Establish and maintain a formal style.<\/option><option value=\"6.W.1.e\">6.W.1.e: Provide a concluding statement or section that follows from the argument presented.<\/option><option value=\"6.W.2\">6.W.2: Write informative\/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.<\/option><option value=\"6.W.2.a\">6.W.2.a: Introduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison\/contrast, and cause\/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"6.W.2.b\">6.W.2.b: Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.<\/option><option value=\"6.W.2.c\">6.W.2.c: Use appropriate transitions to clarify the relationships among ideas and concepts.<\/option><option value=\"6.W.2.d\">6.W.2.d: Use precise language and domain-specific vocabulary to inform about or explain the topic.<\/option><option value=\"6.W.2.e\">6.W.2.e: Establish and maintain a formal style.<\/option><option value=\"6.W.2.f\">6.W.2.f: Provide a concluding statement or section that follows from the information or explanation presented.<\/option><option value=\"6.W.3\">6.W.3: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.<\/option><option value=\"6.W.3.a\">6.W.3.a: 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.<\/option><option value=\"6.W.3.b\">6.W.3.b: Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and\/or characters.<\/option><option value=\"6.W.3.c\">6.W.3.c: Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.<\/option><option value=\"6.W.3.d\">6.W.3.d: Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events.<\/option><option value=\"6.W.3.e\">6.W.3.e: Provide a conclusion that follows from the narrated experiences or events.<\/option><option value=\"6.W.4\">6.W.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"6.W.5\">6.W.5: 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.<\/option><option value=\"6.W.6\">6.W.6: 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 to type a minimum of three pages in a single sitting.<\/option><option value=\"6.W.7\">6.W.7: Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.<\/option><option value=\"6.W.8\">6.W.8: 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 while avoiding plagiarism and providing basic bibliographic information for sources.<\/option><option value=\"6.W.9\">6.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"6.W.9.a\">6.W.9.a: Apply grade 6 Reading standards to literature (e.g., \u201cCompare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories] in terms of their approaches to similar themes and topics\u201d).<\/option><option value=\"6.W.9.b\">6.W.9.b: Apply grade 6 Reading standards to literary nonfiction (e.g., \u201cTrace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not\u201d).<\/option><option value=\"6.W.10\">6.W.10: 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 discipline-specific tasks, purposes, and<\/option><option value=\"7.W.1\">7.W.1: Write arguments to support claims with clear reasons and relevant evidence.<\/option><option value=\"7.W.1.a\">7.W.1.a: Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically.<\/option><option value=\"7.W.1.b\">7.W.1.b: Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.<\/option><option value=\"7.W.1.c\">7.W.1.c: Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence.<\/option><option value=\"7.W.1.d\">7.W.1.d: Establish and maintain a formal style.<\/option><option value=\"7.W.1.e\">7.W.1.e: Provide a concluding statement or section that follows from and supports the argument presented.<\/option><option value=\"7.W.2\">7.W.2: Write informative\/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.<\/option><option value=\"7.W.2.a\">7.W.2.a: Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison\/contrast, and cause\/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"7.W.2.b\">7.W.2.b: Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples.<\/option><option value=\"7.W.2.c\">7.W.2.c: Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts.<\/option><option value=\"7.W.2.d\">7.W.2.d: Use precise language and domain-specific vocabulary to inform about or explain the topic.<\/option><option value=\"7.W.2.e\">7.W.2.e: Establish and maintain a formal style.<\/option><option value=\"7.W.2.f\">7.W.2.f: Provide a concluding statement or section that follows from and supports the information or explanation presented.<\/option><option value=\"7.W.3\">7.W.3: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.<\/option><option value=\"7.W.3.a\">7.W.3.a: Engage and orient the reader by establishing a context and point of view and introducing a narrator and\/or characters; organize an event sequence that unfolds naturally and logically.<\/option><option value=\"7.W.3.b\">7.W.3.b: Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and\/or characters.<\/option><option value=\"7.W.3.c\">7.W.3.c: Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.<\/option><option value=\"7.W.3.d\">7.W.3.d: Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.<\/option><option value=\"7.W.3.e\">7.W.3.e: Provide a conclusion that follows from and reflects on the narrated experiences or events.<\/option><option value=\"7.W.4\">7.W.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"7.W.5\">7.W.5: 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, focusing on how well purpose and audience have been addressed.<\/option><option value=\"7.W.6\">7.W.6: 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, including linking to and citing sources.<\/option><option value=\"7.W.7\">7.W.7: Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.<\/option><option value=\"7.W.8\">7.W.8: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.<\/option><option value=\"7.W.9\">7.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"7.W.9.a\">7.W.9.a: Apply grade 7 Reading standards to literature (e.g., \u201cCompare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history\u201d).<\/option><option value=\"7.W.9.b\">7.W.9.b: Apply grade 7 Reading standards to literary nonfiction (e.g. \u201cTrace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims\u201d).<\/option><option value=\"7.W.10\">7.W.10: 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 discipline-specific tasks, purposes, and audiences.<\/option><option value=\"8.W.1\">8.W.1: Write arguments to support claims with clear reasons and relevant evidence.<\/option><option value=\"8.W.1.a\">8.W.1.a: Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.<\/option><option value=\"8.W.1.b\">8.W.1.b: Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text.<\/option><option value=\"8.W.1.c\">8.W.1.c: Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.<\/option><option value=\"8.W.1.d\">8.W.1.d: Establish and maintain a formal style.<\/option><option value=\"8.W.1.e\">8.W.1.e: Provide a concluding statement or section that follows from and supports the argument presented.<\/option><option value=\"8.W.2\">8.W.2: Write informative\/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content.<\/option><option value=\"8.W.2.a\">8.W.2.a: Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"8.W.2.b\">8.W.2.b: Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.<\/option><option value=\"8.W.2.c\">8.W.2.c: Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.<\/option><option value=\"8.W.2.d\">8.W.2.d: Use precise language and domain-specific vocabulary to inform about or explain the topic.<\/option><option value=\"8.W.2.e\">8.W.2.e: Establish and maintain a formal style.<\/option><option value=\"8.W.2.f\">8.W.2.f: Provide a concluding statement or section that follows from and supports the information or explanation presented.<\/option><option value=\"8.W.3\">8.W.3: Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.<\/option><option value=\"8.W.3.a\">8.W.3.a: Engage and orient the reader by establishing a context and point of view and introducing a narrator and\/or characters; organize an event sequence that unfolds naturally and logically.<\/option><option value=\"8.W.3.b\">8.W.3.b: Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and\/or characters.<\/option><option value=\"8.W.3.c\">8.W.3.c: Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events.<\/option><option value=\"8.W.3.d\">8.W.3.d: Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.<\/option><option value=\"8.W.3.e\">8.W.3.e: Provide a conclusion that follows from and reflects on the narrated experiences or events.<\/option><option value=\"8.W.4\">8.W.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"8.W.5\">8.W.5: 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, focusing on how well purpose and audience have been addressed.<\/option><option value=\"8.W.6\">8.W.6: Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others.<\/option><option value=\"8.W.7\">8.W.7: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.<\/option><option value=\"8.W.8\">8.W.8: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.<\/option><option value=\"8.W.9\">8.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"8.W.9.a\">8.W.9.a: Apply grade 8 Reading standards to literature (e.g., \u201cAnalyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new\u201d).<\/option><option value=\"8.W.9.b\">8.W.9.b: Apply grade 8 Reading standards to literary nonfiction (e.g., \u201cDelineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced\u201d).<\/option><option value=\"8.W.10\">8.W.10: 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 discipline-specific tasks, purposes, and audiences.<\/option><option value=\"9-10.W.1\">9-10.W.1: Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.<\/option><option value=\"9-10.W.1.a\">9-10.W.1.a: Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.<\/option><option value=\"9-10.W.1.b\">9-10.W.1.b: Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience\u2019s knowledge level and concerns.<\/option><option value=\"9-10.W.1.c\">9-10.W.1.c: Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.<\/option><option value=\"9-10.W.1.d\">9-10.W.1.d: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"9-10.W.1.e\">9-10.W.1.e: Provide a concluding statement or section that follows from and supports the argument presented.<\/option><option value=\"9-10.W.2\">9-10.W.2: 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.<\/option><option value=\"9-10.W.2.a\">9-10.W.2.a: Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"9-10.W.2.b\">9-10.W.2.b: Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience\u2019s knowledge of the topic.<\/option><option value=\"9-10.W.2.c\">9-10.W.2.c: Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.<\/option><option value=\"9-10.W.2.d\">9-10.W.2.d: Use precise language and domain-specific vocabulary to manage the complexity of the topic.<\/option><option value=\"9-10.W.2.e\">9-10.W.2.e: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"9-10.W.2.f\">9-10.W.2.f: Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).<\/option><option value=\"9-10.W.3\">9-10.W.3: Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.<\/option><option value=\"9-10.W.3.a\">9-10.W.3.a: Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and\/or characters; create a smooth progression of experiences or events.<\/option><option value=\"9-10.W.3.b\">9-10.W.3.b: Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and\/or characters.<\/option><option value=\"9-10.W.3.c\">9-10.W.3.c: Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.<\/option><option value=\"9-10.W.3.d\">9-10.W.3.d: Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and\/or characters.<\/option><option value=\"9-10.W.3.e\">9-10.W.3.e: Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.<\/option><option value=\"9-10.W.4\">9-10.W.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"9-10.W.5\">9-10.W.5: 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.<\/option><option value=\"9-10.W.6\">9-10.W.6: Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology\u2019s capacity to link to other information and to display information flexibly and dynamically.<\/option><option value=\"9-10.W.7\">9-10.W.7: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.<\/option><option value=\"9-10.W.8\">9-10.W.8: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation.<\/option><option value=\"9-10.W.9\">9-10.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"9-10.W.9.a\">9-10.W.9.a: Apply grades 9\u201310 Reading standards to literature (e.g., \u201cAnalyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]\u201d).<\/option><option value=\"9-10.W.9.b\">9-10.W.9.b: Apply grades 9\u201310 Reading standards to literary nonfiction (e.g., \u201cDelineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning\u201d).<\/option><option value=\"9-10.W.10\">9-10.W.10: 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.<\/option><option value=\"11-12.W.1\">11-12.W.1: Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.<\/option><option value=\"11-12.W.1.a\">11-12.W.1.a: Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence.<\/option><option value=\"11-12.W.1.b\">11-12.W.1.b: Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience\u2019s knowledge level, concerns, values, and possible biases.<\/option><option value=\"11-12.W.1.c\">11-12.W.1.c: Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.<\/option><option value=\"11-12.W.1.d\">11-12.W.1.d: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"11-12.W.1.e\">11-12.W.1.e: Provide a concluding statement or section that follows from and supports the argument presented.<\/option><option value=\"11-12.W.2\">11-12.W.2: 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.<\/option><option value=\"11-12.W.2.a\">11-12.W.2.a: Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"11-12.W.2.b\">11-12.W.2.b: Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience\u2019s knowledge of the topic.<\/option><option value=\"11-12.W.2.c\">11-12.W.2.c: Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.<\/option><option value=\"11-12.W.2.d\">11-12.W.2.d: Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic.<\/option><option value=\"11-12.W.2.e\">11-12.W.2.e: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"11-12.W.2.f\">11-12.W.2.f: Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).<\/option><option value=\"11-12.W.3\">11-12.W.3: Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.<\/option><option value=\"11-12.W.3.a\">11-12.W.3.a: Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and\/or characters; create a smooth progression of experiences or events.<\/option><option value=\"11-12.W.3.b\">11-12.W.3.b: Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and\/or characters.<\/option><option value=\"11-12.W.3.c\">11-12.W.3.c: Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution).<\/option><option value=\"11-12.W.3.d\">11-12.W.3.d: Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and\/or characters.<\/option><option value=\"11-12.W.3.e\">11-12.W.3.e: Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.<\/option><option value=\"11-12.W.4\">11-12.W.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1\u20133 above.)<\/option><option value=\"11-12.W.5\">11-12.W.5: 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.<\/option><option value=\"11-12.W.6\">11-12.W.6: 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.<\/option><option value=\"11-12.W.7\">11-12.W.7: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.<\/option><option value=\"11-12.W.8\">11-12.W.8: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.<\/option><option value=\"11-12.W.9\">11-12.W.9: Draw evidence from literary or informational texts to support analysis, reflection, and research.<\/option><option value=\"11-12.W.9.a\">11-12.W.9.a: Apply grades 11\u201312 Reading standards to literature (e.g., \u201cDemonstrate 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\u201d).<\/option><option value=\"11-12.W.9.b\">11-12.W.9.b: Apply grades 11\u201312 Reading standards to literary nonfiction (e.g., \u201cDelineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]\u201d).<\/option><option value=\"11-12.W.10\">11-12.W.10: 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<\/option><option value=\"6.SL.1\">6.SL.1: 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, building on others\u2019 ideas and expressing their own clearly.<\/option><option value=\"6.SL.1.a\">6.SL.1.a: 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 to probe and reflect on ideas under discussion.<\/option><option value=\"6.SL.1.b\">6.SL.1.b: Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed.<\/option><option value=\"6.SL.1.c\">6.SL.1.c: Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion.<\/option><option value=\"6.SL.1.d\">6.SL.1.d: Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing.<\/option><option value=\"6.SL.2\">6.SL.2: 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.<\/option><option value=\"6.SL.3\">6.SL.3: Delineate a speaker\u2019s argument and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not.<\/option><option value=\"6.SL.4\">6.SL.4: Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.<\/option><option value=\"6.SL.5\">6.SL.5: Include multimedia components (e.g., graphics, images, music, sound) and visual displays in presentations to clarify information.<\/option><option value=\"6.SL.6\">6.SL.6: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.<\/option><option value=\"7.SL.1\">7.SL.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others\u2019 ideas and expressing their own clearly.<\/option><option value=\"7.SL.1.a\">7.SL.1.a: Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.<\/option><option value=\"7.SL.1.b\">7.SL.1.b: Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed.<\/option><option value=\"7.SL.1.c\">7.SL.1.c: Pose questions that elicit elaboration and respond to others\u2019 questions and comments with relevant observations and ideas that bring the discussion back on topic as needed.<\/option><option value=\"7.SL.1.d\">7.SL.1.d: Acknowledge new information expressed by others and, when warranted, modify their own views.<\/option><option value=\"7.SL.2\">7.SL.2: Analyze the main ideas and supporting details presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how the ideas clarify a topic, text, or issue under study.<\/option><option value=\"7.SL.3\">7.SL.3: Delineate a speaker\u2019s argument and specific claims, evaluating the soundness of the reasoning and the relevance and sufficiency of the evidence.<\/option><option value=\"7.SL.4\">7.SL.4: Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts, details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation.<\/option><option value=\"7.SL.5\">7.SL.5: Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points.<\/option><option value=\"7.SL.6\">7.SL.6: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.<\/option><option value=\"8.SL.1\">8.SL.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others\u2019 ideas and expressing their own clearly.<\/option><option value=\"8.SL.1.a\">8.SL.1.a: Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion.<\/option><option value=\"8.SL.1.b\">8.SL.1.b: Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed.<\/option><option value=\"8.SL.1.c\">8.SL.1.c: Pose questions that connect the ideas of several speakers and respond to others\u2019 questions and comments with relevant evidence, observations, and ideas.<\/option><option value=\"8.SL.1.d\">8.SL.1.d: Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented.<\/option><option value=\"8.SL.2\">8.SL.2: Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation.<\/option><option value=\"8.SL.3\">8.SL.3: Delineate a speaker\u2019s argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced.<\/option><option value=\"8.SL.4\">8.SL.4: Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation.<\/option><option value=\"8.SL.5\">8.SL.5: Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest.<\/option><option value=\"8.SL.6\">8.SL.6: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.<\/option><option value=\"9-10.SL.1\">9-10.SL.1: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9\u201310 topics, texts, and issues, building on others\u2019 ideas and expressing their own clearly and persuasively.<\/option><option value=\"9-10.SL.1.a\">9-10.SL.1.a: Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.<\/option><option value=\"9-10.SL.1.b\">9-10.SL.1.b: Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed.<\/option><option value=\"9-10.SL.1.c\">9-10.SL.1.c: Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions.<\/option><option value=\"9-10.SL.1.d\">9-10.SL.1.d: Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented.<\/option><option value=\"9-10.SL.2\">9-10.SL.2: Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source.<\/option><option value=\"9-10.SL.3\">9-10.SL.3: Evaluate a speaker\u2019s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence.<\/option><option value=\"9-10.SL.4\">9-10.SL.4: Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task.<\/option><option value=\"9-10.SL.5\">9-10.SL.5: 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.<\/option><option value=\"9-10.SL.6\">9-10.SL.6: Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate.<\/option><option value=\"11-12.SL.1\">11-12.SL.1: Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 11\u201312 topics, texts, and issues, building on others\u2019 ideas and expressing their own clearly and persuasively.<\/option><option value=\"11-12.SL.1.a\">11-12.SL.1.a: Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas.<\/option><option value=\"11-12.SL.1.b\">11-12.SL.1.b: Work with peers to promote civil, democratic discussions and decision-making, set clear goals and deadlines, and establish individual roles as needed.<\/option><option value=\"11-12.SL.1.c\">11-12.SL.1.c: Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives.<\/option><option value=\"11-12.SL.1.d\">11-12.SL.1.d: Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task.<\/option><option value=\"11-12.SL.2\">11-12.SL.2: Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data.<\/option><option value=\"11-12.SL.3\">11-12.SL.3: Evaluate a speaker\u2019s 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.<\/option><option value=\"11-12.SL.4\">11-12.SL.4: Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks.<\/option><option value=\"11-12.SL.5\">11-12.SL.5: 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.<\/option><option value=\"11-12.SL.6\">11-12.SL.6: Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when indicated or appropriate.<\/option><option value=\"6.L.1\">6.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"6.L.2\">6.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"6.L.3\">6.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"6.L.4\">6.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"6.L.5\">6.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"6.L.6\">6.L.6: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.<\/option><option value=\"7.L.1\">7.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"7.L.1.a\">7.L.1.a: Explain the function of phrases and clauses in general and their function in specific sentences.<\/option><option value=\"7.L.1.b\">7.L.1.b: Choose among simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas.<\/option><option value=\"7.L.1.c\">7.L.1.c: Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers.*<\/option><option value=\"7.L.2\">7.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"7.L.2.a\">7.L.2.a: Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt).<\/option><option value=\"7.L.2.b\">7.L.2.b: Spell correctly.<\/option><option value=\"7.L.3\">7.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"7.L.3.a\">7.L.3.a: Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy.*<\/option><option value=\"7.L.4\">7.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade 7 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"7.L.4.a\">7.L.4.a: Use context (e.g., the overall meaning of a sentence or paragraph; a word\u2019s position or function in a sentence) as a clue to the meaning of a word or phrase.<\/option><option value=\"7.L.4.b\">7.L.4.b: Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel).<\/option><option value=\"7.L.4.c\">7.L.4.c: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.<\/option><option value=\"7.L.4.d\">7.L.4.d: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).<\/option><option value=\"7.L.5\">7.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"7.L.5.a\">7.L.5.a: Interpret figures of speech (e.g., literary, biblical, and mythological allusions) in context.<\/option><option value=\"7.L.5.b\">7.L.5.b: Use the relationship between particular words (e.g., synonym\/antonym, analogy) to better understand each of the words.<\/option><option value=\"7.L.5.c\">7.L.5.c: Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending).<\/option><option value=\"7.L.6\">7.L.6: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.<\/option><option value=\"8.L.1\">8.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"8.L.1.a\">8.L.1.a: Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences.<\/option><option value=\"8.L.1.b\">8.L.1.b: Form and use verbs in the active and passive voice.<\/option><option value=\"8.L.1.c\">8.L.1.c: Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood.<\/option><option value=\"8.L.1.d\">8.L.1.d: Recognize and correct inappropriate shifts in verb voice and mood.*<\/option><option value=\"8.L.2\">8.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"8.L.2.a\">8.L.2.a: Use punctuation (comma, ellipsis, dash) to indicate a pause or break.<\/option><option value=\"8.L.2.b\">8.L.2.b: Use an ellipsis to indicate an omission.<\/option><option value=\"8.L.2.c\">8.L.2.c: Spell correctly.<\/option><option value=\"8.L.3\">8.L.3: Use knowledge of language and its conventions when writing, speaking, reading, or listening.<\/option><option value=\"8.L.3.a\">8.L.3.a: Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact).<\/option><option value=\"8.L.4\">8.L.4: Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"8.L.4.a\">8.L.4.a: Use context (e.g., the overall meaning of a sentence or paragraph; a word\u2019s position or function in a sentence) as a clue to the meaning of a word or phrase.<\/option><option value=\"8.L.4.b\">8.L.4.b: Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede).<\/option><option value=\"8.L.4.c\">8.L.4.c: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech.<\/option><option value=\"8.L.4.d\">8.L.4.d: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).<\/option><option value=\"8.L.5\">8.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"8.L.5.a\">8.L.5.a: Interpret figures of speech (e.g. verbal irony, puns) in context.<\/option><option value=\"8.L.5.b\">8.L.5.b: Use the relationship between particular words to better understand each of the words.<\/option><option value=\"8.L.5.c\">8.L.5.c: Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., bullheaded, willful, firm, persistent, resolute).<\/option><option value=\"8.L.6\">8.L.6: Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.<\/option><option value=\"9-10.L.1\">9-10.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"9-10.L.1.a\">9-10.L.1.a: Use parallel structure.*<\/option><option value=\"9-10.L.1.b\">9-10.L.1.b: Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations.<\/option><option value=\"9-10.L.2\">9-10.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"9-10.L.2.a\">9-10.L.2.a: Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses.<\/option><option value=\"9-10.L.2.b\">9-10.L.2.b: Use a colon to introduce a list or quotation.<\/option><option value=\"9-10.L.2.c\">9-10.L.2.c: Spell correctly.<\/option><option value=\"9-10.L.3\">9-10.L.3: 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.<\/option><option value=\"9-10.L.3.a\">9-10.L.3.a: Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabian\u2019s Manual for Writers) appropriate for the discipline and writing type.<\/option><option value=\"9-10.L.4\">9-10.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9\u201310 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"9-10.L.4.a\">9-10.L.4.a: Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word\u2019s position or function in a sentence) as a clue to the meaning of a word or phrase.<\/option><option value=\"9-10.L.4.b\">9-10.L.4.b: Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy).<\/option><option value=\"9-10.L.4.c\">9-10.L.4.c: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology.<\/option><option value=\"9-10.L.4.d\">9-10.L.4.d: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).<\/option><option value=\"9-10.L.5\">9-10.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"9-10.L.5.a\">9-10.L.5.a: Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text.<\/option><option value=\"9-10.L.5.b\">9-10.L.5.b: Analyze nuances in the meaning of words with similar denotations.<\/option><option value=\"9-10.L.6\">9-10.L.6: Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.<\/option><option value=\"11-12.L.1\">11-12.L.1: Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.<\/option><option value=\"11-12.L.1.a\">11-12.L.1.a: Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested.<\/option><option value=\"11-12.L.1.b\">11-12.L.1.b: Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster\u2019s Dictionary of English Usage, Garner\u2019s Modern American Usage) as needed.<\/option><option value=\"11-12.L.2\">11-12.L.2: Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.<\/option><option value=\"11-12.L.2.a\">11-12.L.2.a: Observe hyphenation conventions.<\/option><option value=\"11-12.L.2.b\">11-12.L.2.b: Spell correctly.<\/option><option value=\"11-12.L.3\">11-12.L.3: 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.<\/option><option value=\"11-12.L.3.a\">11-12.L.3.a: Vary syntax for effect, consulting references (e.g., Tufte\u2019s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading.<\/option><option value=\"11-12.L.4\">11-12.L.4: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 11\u201312 reading and content, choosing flexibly from a range of strategies.<\/option><option value=\"11-12.L.4.a\">11-12.L.4.a: Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word\u2019s position or function in a sentence) as a clue to the meaning of a word or phrase.<\/option><option value=\"11-12.L.4.b\">11-12.L.4.b: Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable).<\/option><option value=\"11-12.L.4.c\">11-12.L.4.c: Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage.<\/option><option value=\"11-12.L.4.d\">11-12.L.4.d: Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary).<\/option><option value=\"11-12.L.5\">11-12.L.5: Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.<\/option><option value=\"11-12.L.5.a\">11-12.L.5.a: Interpret figures of speech (e.g., hyperbole, paradox) in context and analyze their role in the text.<\/option><option value=\"11-12.L.5.b\">11-12.L.5.b: Analyze nuances in the meaning of words with similar denotations.<\/option><option value=\"11-12.L.6\">11-12.L.6: Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.<\/option><option value=\"6-8.RH.1\">6-8.RH.1: Cite specific textual evidence to support analysis of primary and secondary sources.<\/option><option value=\"6-8.RH.2\">6-8.RH.2: Determine the central ideas or information of a primary or secondary source; provide an accurate summary of the source distinct from prior knowledge or opinions.<\/option><option value=\"6-8.RH.3\">6-8.RH.3: Identify key steps in a text\u2019s description of a process related to history\/social studies (e.g., how a bill becomes law, how interest rates are raised or lowered).<\/option><option value=\"6-8.RH.4\">6-8.RH.4: Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history\/social studies.<\/option><option value=\"6-8.RH.5\">6-8.RH.5: Describe how a text presents information (e.g., sequentially, comparatively, causally).<\/option><option value=\"6-8.RH.6\">6-8.RH.6: Identify aspects of a text that reveal an author\u2019s point of view or purpose (e.g., loaded language, inclusion or avoidance of particular facts).<\/option><option value=\"6-8.RH.7\">6-8.RH.7: Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.<\/option><option value=\"6-8.RH.8\">6-8.RH.8: Distinguish among fact, opinion, and reasoned judgment in a text.<\/option><option value=\"6-8.RH.9\">6-8.RH.9: Analyze the relationship between a primary and secondary source on the same topic.<\/option><option value=\"6-8.RH.10\">6-8.RH.10: By the end of grade 8, read and comprehend history\/social studies texts in the grades 6\u20138 text complexity band independently and proficiently.<\/option><option value=\"9-10.RH.1\">9-10.RH.1: Cite specific textual evidence to support analysis of primary and secondary sources, attending to such features as the date and origin of the information.<\/option><option value=\"9-10.RH.2\">9-10.RH.2: Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events or ideas develop over the course of the text.<\/option><option value=\"9-10.RH.3\">9-10.RH.3: Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them.<\/option><option value=\"9-10.RH.4\">9-10.RH.4: Determine the meaning of words and phrases as they are used in a text, including vocabulary describing political, social, or economic aspects of history\/social science.<\/option><option value=\"9-10.RH.5\">9-10.RH.5: Analyze how a text uses structure to emphasize key points or advance an explanation or analysis.<\/option><option value=\"9-10.RH.6\">9-10.RH.6: Compare the point of view of two or more authors for how they treat the same or similar topics, including which details they include and emphasize in their respective accounts.<\/option><option value=\"9-10.RH.7\">9-10.RH.7: Integrate quantitative or technical analysis (e.g., charts, research data) with qualitative analysis in print or digital text.<\/option><option value=\"9-10.RH.8\">9-10.RH.8: Assess the extent to which the reasoning and evidence in a text support the author\u2019s claims.<\/option><option value=\"9-10.RH.9\">9-10.RH.9: Compare and contrast treatments of the same topic in several primary and secondary sources.<\/option><option value=\"9-10.RH.10\">9-10.RH.10: By the end of grade 10, read and comprehend history\/social studies texts in the grades 9\u201310 text complexity band independently and proficiently.<\/option><option value=\"11-12.RH.1\">11-12.RH.1: 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.<\/option><option value=\"11-12.RH.2\">11-12.RH.2: 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.<\/option><option value=\"11-12.RH.3\">11-12.RH.3: Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain.<\/option><option value=\"11-12.RH.4\">11-12.RH.4: 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 (e.g., how Madison defines faction in Federalist No. 10).<\/option><option value=\"11-12.RH.5\">11-12.RH.5: 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.<\/option><option value=\"11-12.RH.6\">11-12.RH.6: Evaluate authors\u2019 differing points of view on the same historical event or issue by assessing the authors\u2019 claims, reasoning, and evidence.<\/option><option value=\"11-12.RH.7\">11-12.RH.7: Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem.<\/option><option value=\"11-12.RH.8\">11-12.RH.8: Evaluate an author\u2019s premises, claims, and evidence by corroborating or challenging them with other information.<\/option><option value=\"11-12.RH.9\">11-12.RH.9: Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources.<\/option><option value=\"11-12.RH.10\">11-12.RH.10: By the end of grade 12, read and comprehend history\/social studies texts in the grades 11\u2013CCR text complexity band independently and proficiently.<\/option><option value=\"6-8.RST.1\">6-8.RST.1: Cite specific textual evidence to support analysis of science and technical texts.<\/option><option value=\"6-8.RST.2\">6-8.RST.2: Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.<\/option><option value=\"6-8.RST.3\">6-8.RST.3: Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.<\/option><option value=\"6-8.RST.4\">6-8.RST.4: 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 6\u20138 texts and topics.<\/option><option value=\"6-8.RST.5\">6-8.RST.5: Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to an understanding of the topic.<\/option><option value=\"6-8.RST.6\">6-8.RST.6: Analyze the author\u2019s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text.<\/option><option value=\"6-8.RST.7\">6-8.RST.7: Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).<\/option><option value=\"6-8.RST.8\">6-8.RST.8: Distinguish among facts, reasoned judgment based on research findings, and speculation in a text.<\/option><option value=\"6-8.RST.9\">6-8.RST.9: Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.<\/option><option value=\"6-8.RST.10\">6-8.RST.10: By the end of grade 8, read and comprehend science\/technical texts in the grades 6\u20138 text complexity band independently and proficiently.<\/option><option value=\"9-10.RST.1\">9-10.RST.1: Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.<\/option><option value=\"9-10.RST.2\">9-10.RST.2: Determine the central ideas or conclusions of a text; trace the text\u2019s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text.<\/option><option value=\"9-10.RST.3\">9-10.RST.3: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.<\/option><option value=\"9-10.RST.4\">9-10.RST.4: 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 9\u201310 texts and topics.<\/option><option value=\"9-10.RST.5\">9-10.RST.5: Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy).<\/option><option value=\"9-10.RST.6\">9-10.RST.6: Analyze the author\u2019s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, defining the question the author seeks to address.<\/option><option value=\"9-10.RST.7\">9-10.RST.7: Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.<\/option><option value=\"9-10.RST.8\">9-10.RST.8: Assess the extent to which the reasoning and evidence in a text support the author\u2019s claim or a recommendation for solving a scientific or technical problem.<\/option><option value=\"9-10.RST.9\">9-10.RST.9: Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts.<\/option><option value=\"9-10.RST.10\">9-10.RST.10: By the end of grade 10, read and comprehend science\/technical texts in the grades 9\u201310 text complexity band independently and proficiently.<\/option><option value=\"11-12.RST.1\">11-12.RST.1: 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.<\/option><option value=\"11-12.RST.2\">11-12.RST.2: 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.<\/option><option value=\"11-12.RST.3\">11-12.RST.3: 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.<\/option><option value=\"11-12.RST.4\">11-12.RST.4: 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\u201312 texts and topics.<\/option><option value=\"11-12.RST.5\">11-12.RST.5: Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas.<\/option><option value=\"11-12.RST.6\">11-12.RST.6: Analyze the author\u2019s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved.<\/option><option value=\"11-12.RST.7\">11-12.RST.7: Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.<\/option><option value=\"11-12.RST.8\">11-12.RST.8: 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.<\/option><option value=\"11-12.RST.9\">11-12.RST.9: 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 when possible.<\/option><option value=\"11-12.RST.10\">11-12.RST.10: By the end of grade 12, read and comprehend science\/technical texts in the grades 11\u201312 text complexity band independently and proficiently.<\/option><option value=\"6-8.WHST.1\">6-8.WHST.1: Write arguments focused on discipline-specific content.<\/option><option value=\"6-8.WHST.1.a\">6-8.WHST.1.a: Introduce claim(s) about a topic or issue, acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically.<\/option><option value=\"6-8.WHST.1.b\">6-8.WHST.1.b: Support claim(s) with logical reasoning and relevant, accurate data and evidence that demonstrate an understanding of the topic or text, using credible sources.<\/option><option value=\"6-8.WHST.1.c\">6-8.WHST.1.c: Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence.<\/option><option value=\"6-8.WHST.1.d\">6-8.WHST.1.d: Establish and maintain a formal style.<\/option><option value=\"6-8.WHST.1.e\">6-8.WHST.1.e: Provide a concluding statement or section that follows from and supports the argument presented.<\/option><option value=\"6-8.WHST.2\">6-8.WHST.2: Write informative\/explanatory texts, including the narration of historical events, scientific procedures\/ experiments, or technical processes.<\/option><option value=\"6-8.WHST.2.a\">6-8.WHST.2.a: Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories as appropriate to achieving purpose; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"6-8.WHST.2.b\">6-8.WHST.2.b: Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples.<\/option><option value=\"6-8.WHST.2.c\">6-8.WHST.2.c: Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts.<\/option><option value=\"6-8.WHST.2.d\">6-8.WHST.2.d: Use precise language and domain-specific vocabulary to inform about or explain the topic.<\/option><option value=\"6-8.WHST.2.e\">6-8.WHST.2.e: Establish and maintain a formal style and objective tone.<\/option><option value=\"6-8.WHST.2.f\">6-8.WHST.2.f: Provide a concluding statement or section that follows from and supports the information or explanation presented.<\/option><option value=\"6-8.WHST.3\">6-8.WHST.3: (See note; not applicable as a separate requirement)<\/option><option value=\"6-8.WHST.4\">6-8.WHST.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.<\/option><option value=\"6-8.WHST.5\">6-8.WHST.5: 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, focusing on how well purpose and audience have been addressed.<\/option><option value=\"6-8.WHST.6\">6-8.WHST.6: Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently.<\/option><option value=\"6-8.WHST.7\">6-8.WHST.7: Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.<\/option><option value=\"6-8.WHST.8\">6-8.WHST.8: Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.<\/option><option value=\"6-8.WHST.9\">6-8.WHST.9: Draw evidence from informational texts to support analysis reflection, and research.<\/option><option value=\"6-8.WHST.10\">6-8.WHST.10: 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, purposes, and audiences.<\/option><option value=\"9-10.WHST.1\">9-10.WHST.1: Write arguments focused on discipline-specific content.<\/option><option value=\"9-10.WHST.1.a\">9-10.WHST.1.a: Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence.<\/option><option value=\"9-10.WHST.1.b\">9-10.WHST.1.b: Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form and in a manner that anticipates the audience\u2019s knowledge level and concerns.<\/option><option value=\"9-10.WHST.1.c\">9-10.WHST.1.c: Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.<\/option><option value=\"9-10.WHST.1.d\">9-10.WHST.1.d: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"9-10.WHST.1.e\">9-10.WHST.1.e: Provide a concluding statement or section that follows from or supports the argument presented.<\/option><option value=\"9-10.WHST.2\">9-10.WHST.2: Write informative\/explanatory texts, including the narration of historical events, scientific procedures\/ experiments, or technical processes.<\/option><option value=\"9-10.WHST.2.a\">9-10.WHST.2.a: Introduce a topic and organize ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"9-10.WHST.2.b\">9-10.WHST.2.b: Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience\u2019s knowledge of the topic.<\/option><option value=\"9-10.WHST.2.c\">9-10.WHST.2.c: Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.<\/option><option value=\"9-10.WHST.2.d\">9-10.WHST.2.d: Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.<\/option><option value=\"9-10.WHST.2.e\">9-10.WHST.2.e: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"9-10.WHST.2.f\">9-10.WHST.2.f: Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).<\/option><option value=\"9-10.WHST.3\">9-10.WHST.3: (See note; not applicable as a separate requirement)<\/option><option value=\"9-10.WHST.4\">9-10.WHST.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.<\/option><option value=\"9-10.WHST.5\">9-10.WHST.5: 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.<\/option><option value=\"9-10.WHST.6\">9-10.WHST.6: Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology\u2019s capacity to link to other information and to display information flexibly and dynamically.<\/option><option value=\"9-10.WHST.7\">9-10.WHST.7: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.<\/option><option value=\"9-10.WHST.8\">9-10.WHST.8: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation.<\/option><option value=\"9-10.WHST.9\">9-10.WHST.9: Draw evidence from informational texts to support analysis, reflection, and research.<\/option><option value=\"9-10.WHST.10\">9-10.WHST.10: 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, purposes, and audiences.<\/option><option value=\"11-12.WHST.1\">11-12.WHST.1: Write arguments focused on discipline-specific content.<\/option><option value=\"11-12.WHST.1.a\">11-12.WHST.1.a: Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence.<\/option><option value=\"11-12.WHST.1.b\">11-12.WHST.1.b: Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience\u2019s knowledge level, concerns, values, and possible biases.<\/option><option value=\"11-12.WHST.1.c\">11-12.WHST.1.c: Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.<\/option><option value=\"11-12.WHST.1.d\">11-12.WHST.1.d: Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.<\/option><option value=\"11-12.WHST.1.e\">11-12.WHST.1.e: Provide a concluding statement or section that follows from or supports the argument presented.<\/option><option value=\"11-12.WHST.2\">11-12.WHST.2: Write informative\/explanatory texts, including the narration of historical events, scientific procedures\/ experiments, or technical processes.<\/option><option value=\"11-12.WHST.2.a\">11-12.WHST.2.a: Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.<\/option><option value=\"11-12.WHST.2.b\">11-12.WHST.2.b: Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience\u2019s knowledge of the topic.<\/option><option value=\"11-12.WHST.2.c\">11-12.WHST.2.c: Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.<\/option><option value=\"11-12.WHST.2.d\">11-12.WHST.2.d: Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers.<\/option><option value=\"11-12.WHST.2.e\">11-12.WHST.2.e: Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or the significance of the topic).<\/option><option value=\"11-12.WHST.3\">11-12.WHST.3: (See note; not applicable as a separate requirement)<\/option><option value=\"11-12.WHST.4\">11-12.WHST.4: Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.<\/option><option value=\"11-12.WHST.5\">11-12.WHST.5: 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.<\/option><option value=\"11-12.WHST.6\">11-12.WHST.6: 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.<\/option><option value=\"11-12.WHST.7\">11-12.WHST.7: Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.<\/option><option value=\"11-12.WHST.8\">11-12.WHST.8: Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the specific task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.<\/option><option value=\"11-12.WHST.9\">11-12.WHST.9: Draw evidence from informational texts to support analysis, reflection, and research.<\/option><option value=\"11-12.WHST.10\">11-12.WHST.10: 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, purposes, and audiences.<\/option><\/select>\r\n<select class=\"standards-math\" multiple=\"\" style=\"display:none;\"><option value=\"1.MD.A.1\" data-msa=\"0\" data-wap=\"1\">1.MD.A.1: &lt;p&gt;Order three objects by length; compare the lengths of two objects indirectly by using a third object.&lt;\/p&gt;\r\n<\/option><option value=\"1.MD.A.2\" data-msa=\"0\" data-wap=\"1\">1.MD.A.2: &lt;p&gt;Express the length of an object as a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.&lt;\/p&gt;\r\n<\/option><option value=\"1.G.A.3\" data-msa=\"2\" data-wap=\"1\">1.G.A.3: &lt;p&gt;Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.&lt;\/p&gt;\r\n<\/option><option value=\"1.G.A.1\" data-msa=\"2\" data-wap=\"1\">1.G.A.1: &lt;p&gt;Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.&lt;\/p&gt;\r\n<\/option><option value=\"1.G.A.2\" data-msa=\"2\" data-wap=\"1\">1.G.A.2: &lt;p&gt;Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Students do not need to learn formal names such as &amp;ldquo;right rectangular prism.&amp;rdquo;&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"1.MD.B.3\" data-msa=\"2\" data-wap=\"1\">1.MD.B.3: Tell and write time in hours and half-hours using analog and digital clocks.<\/option><option value=\"1.MD.C.4\" data-msa=\"1\" data-wap=\"1\">1.MD.C.4: &lt;p&gt;Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.&lt;\/p&gt;\r\n<\/option><option value=\"1.NBT.A.1\" data-msa=\"0\" data-wap=\"1\">1.NBT.A.1: &lt;p&gt;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.&lt;\/p&gt;\r\n<\/option><option value=\"1.NBT.B.2\" data-msa=\"0\" data-wap=\"1\">1.NBT.B.2: &lt;p&gt;Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:&lt;\/p&gt;\r\n<\/option><option value=\"1.NBT.B.2.a\" data-msa=\"0\" data-wap=\"1\">1.NBT.B.2.a: 10 can be thought of as a bundle of ten ones \u2014 called a \u201cten.\u201d b.<\/option><option value=\"1.NBT.B.2.b\" data-msa=\"0\" data-wap=\"1\">1.NBT.B.2.b: The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.<\/option><option value=\"1.NBT.B.2.c\" data-msa=\"0\" data-wap=\"1\">1.NBT.B.2.c: 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).<\/option><option value=\"1.NBT.B.3\" data-msa=\"0\" data-wap=\"1\">1.NBT.B.3: &lt;p&gt;Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols &amp;gt;, =, and &amp;lt;.&lt;\/p&gt;\r\n<\/option><option value=\"1.NBT.C.4\" data-msa=\"0\" data-wap=\"1\">1.NBT.C.4: &lt;p&gt;Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.&lt;\/p&gt;\r\n<\/option><option value=\"1.NBT.C.5\" data-msa=\"0\" data-wap=\"1\">1.NBT.C.5: &lt;p&gt;Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.&lt;\/p&gt;\r\n<\/option><option value=\"1.NBT.C.6\" data-msa=\"0\" data-wap=\"1\">1.NBT.C.6: &lt;p&gt;Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.A.1\" data-msa=\"0\" data-wap=\"1\">1.OA.A.1: &lt;p&gt;Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*See &lt;a href=&quot;https:\/\/achievethecore.org\/content\/upload\/CCSSM%20Glossary%20Table%201.pdf&quot;&gt;Glossary, Table 1&lt;\/a&gt;.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.A.2\" data-msa=\"0\" data-wap=\"1\">1.OA.A.2: &lt;p&gt;Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.B.3\" data-msa=\"0\" data-wap=\"1\">1.OA.B.3: &lt;p&gt;Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; as strategies to add and subtract.* Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Students need not use formal terms for these properties.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.B.4\" data-msa=\"0\" data-wap=\"1\">1.OA.B.4: &lt;p&gt;Understand subtraction as an unknown-addend problem. For example, subtract 10 &amp;ndash; 8 by finding the number that makes 10 when added to 8.&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.C.5\" data-msa=\"0\" data-wap=\"1\">1.OA.C.5: &lt;p&gt;Relate counting to addition and subtraction (e.g., by &lt;a id=&quot;A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on\u2014pointing to the top book and saying \u201ceight,\u201d following this with \u201cnine, ten, eleven. There are eleven books now.\u201d&quot; name=&quot;A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on\u2014pointing to the top book and saying \u201ceight,\u201d following this with \u201cnine, ten, eleven. There are eleven books now.\u201d&quot;&gt;counting on&lt;\/a&gt; 2 to add 2).&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.C.6\" data-msa=\"0\" data-wap=\"1\">1.OA.C.6: &lt;p&gt;Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as&lt;a id=&quot;A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on\u2014pointing to the top book and saying \u201ceight,\u201d following this with \u201cnine, ten, eleven. There are eleven books now.\u201d&quot; name=&quot;A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on\u2014pointing to the top book and saying \u201ceight,\u201d following this with \u201cnine, ten, eleven. There are eleven books now.\u201d&quot;&gt; counting on&lt;\/a&gt;; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 &amp;ndash; 4 = 13 &amp;ndash; 3 &amp;ndash; 1 = 10 &amp;ndash; 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 &amp;ndash; 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.D.7\" data-msa=\"0\" data-wap=\"1\">1.OA.D.7: &lt;p&gt;Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 &amp;ndash; 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.D.8\" data-msa=\"0\" data-wap=\"1\">1.OA.D.8: &lt;p&gt;Determine the unknown &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? &amp;ndash; 3, 6 + 6 = ?.&lt;\/p&gt;\r\n<\/option><option value=\"2.G.A.1\" data-msa=\"2\" data-wap=\"1\">2.G.A.1: &lt;p&gt;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.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Sizes are compared directly or visually, not compared by measuring.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"2.G.A.2\" data-msa=\"2\" data-wap=\"1\">2.G.A.2: &lt;p&gt;Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.&lt;\/p&gt;\r\n<\/option><option value=\"2.G.A.3\" data-msa=\"2\" data-wap=\"1\">2.G.A.3: &lt;p&gt;Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.A.1\" data-msa=\"0\" data-wap=\"1\">2.MD.A.1: &lt;p&gt;Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.A.2\" data-msa=\"0\" data-wap=\"1\">2.MD.A.2: &lt;p&gt;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.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.A.3\" data-msa=\"0\" data-wap=\"1\">2.MD.A.3: &lt;p&gt;Estimate lengths using units of inches, feet, centimeters, and meters.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.A.4\" data-msa=\"0\" data-wap=\"1\">2.MD.A.4: &lt;p&gt;Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.B.5\" data-msa=\"0\" data-wap=\"1\">2.MD.B.5: &lt;p&gt;Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.B.6\" data-msa=\"0\" data-wap=\"1\">2.MD.B.6: &lt;p&gt;Represent &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.C.7\" data-msa=\"1\" data-wap=\"1\">2.MD.C.7: &lt;p&gt;Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.C.8\" data-msa=\"1\" data-wap=\"1\">2.MD.C.8: &lt;p&gt;Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and &amp;cent; symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.D.9\" data-msa=\"1\" data-wap=\"1\">2.MD.D.9: &lt;p&gt;Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a &lt;a id=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;line plot&lt;\/a&gt;, where the horizontal scale is marked off in whole-number units.&lt;\/p&gt;\r\n<\/option><option value=\"2.MD.D.10\" data-msa=\"1\" data-wap=\"1\">2.MD.D.10: &lt;p&gt;Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems* using information presented in a bar graph.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*See &lt;a href=&quot;https:\/\/achievethecore.org\/content\/upload\/CCSSM%20Glossary%20Table%201.pdf&quot;&gt;Glossary, Table 1&lt;\/a&gt;&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.A.1\" data-msa=\"0\" data-wap=\"1\">2.NBT.A.1: &lt;p&gt;Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.A.1.a\" data-msa=\"0\" data-wap=\"1\">2.NBT.A.1.a: 100 can be thought of as a bundle of ten tens \u2014 called a \u201chundred.\u201d<\/option><option value=\"2.NBT.A.1.b\" data-msa=\"0\" data-wap=\"1\">2.NBT.A.1.b: 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).<\/option><option value=\"2.NBT.A.2\" data-msa=\"0\" data-wap=\"1\">2.NBT.A.2: &lt;p&gt;Count within 1000; skip-count by 5s, 10s, and 100s.&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.A.3\" data-msa=\"0\" data-wap=\"1\">2.NBT.A.3: &lt;p&gt;Read and write numbers to 1000 using base-ten numerals, number names, and &lt;a id=&quot;&amp;quot;A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.&amp;quot;&quot; name=&quot;&amp;quot;A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.&amp;quot;&quot;&gt;expanded form&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.A.4\" data-msa=\"0\" data-wap=\"1\">2.NBT.A.4: &lt;p&gt;Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using &amp;gt;, =, and &amp;lt; symbols to record the results of comparisons.&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.B.5\" data-msa=\"0\" data-wap=\"1\">2.NBT.B.5: &lt;p&gt;Fluently add and subtract within 100 using strategies based on place value, &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between addition and subtraction.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.D.6\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.D.6: &lt;p&gt;Rewrite simple &lt;a id=&quot;A quotient of two polynomials with a non-zero denominator.&quot; name=&quot;A quotient of two polynomials with a non-zero denominator.&quot;&gt;rational expressions&lt;\/a&gt; in different forms; write&amp;nbsp;a(x)b(x)&amp;nbsp;in the form&amp;nbsp;q(x)+r(x)b(x), where&amp;nbsp;a(x),&amp;nbsp;b(x),&amp;nbsp;q(x), and&amp;nbsp;r(x)&amp;nbsp;are polynomials with the degree of&amp;nbsp;r(x)&amp;nbsp;less than the degree of&amp;nbsp;b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.D.7\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.D.7: &lt;p&gt;(+) Understand that &lt;a id=&quot;A quotient of two polynomials with a non-zero  denominator.&quot; name=&quot;A quotient of two polynomials with a non-zero  denominator.&quot;&gt;rational expressions&lt;\/a&gt; form a system analogous to the &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;, closed under addition, subtraction, multiplication, and division by a nonzero &lt;a id=&quot;A quotient of two polynomials with a non-zero  denominator.&quot; name=&quot;A quotient of two polynomials with a non-zero  denominator.&quot;&gt;rational expression&lt;\/a&gt;; add, subtract, multiply, and divide &lt;a id=&quot;A quotient of two polynomials with a non-zero  denominator.&quot; name=&quot;A quotient of two polynomials with a non-zero  denominator.&quot;&gt;rational expressions&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-CED.A.1\" data-msa=\"0\" data-wap=\"0\">HS.A-CED.A.1: &lt;p&gt;Create equations and inequalities in one variable and use them to solve problems. &lt;em&gt;Include equations arising from linear and quadratic functions, and simple rational and exponential functions.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-CED.A.2\" data-msa=\"0\" data-wap=\"0\">HS.A-CED.A.2: &lt;p&gt;Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-CED.A.3\" data-msa=\"0\" data-wap=\"0\">HS.A-CED.A.3: &lt;p&gt;Represent constraints by equations or inequalities, and by systems of equations and\/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. &lt;em&gt;For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-CED.A.4\" data-msa=\"0\" data-wap=\"0\">HS.A-CED.A.4: &lt;p&gt;Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. &lt;em&gt;For example, rearrange Ohm&amp;rsquo;s law V = IR to highlight resistance R.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.B.6\" data-msa=\"0\" data-wap=\"1\">2.NBT.B.6: &lt;p&gt;Add up to four two-digit numbers using strategies based on place value and &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.B.7\" data-msa=\"0\" data-wap=\"1\">2.NBT.B.7: &lt;p&gt;Add and subtract within 1000, using concrete models or drawings and strategies based on place value, &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.B.8\" data-msa=\"0\" data-wap=\"1\">2.NBT.B.8: &lt;p&gt;Mentally add 10 or 100 to a given number 100&amp;ndash;900, and mentally subtract 10 or 100 from a given number 100&amp;ndash;900.&lt;\/p&gt;\r\n<\/option><option value=\"2.NBT.B.9\" data-msa=\"0\" data-wap=\"1\">2.NBT.B.9: &lt;p&gt;Explain why addition and subtraction strategies work, using place value and the &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Explanations may be supported by drawings or objects.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"2.OA.A.1\" data-msa=\"0\" data-wap=\"1\">2.OA.A.1: &lt;p&gt;Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*See &lt;a href=&quot;https:\/\/achievethecore.org\/content\/upload\/CCSSM%20Glossary%20Table%201.pdf&quot;&gt;Glossary, Table 1&lt;\/a&gt;&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"2.OA.B.2\" data-msa=\"0\" data-wap=\"1\">2.OA.B.2: &lt;p&gt;Fluently add and subtract within 20 using mental strategies.* By end of Grade 2, know from memory all sums of two one-digit numbers.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*See standard 1.OA.6 for a list of mental strategies.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"2.OA.C.3\" data-msa=\"1\" data-wap=\"1\">2.OA.C.3: &lt;p&gt;Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.&lt;\/p&gt;\r\n<\/option><option value=\"2.OA.C.4\" data-msa=\"1\" data-wap=\"1\">2.OA.C.4: &lt;p&gt;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.&lt;\/p&gt;\r\n<\/option><option value=\"3.G.A.1\" data-msa=\"1\" data-wap=\"1\">3.G.A.1: &lt;p&gt;Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.&lt;\/p&gt;\r\n<\/option><option value=\"3.G.A.2\" data-msa=\"1\" data-wap=\"1\">3.G.A.2: &lt;p&gt;Partition shapes into parts with equal areas. Express the area of each part as a unit &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1\/4 of the area of the shape.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.A.1\" data-msa=\"0\" data-wap=\"1\">3.MD.A.1: &lt;p&gt;Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.A.2\" data-msa=\"0\" data-wap=\"1\">3.MD.A.2: &lt;p&gt;Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).* Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.**&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Excludes compound units such as cm3 and finding the geometric volume of a container.&lt;\/sup&gt;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;**Excludes multiplicative comparison problems (problems involving notions of &amp;ldquo;times as much&amp;rdquo;; see &lt;a href=&quot;https:\/\/achievethecore.org\/content\/upload\/CCSSM%20Glossary%20Table%202.pdf&quot;&gt;Glossary, Table 2&lt;\/a&gt;)&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.B.3\" data-msa=\"1\" data-wap=\"1\">3.MD.B.3: &lt;p&gt;Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step &amp;ldquo;how many more&amp;rdquo; and &amp;ldquo;how many less&amp;rdquo; problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.B.4\" data-msa=\"1\" data-wap=\"1\">3.MD.B.4: &lt;p&gt;Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a &lt;a id=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;line plot&lt;\/a&gt;, where the horizontal scale is marked off in appropriate units&amp;mdash; &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt;, halves, or quarters.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.C.5\" data-msa=\"0\" data-wap=\"1\">3.MD.C.5: &lt;p&gt;Recognize area as an attribute of plane figures and understand concepts of area measurement.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.C.5.a\" data-msa=\"0\" data-wap=\"1\">3.MD.C.5.a: A square with side length 1 unit, called \u201ca unit square,\u201d is said to have \u201cone square unit\u201d of area, and can be used to measure area.<\/option><option value=\"3.MD.C.5.b\" data-msa=\"0\" data-wap=\"1\">3.MD.C.5.b: 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.<\/option><option value=\"3.MD.C.6\" data-msa=\"0\" data-wap=\"1\">3.MD.C.6: &lt;p&gt;Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.C.7\" data-msa=\"0\" data-wap=\"1\">3.MD.C.7: &lt;p&gt;Relate area to the operations of multiplication and addition.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.C.7.a\" data-msa=\"0\" data-wap=\"1\">3.MD.C.7.a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.<\/option><option value=\"3.MD.C.7.b\" data-msa=\"0\" data-wap=\"1\">3.MD.C.7.b: Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.<\/option><option value=\"3.MD.C.7.c\" data-msa=\"0\" data-wap=\"1\">3.MD.C.7.c: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a \u00d7 b and a \u00d7 c. Use area models to represent the distributive property in mathematical reasoning.<\/option><option value=\"3.MD.C.7.d\" data-msa=\"0\" data-wap=\"1\">3.MD.C.7.d: &lt;p&gt;Recognize area as additive. Find areas of &lt;a id=&quot;A polygon all angles of which are right angles.&quot; name=&quot;A polygon all angles of which are right angles.&quot;&gt;rectilinear figures&lt;\/a&gt; by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.D.8\" data-msa=\"2\" data-wap=\"1\">3.MD.D.8: &lt;p&gt;Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.&lt;\/p&gt;\r\n<\/option><option value=\"3.NBT.A.1\" data-msa=\"2\" data-wap=\"1\">3.NBT.A.1: &lt;p&gt;Use place value understanding to round &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; to the nearest 10 or 100.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*A range of algorithms may be used.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NBT.A.2\" data-msa=\"2\" data-wap=\"1\">3.NBT.A.2: &lt;p&gt;Fluently add and subtract within 1000 using strategies and algorithms based on place value, &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between addition and subtraction.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*A range of algorithms may be used.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NBT.A.3\" data-msa=\"2\" data-wap=\"1\">3.NBT.A.3: &lt;p&gt;Multiply one-digit &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; by multiples of 10 in the range 10&amp;ndash;90 (e.g., 9 &amp;times; 80, 5 &amp;times; 60) using strategies based on place value and &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*A range of algorithms may be used.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.1\" data-msa=\"0\" data-wap=\"1\">3.NF.A.1: &lt;p&gt;Understand a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; 1\/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a\/b as the quantity formed by a parts of size 1\/b.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.2\" data-msa=\"0\" data-wap=\"1\">3.NF.A.2: &lt;p&gt;Understand a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; as a number on the number line; represent fractions on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.2.a\" data-msa=\"0\" data-wap=\"1\">3.NF.A.2.a: &lt;p&gt;Represent a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; 1\/b on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt; by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1\/b and that the endpoint of the part based at 0 locates the number 1\/b on the number line.&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.2.b\" data-msa=\"0\" data-wap=\"1\">3.NF.A.2.b: &lt;p&gt;Represent a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; a\/b on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt; by marking off a lengths 1\/b from 0. Recognize that the resulting interval has size a\/b and that its endpoint locates the number a\/b on the number line.&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.3\" data-msa=\"0\" data-wap=\"1\">3.NF.A.3: &lt;p&gt;Explain equivalence of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; in special cases, and compare fractions by reasoning about their size.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.3.a\" data-msa=\"0\" data-wap=\"1\">3.NF.A.3.a: &lt;p&gt;Understand two &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; as equivalent (equal) if they are the same size, or the same point on a number line.&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.3.b\" data-msa=\"0\" data-wap=\"1\">3.NF.A.3.b: &lt;p&gt;Recognize and generate simple equivalent &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt;, e.g., 1\/2 = 2\/4, 4\/6 = 2\/3). Explain why the fractions are equivalent, e.g., by using a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.3.c\" data-msa=\"0\" data-wap=\"1\">3.NF.A.3.c: &lt;p&gt;Express whole numbers as &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt;, and recognize fractions that are equivalent to &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt;. Examples: Express 3 in the form 3 = 3\/1; recognize that 6\/1 = 6; locate 4\/4 and 1 at the same point of a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A.3.d\" data-msa=\"0\" data-wap=\"1\">3.NF.A.3.d: &lt;p&gt;Compare two &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols &amp;gt;, =, or &amp;lt;, and justify the conclusions, e.g., by using a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.A.1\" data-msa=\"0\" data-wap=\"1\">3.OA.A.1: &lt;p&gt;Interpret products of &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt;, e.g., interpret 5 &amp;times; 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 &amp;times; 7.&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.A.2\" data-msa=\"0\" data-wap=\"1\">3.OA.A.2: &lt;p&gt;Interpret whole-number quotients of &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt;, e.g., interpret 56 &amp;divide; 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 &amp;divide; 8.&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.A.3\" data-msa=\"0\" data-wap=\"1\">3.OA.A.3: &lt;p&gt;Use &lt;a id=&quot;&amp;quot;Multiplication or division of two whole numbers with whole number answers, and with product or dividend in the range 0-100. Example: 72 \u00f7 8 = 9.&amp;quot;&quot; name=&quot;&amp;quot;Multiplication or division of two whole numbers with whole number answers, and with product or dividend in the range 0-100. Example: 72 \u00f7 8 = 9.&amp;quot;&quot;&gt;multiplication and division within 100&lt;\/a&gt; to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*See &lt;a href=&quot;https:\/\/achievethecore.org\/content\/upload\/CCSSM%20Glossary%20Table%202.pdf&quot;&gt;Glossary, Table 2&lt;\/a&gt;&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.A.4\" data-msa=\"0\" data-wap=\"1\">3.OA.A.4: &lt;p&gt;Determine the unknown &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 &amp;times; ? = 48, 5 = ? &amp;divide; 3, 6 &amp;times; 6 = ?.&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.B.5\" data-msa=\"0\" data-wap=\"1\">3.OA.B.5: &lt;p&gt;Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; as strategies to multiply and divide.* Examples: If 6 &amp;times; 4 = 24 is known, then 4 &amp;times; 6 = 24 is also known. (Commutative property of multiplication.) 3 &amp;times; 5 &amp;times; 2 can be found by 3 &amp;times; 5 = 15, then 15 &amp;times; 2 = 30, or by 5 &amp;times; 2 = 10, then 3 &amp;times; 10 = 30. (Associative property of multiplication.) Knowing that 8 &amp;times; 5 = 40 and 8 &amp;times; 2 = 16, one can find 8 &amp;times; 7 as 8 &amp;times; (5 + 2) = (8 &amp;times; 5) + (8 &amp;times; 2) = 40 + 16 = 56. (Distributive property.)&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Students need not use formal terms for these properties.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.B.6\" data-msa=\"0\" data-wap=\"1\">3.OA.B.6: &lt;p&gt;Understand division as an unknown-factor problem. For example, find 32 &amp;divide; 8 by finding the number that makes 32 when multiplied by 8.&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.C.7\" data-msa=\"0\" data-wap=\"1\">3.OA.C.7: &lt;p&gt;Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 &amp;times; 5 = 40, one knows 40 &amp;divide; 5 = 8) or &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;. By the end of Grade 3, know from memory all products of two one-digit numbers.&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.D.8\" data-msa=\"0\" data-wap=\"1\">3.OA.D.8: &lt;p&gt;Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*This standard is limited to problems posed with whole numbers and having wholenumber answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.OA.D.9\" data-msa=\"0\" data-wap=\"1\">3.OA.D.9: &lt;p&gt;Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.&lt;\/p&gt;\r\n<\/option><option value=\"4.G.A.1\" data-msa=\"2\" data-wap=\"1\">4.G.A.1: &lt;p&gt;Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.&lt;\/p&gt;\r\n<\/option><option value=\"4.G.A.2\" data-msa=\"2\" data-wap=\"1\">4.G.A.2: &lt;p&gt;Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.&lt;\/p&gt;\r\n<\/option><option value=\"4.G.A.3\" data-msa=\"2\" data-wap=\"1\">4.G.A.3: &lt;p&gt;Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.A.1\" data-msa=\"1\" data-wap=\"1\">4.MD.A.1: &lt;p&gt;Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.A.2\" data-msa=\"1\" data-wap=\"1\">4.MD.A.2: &lt;p&gt;Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagrams&lt;\/a&gt; that feature a measurement scale.&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.A.3\" data-msa=\"1\" data-wap=\"1\">4.MD.A.3: &lt;p&gt;Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.B.4\" data-msa=\"1\" data-wap=\"1\">4.MD.B.4: &lt;p&gt;Make a line plot to display a data set of measurements in &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; of a unit (1\/2, 1\/4, 1\/8). Solve problems involving addition and subtraction of fractions by using information presented in &lt;a id=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;line plots&lt;\/a&gt;. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.C.5\" data-msa=\"2\" data-wap=\"1\">4.MD.C.5: &lt;p&gt;Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.C.5.a\" data-msa=\"2\" data-wap=\"1\">4.MD.C.5.a: &lt;p&gt;An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1\/360 of a circle is called a &amp;ldquo;one-degree angle,&amp;rdquo; and can be used to measure angles.&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.C.5.b\" data-msa=\"2\" data-wap=\"1\">4.MD.C.5.b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.<\/option><option value=\"4.MD.C.6\" data-msa=\"2\" data-wap=\"1\">4.MD.C.6: &lt;p&gt;Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.&lt;\/p&gt;\r\n<\/option><option value=\"4.MD.C.7\" data-msa=\"2\" data-wap=\"1\">4.MD.C.7: &lt;p&gt;Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.A.1\" data-msa=\"0\" data-wap=\"1\">4.NBT.A.1: &lt;p&gt;Recognize that in a multi-digit &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt;, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 &amp;divide; 70 = 10 by applying concepts of place value and division.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.A.2\" data-msa=\"0\" data-wap=\"1\">4.NBT.A.2: &lt;p&gt;Read and write multi-digit &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; using base-ten numerals, number names, and &lt;a id=&quot;&amp;quot;A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.&amp;quot;&quot; name=&quot;&amp;quot;A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.&amp;quot;&quot;&gt;expanded form&lt;\/a&gt;. Compare two multi-digit numbers based on meanings of the digits in each place, using &amp;gt;, =, and &amp;lt; symbols to record the results of comparisons.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.A.3\" data-msa=\"0\" data-wap=\"1\">4.NBT.A.3: &lt;p&gt;Use place value understanding to round multi-digit &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; to any place.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.B.4\" data-msa=\"0\" data-wap=\"1\">4.NBT.B.4: &lt;p&gt;Fluently add and subtract multi-digit &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; using the standard algorithm.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.B.5\" data-msa=\"0\" data-wap=\"1\">4.NBT.B.5: &lt;p&gt;Multiply a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;. Illustrate and explain the calculation by using equations, rectangular arrays, and\/or area models.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.B.6\" data-msa=\"0\" data-wap=\"1\">4.NBT.B.6: &lt;p&gt;Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and\/or area models.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.A.1\" data-msa=\"0\" data-wap=\"1\">4.NF.A.1: &lt;p&gt;Explain why a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; a\/b is equivalent to a fraction (n &amp;times; a)\/(n &amp;times; b) by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt;, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.A.2\" data-msa=\"0\" data-wap=\"1\">4.NF.A.2: &lt;p&gt;Compare two &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1\/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols &amp;gt;, =, or &amp;lt;, and justify the conclusions, e.g., by using a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt;.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.3\" data-msa=\"0\" data-wap=\"1\">4.NF.B.3: &lt;p&gt;Understand a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; a\/b with a &amp;gt; 1 as a sum of fractions 1\/b.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.3.a\" data-msa=\"0\" data-wap=\"1\">4.NF.B.3.a: &lt;p&gt;Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.3.b\" data-msa=\"0\" data-wap=\"1\">4.NF.B.3.b: &lt;p&gt;Decompose a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt;. Examples: 3\/8 = 1\/8 + 1\/8 + 1\/8 ; 3\/8 = 1\/8 + 2\/8 ; 2 1\/8 = 1 + 1 + 1\/8 = 8\/8 + 8\/8 + 1\/8.&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.3.c\" data-msa=\"0\" data-wap=\"1\">4.NF.B.3.c: &lt;p&gt;Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt;, and\/or by using &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; and the relationship between addition and subtraction.&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.3.d\" data-msa=\"0\" data-wap=\"1\">4.NF.B.3.d: &lt;p&gt;Solve word problems involving addition and subtraction of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; referring to the same whole and having like denominators, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt; and equations to represent the problem.&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.4\" data-msa=\"0\" data-wap=\"1\">4.NF.B.4: &lt;p&gt;Apply and extend previous understandings of multiplication to multiply a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; by a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt;.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.4.a\" data-msa=\"0\" data-wap=\"1\">4.NF.B.4.a: &lt;p&gt;Understand a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; a\/b as a multiple of 1\/b. For example, use a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt; to represent 5\/4 as the product 5 &amp;times; (1\/4), recording the conclusion by the equation 5\/4 = 5 &amp;times; (1\/4).&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.4.b\" data-msa=\"0\" data-wap=\"1\">4.NF.B.4.b: &lt;p&gt;Understand a multiple of a\/b as a multiple of 1\/b, and use this understanding to multiply a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; by a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt;. For example, use a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model &lt;\/a&gt;to express 3 &amp;times; (2\/5) as 6 &amp;times; (1\/5), recognizing this product as 6\/5. (In general, n &amp;times; (a\/b) = (n &amp;times; a)\/b.)&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.B.4.c\" data-msa=\"0\" data-wap=\"1\">4.NF.B.4.c: &lt;p&gt;Solve word problems involving multiplication of a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; by a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt;, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt; and equations to represent the problem. For example, if each person at a party will eat 3\/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.C.5\" data-msa=\"0\" data-wap=\"1\">4.NF.C.5: &lt;p&gt;Express a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.* For example, express 3\/10 as 30\/100, and add 3\/10 + 4\/100 = 34\/100.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.&lt;\/sup&gt;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;**Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.C.6\" data-msa=\"0\" data-wap=\"1\">4.NF.C.6: &lt;p&gt;Use decimal notation for &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; with denominators 10 or 100. For example, rewrite 0.62 as 62\/100; describe a length as 0.62 meters; locate 0.62 on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.C.7\" data-msa=\"0\" data-wap=\"1\">4.NF.C.7: &lt;p&gt;Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols &amp;gt;, =, or &amp;lt;, and justify the conclusions, e.g., by using a visual model.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.OA.A.1\" data-msa=\"0\" data-wap=\"1\">4.OA.A.1: &lt;p&gt;Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 &amp;times; 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.&lt;\/p&gt;\r\n<\/option><option value=\"4.OA.A.2\" data-msa=\"0\" data-wap=\"1\">4.OA.A.2: &lt;p&gt;Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*See &lt;a href=&quot;https:\/\/achievethecore.org\/content\/upload\/CCSSM%20Glossary%20Table%202.pdf&quot;&gt;Glossary, Table 2&lt;\/a&gt;&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"4.OA.A.3\" data-msa=\"0\" data-wap=\"1\">4.OA.A.3: &lt;p&gt;Solve multistep word problems posed with &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.&lt;\/p&gt;\r\n<\/option><option value=\"4.OA.B.4\" data-msa=\"1\" data-wap=\"1\">4.OA.B.4: &lt;p&gt;Find all factor pairs for a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; in the range 1&amp;ndash;100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1&amp;ndash;100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1&amp;ndash;100 is prime or composite.&lt;\/p&gt;\r\n<\/option><option value=\"4.OA.C.5\" data-msa=\"2\" data-wap=\"1\">4.OA.C.5: &lt;p&gt;Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule &amp;ldquo;Add 3&amp;rdquo; and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.&lt;\/p&gt;\r\n<\/option><option value=\"5.G.A.1\" data-msa=\"2\" data-wap=\"1\">5.G.A.1: &lt;p&gt;Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).&lt;\/p&gt;\r\n<\/option><option value=\"5.G.A.2\" data-msa=\"2\" data-wap=\"1\">5.G.A.2: &lt;p&gt;Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.&lt;\/p&gt;\r\n<\/option><option value=\"5.G.B.3\" data-msa=\"2\" data-wap=\"1\">5.G.B.3: &lt;p&gt;Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.&lt;\/p&gt;\r\n<\/option><option value=\"5.G.B.4\" data-msa=\"2\" data-wap=\"1\">5.G.B.4: &lt;p&gt;Classify two-dimensional figures in a hierarchy based on properties.&lt;\/p&gt;\r\n<\/option><option value=\"5.MD.A.1\" data-msa=\"1\" data-wap=\"1\">5.MD.A.1: &lt;p&gt;Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.&lt;\/p&gt;\r\n<\/option><option value=\"5.MD.B.2\" data-msa=\"1\" data-wap=\"1\">5.MD.B.2: &lt;p&gt;Make a line plot to display a data set of measurements in &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; of a unit (1\/2, 1\/4, 1\/8). Use operations on fractions for this grade to solve problems involving information presented in &lt;a id=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;line plots&lt;\/a&gt;. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.&lt;\/p&gt;\r\n<\/option><option value=\"5.MD.C.3\" data-msa=\"0\" data-wap=\"1\">5.MD.C.3: &lt;p&gt;Recognize volume as an attribute of solid figures and understand concepts of volume measurement.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.B.4\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.B.4: &lt;p&gt;Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.&lt;em&gt; For example, calculate mortgage payments.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.A.1\" data-msa=\"0\" data-wap=\"0\">HS.F-BF.A.1: &lt;p&gt;Write a function that describes a relationship between two quantities.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.A.1.a\" data-msa=\"0\" data-wap=\"0\">HS.F-BF.A.1.a: &lt;p&gt;Determine an explicit expression, a recursive process, or steps for calculation from a context.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.A.1.b\" data-msa=\"0\" data-wap=\"0\">HS.F-BF.A.1.b: &lt;p&gt;Combine standard function types using arithmetic operations.&lt;em&gt; For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.A.2\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.A.2: &lt;p&gt;Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.3\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.3: &lt;p&gt;Identify the effect on the graph of replacing &lt;em&gt;f(x)&lt;\/em&gt; by &lt;em&gt;f(x)&lt;\/em&gt; + &lt;em&gt;k&lt;\/em&gt;, &lt;em&gt;k f(x), f(kx)&lt;\/em&gt;, and&lt;em&gt; f(x + k)&lt;\/em&gt; for specific values of k (both positive and negative); find the value of &lt;em&gt;k&lt;\/em&gt; given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.4\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.4: &lt;p&gt;Find inverse functions:&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.5\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.5: &lt;p&gt;(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.A.1\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.A.1: &lt;p&gt;Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.A.2\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.A.2: &lt;p&gt;Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.A.3\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.A.3: &lt;p&gt;Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integers&lt;\/a&gt;. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n &amp;ge; 1.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.B.4\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.B.4: &lt;p&gt;For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. &lt;em&gt;Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.B.5\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.B.5: &lt;p&gt;Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. &lt;em&gt;For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive&lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt; integers&lt;\/a&gt; would be an appropriate domain for the function.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"5.MD.C.3.a\" data-msa=\"0\" data-wap=\"1\">5.MD.C.3.a: A cube with side length 1 unit, called a \u201cunit cube,\u201d is said to have \u201cone cubic unit\u201d of volume, and can be used to measure volume.<\/option><option value=\"5.MD.C.3.b\" data-msa=\"0\" data-wap=\"1\">5.MD.C.3.b: 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.<\/option><option value=\"5.MD.C.4\" data-msa=\"0\" data-wap=\"1\">5.MD.C.4: &lt;p&gt;Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.B.6\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.B.6: &lt;p&gt;Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.7\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.7: &lt;p&gt;Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.7.a\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.7.a: &lt;p&gt;Graph linear and quadratic functions and show intercepts, maxima, and minima.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.7.b\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.7.b: &lt;p&gt;Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.7.c\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.7.c: &lt;p&gt;Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.7.d\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.7.d: &lt;p&gt;(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.7.e\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.7.e: &lt;p&gt;Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, &lt;a id=&quot;In the graph of a trigonometric function, the horizontal line halfway  between its maximum and minimum values.&quot; name=&quot;In the graph of a trigonometric function, the horizontal line halfway  between its maximum and minimum values.&quot;&gt;midline&lt;\/a&gt;, and amplitude.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.8\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.8: &lt;p&gt;Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.8.a\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.8.a: &lt;p&gt;Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.8.b\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.8.b: &lt;p&gt;Use the properties of exponents to interpret expressions for exponential functions. For example, identify &lt;a id=&quot;A rate of change expressed as a percent. Example: if a  population grows from 50 to 55 in a year, it grows by 5\/50 = 10% per year.&quot; name=&quot;A rate of change expressed as a percent. Example: if a  population grows from 50 to 55 in a year, it grows by 5\/50 = 10% per year.&quot;&gt;percent rate of change&lt;\/a&gt; in functions such as y = (1.02)&lt;sup&gt;t&lt;\/sup&gt;, y = (0.97)&lt;sup&gt;t&lt;\/sup&gt;, y = (1.01)&lt;sup&gt;12&lt;\/sup&gt;&lt;sup&gt;t&lt;\/sup&gt;, y = (1.2)&lt;sup&gt;t\/10&lt;\/sup&gt;, and classify them as representing exponential growth or decay.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-IF.C.9\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C.9: &lt;p&gt;Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). &lt;em&gt;For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.1\" data-msa=\"0\" data-wap=\"0\">HS.F-LE.A.1: &lt;p&gt;Distinguish between situations that can be modeled with linear functions and with exponential functions:&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.2\" data-msa=\"0\" data-wap=\"1\">HS.F-LE.A.2: &lt;p&gt;Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.3\" data-msa=\"0\" data-wap=\"1\">HS.F-LE.A.3: &lt;p&gt;Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.4\" data-msa=\"0\" data-wap=\"1\">HS.F-LE.A.4: &lt;p&gt;For exponential models, express as a logarithm the solution to &lt;em&gt;ab&lt;sup&gt;ct&lt;\/sup&gt;&lt;\/em&gt; =&lt;em&gt;d&lt;\/em&gt; where &lt;em&gt;a&lt;\/em&gt;,&lt;em&gt;c&lt;\/em&gt;,and &lt;em&gt;d&lt;\/em&gt; are numbers and the base &lt;em&gt;b&lt;\/em&gt; is 2,10, or &lt;em&gt;e&lt;\/em&gt;; evaluate the logarithm using technology.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.B.5\" data-msa=\"0\" data-wap=\"1\">HS.F-LE.B.5: &lt;p&gt;Interpret the parameters in a linear or exponential function in terms of a context.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.A.1\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.A.1: &lt;p&gt;Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.A.2\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.A.2: &lt;p&gt;Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.A.3\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.A.3: &lt;p&gt;(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for &amp;pi;\/3, &amp;pi;\/4 and &amp;pi;\/6, and use the unit circle to express the values of sine, cosine, and tangent for &amp;pi;&amp;ndash;x, &amp;pi;+x, and 2&amp;pi;&amp;ndash;x in terms of their values for x, where x is any real number.&lt;\/p&gt;\r\n<\/option><option value=\"5.MD.C.5\" data-msa=\"0\" data-wap=\"1\">5.MD.C.5: &lt;p&gt;Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.&lt;\/p&gt;\r\n<\/option><option value=\"5.MD.C.5.a\" data-msa=\"0\" data-wap=\"1\">5.MD.C.5.a: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.<\/option><option value=\"5.MD.C.5.b\" data-msa=\"0\" data-wap=\"1\">5.MD.C.5.b: Apply the formulas V=l\u00d7w\u00d7handV=b\u00d7h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems.<\/option><option value=\"5.MD.C.5.c\" data-msa=\"0\" data-wap=\"1\">5.MD.C.5.c: &lt;p&gt;Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.A.1\" data-msa=\"0\" data-wap=\"1\">5.NBT.A.1: &lt;p&gt;Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1\/10 of what it represents in the place to its left.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.A.2\" data-msa=\"0\" data-wap=\"1\">5.NBT.A.2: &lt;p&gt;Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.A.3\" data-msa=\"0\" data-wap=\"1\">5.NBT.A.3: &lt;p&gt;Read, write, and compare decimals to thousandths.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.A.3.a\" data-msa=\"0\" data-wap=\"1\">5.NBT.A.3.a: &lt;p&gt;Read and write decimals to thousandths using base-ten numerals, number names, and &lt;a id=&quot;&amp;quot;A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.&amp;quot;&quot; name=&quot;&amp;quot;A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.&amp;quot;&quot;&gt;expanded form&lt;\/a&gt;, e.g., 347.392 = 3 &amp;times; 100 + 4 &amp;times; 10 + 7 &amp;times; 1 + 3 &amp;times; (1\/10) + 9 &amp;times; (1\/100) + 2 &amp;times; (1\/1000).&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.A.3.b\" data-msa=\"0\" data-wap=\"1\">5.NBT.A.3.b: &lt;p&gt;Compare two decimals to thousandths based on meanings of the digits in each place, using &amp;gt;, =, and &amp;lt; symbols to record the results of comparisons.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.A.4\" data-msa=\"0\" data-wap=\"1\">5.NBT.A.4: &lt;p&gt;Use place value understanding to round decimals to any place.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.B.5\" data-msa=\"0\" data-wap=\"1\">5.NBT.B.5: &lt;p&gt;Fluently multiply multi-digit &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; using the standard algorithm.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.B.6\" data-msa=\"0\" data-wap=\"1\">5.NBT.B.6: &lt;p&gt;Find whole-number quotients of &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; with up to four-digit dividends and two-digit divisors, using strategies based on place value, the &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and\/or area models.&lt;\/p&gt;\r\n<\/option><option value=\"5.NBT.B.7\" data-msa=\"0\" data-wap=\"1\">5.NBT.B.7: &lt;p&gt;Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, and\/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.A.1\" data-msa=\"0\" data-wap=\"1\">5.NF.A.1: &lt;p&gt;Add and subtract &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2\/3 + 5\/4 = 8\/12 + 15\/12 = 23\/12. (In general, a\/b + c\/d = (ad + bc)\/bd.)&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.A.2\" data-msa=\"0\" data-wap=\"1\">5.NF.A.2: &lt;p&gt;Solve word problems involving addition and subtraction of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; referring to the same whole, including cases of unlike denominators, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt; or equations to represent the problem. Use benchmark fractions and number sense of fractions&amp;nbsp;to estimate mentally and assess the reasonableness of answers. &lt;em&gt;For example, recognize an incorrect result 2\/5 + 1\/2 = 3\/7, by observing that 3\/7 &amp;lt; 1\/2.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.3\" data-msa=\"0\" data-wap=\"1\">5.NF.B.3: &lt;p&gt;Interpret a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; as division of the numerator by the denominator (a\/b = a &amp;divide; b). Solve word problems involving division of &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; leading to answers in the form of fractions or mixed numbers, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt; or equations to represent the problem. For example, interpret 3\/4 as the result of dividing 3 by 4, noting that 3\/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3\/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.4\" data-msa=\"0\" data-wap=\"1\">5.NF.B.4: &lt;p&gt;Apply and extend previous understandings of multiplication to multiply a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; or &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; by a fraction.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.4.a\" data-msa=\"0\" data-wap=\"1\">5.NF.B.4.a: &lt;p&gt;Interpret the product (a\/b) &amp;times; q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a &amp;times; q &amp;divide; b. For example, use a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt; to show (2\/3) &amp;times; 4 = 8\/3, and create a story context for this equation. Do the same with (2\/3) &amp;times; (4\/5) = 8\/15. (In general, (a\/b) &amp;times; (c\/d) = ac\/bd.)&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.4.b\" data-msa=\"0\" data-wap=\"1\">5.NF.B.4.b: &lt;p&gt;Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.5\" data-msa=\"0\" data-wap=\"1\">5.NF.B.5: &lt;p&gt;Interpret multiplication as scaling (resizing), by:&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.5.a\" data-msa=\"0\" data-wap=\"1\">5.NF.B.5.a: &lt;p&gt;Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.5.b\" data-msa=\"0\" data-wap=\"1\">5.NF.B.5.b: &lt;p&gt;Explaining why multiplying a given number by a &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; greater than 1 results in a product greater than the given number (recognizing multiplication by &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a\/b = (n&amp;times;a)\/(n&amp;times;b) to the effect of multiplying a\/b by 1.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.6\" data-msa=\"0\" data-wap=\"1\">5.NF.B.6: &lt;p&gt;Solve real world problems involving multiplication of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; and mixed numbers, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt; or equations to represent the problem.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.7\" data-msa=\"0\" data-wap=\"1\">5.NF.B.7: &lt;p&gt;Apply and extend previous understandings of division to divide unit &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; by &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; and whole numbers by unit fractions.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.B.4.b\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.B.4.b: &lt;p&gt;Solve quadratic equations by inspection (e.g., for &lt;em&gt;x&lt;sup&gt;2&lt;\/sup&gt;&lt;\/em&gt; = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as &lt;em&gt;a &amp;plusmn; bi&lt;\/em&gt; for real numbers &lt;em&gt;a&lt;\/em&gt; and &lt;em&gt;b&lt;\/em&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.C.5\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.C.5: &lt;p&gt;Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.C.6\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.C.6: &lt;p&gt;Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.C.7\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.C.7: &lt;p&gt;Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = &amp;ndash;3x and the circle x&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;+ y&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;= 3.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.D.10\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.D.10: &lt;p&gt;Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.D.11\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.D.11: &lt;p&gt;Explain why the x-coordinates of the points where the graphs of the equations &lt;em&gt;y = f(x)&lt;\/em&gt; and &lt;em&gt;y = g(x)&lt;\/em&gt; intersect are the solutions of the equation &lt;em&gt;f(x)&lt;\/em&gt; = &lt;em&gt;g(x)&lt;\/em&gt;; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where &lt;em&gt;f(x)&lt;\/em&gt; and\/or &lt;em&gt;g(x)&lt;\/em&gt; are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.7.a\" data-msa=\"0\" data-wap=\"1\">5.NF.B.7.a: &lt;p&gt;Interpret division of a unit &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; by a non-zero &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt;, and compute such quotients. For example, create a story context for (1\/3) &amp;divide; 4, and use a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt; to show the quotient. Use the relationship between multiplication and division to explain that (1\/3) &amp;divide; 4 = 1\/12 because (1\/12) &amp;times; 4 = 1\/3.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.7.b\" data-msa=\"0\" data-wap=\"1\">5.NF.B.7.b: &lt;p&gt;Interpret division of a &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole number&lt;\/a&gt; by a unit &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt;, and compute such quotients. For example, create a story context for 4 &amp;divide; (1\/5), and use a &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model &lt;\/a&gt;to show the quotient. Use the relationship between multiplication and division to explain that 4 &amp;divide; (1\/5) = 20 because 20 &amp;times; (1\/5) = 4.&lt;\/p&gt;\r\n<\/option><option value=\"5.NF.B.7.c\" data-msa=\"0\" data-wap=\"1\">5.NF.B.7.c: &lt;p&gt;Solve real world problems involving division of unit &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; by non-zero &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; and division of whole numbers by unit fractions, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction model&lt;\/a&gt;s and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1\/2 lb of chocolate equally? How many 1\/3-cup servings are in 2 cups of raisins?&lt;\/p&gt;\r\n<\/option><option value=\"5.OA.A.1\" data-msa=\"2\" data-wap=\"1\">5.OA.A.1: &lt;p&gt;Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.&lt;\/p&gt;\r\n<\/option><option value=\"5.OA.A.2\" data-msa=\"2\" data-wap=\"1\">5.OA.A.2: &lt;p&gt;Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation &amp;ldquo;add 8 and 7, then multiply by 2&amp;rdquo; as 2 &amp;times; (8 + 7). Recognize that 3 &amp;times; (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.&lt;\/p&gt;\r\n<\/option><option value=\"5.OA.B.3\" data-msa=\"2\" data-wap=\"1\">5.OA.B.3: &lt;p&gt;Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule &amp;ldquo;Add 3&amp;rdquo; and the starting number 0, and given the rule &amp;ldquo;Add 6&amp;rdquo; and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.A.1\" data-msa=\"0\" data-wap=\"1\">6.EE.A.1: &lt;p&gt;Write and evaluate numerical expressions involving whole-number exponents.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.A.2\" data-msa=\"0\" data-wap=\"1\">6.EE.A.2: &lt;p&gt;Write, read, and evaluate expressions in which letters stand for numbers.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.A.2.a\" data-msa=\"0\" data-wap=\"1\">6.EE.A.2.a: Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation \u201cSubtract y from 5\u201d as 5 \u2013 y.<\/option><option value=\"6.EE.A.2.b\" data-msa=\"0\" data-wap=\"1\">6.EE.A.2.b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.<\/option><option value=\"6.EE.A.2.c\" data-msa=\"0\" data-wap=\"1\">6.EE.A.2.c: &lt;p&gt;Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). &lt;em&gt;For example, use the formulas V = s&lt;sup&gt;3&lt;\/sup&gt; and A = 6 s&lt;sup&gt;2&lt;\/sup&gt; to find the volume and surface area of a cube with sides of length s = 1\/2.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.A.3\" data-msa=\"0\" data-wap=\"1\">6.EE.A.3: &lt;p&gt;Apply the &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; to generate equivalent expressions.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.A.4\" data-msa=\"0\" data-wap=\"1\">6.EE.A.4: &lt;p&gt;Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.B.5\" data-msa=\"0\" data-wap=\"1\">6.EE.B.5: &lt;p&gt;Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.B.6\" data-msa=\"0\" data-wap=\"1\">6.EE.B.6: &lt;p&gt;Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.B.7\" data-msa=\"0\" data-wap=\"1\">6.EE.B.7: &lt;p&gt;Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.B.8\" data-msa=\"0\" data-wap=\"1\">6.EE.B.8: &lt;p&gt;Write an inequality of the form x &amp;gt; c or x &amp;lt; c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x &amp;gt; c or x &amp;lt; c have infinitely many solutions; represent solutions of such inequalities on &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagrams&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"6.EE.C.9\" data-msa=\"0\" data-wap=\"1\">6.EE.C.9: &lt;p&gt;Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.&lt;\/p&gt;\r\n<\/option><option value=\"6.G.A.1\" data-msa=\"1\" data-wap=\"1\">6.G.A.1: &lt;p&gt;Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.&lt;\/p&gt;\r\n<\/option><option value=\"6.G.A.2\" data-msa=\"1\" data-wap=\"1\">6.G.A.2: &lt;p&gt;Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.&lt;\/p&gt;\r\n<\/option><option value=\"6.G.A.3\" data-msa=\"1\" data-wap=\"1\">6.G.A.3: &lt;p&gt;Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.&lt;\/p&gt;\r\n<\/option><option value=\"6.G.A.4\" data-msa=\"1\" data-wap=\"1\">6.G.A.4: &lt;p&gt;Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.A.1\" data-msa=\"0\" data-wap=\"1\">6.NS.A.1: &lt;p&gt;Interpret and compute quotients of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt;, and solve word problems involving division of fractions by fractions, e.g., by using &lt;a id=&quot;A tape diagram, number line diagram, or area model.&quot; name=&quot;A tape diagram, number line diagram, or area model.&quot;&gt;visual fraction models&lt;\/a&gt; and equations to represent the problem. For example, create a story context for (2\/3) &amp;divide; (3\/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2\/3) &amp;divide; (3\/4) = 8\/9 because 3\/4 of 8\/9 is 2\/3. (In general, (a\/b) &amp;divide; (c\/d) = ad\/bc.) How much chocolate will each person get if 3 people share 1\/2 lb of chocolate equally? How many 3\/4-cup servings are in 2\/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3\/4 mi and area 1\/2 square mi?&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.B.2\" data-msa=\"2\" data-wap=\"1\">6.NS.B.2: &lt;p&gt;Fluently divide multi-digit numbers using the standard algorithm.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.B.3\" data-msa=\"2\" data-wap=\"1\">6.NS.B.3: &lt;p&gt;Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.B.4\" data-msa=\"2\" data-wap=\"1\">6.NS.B.4: &lt;p&gt;Find the greatest common factor of two &lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt; less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1&amp;ndash;100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.5\" data-msa=\"0\" data-wap=\"1\">6.NS.C.5: &lt;p&gt;Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above\/below zero, elevation above\/below sea level, credits\/debits, positive\/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.6\" data-msa=\"0\" data-wap=\"1\">6.NS.C.6: &lt;p&gt;Understand a &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt; as a point on the number line. Extend &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagrams&lt;\/a&gt; and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.6.a\" data-msa=\"0\" data-wap=\"1\">6.NS.C.6.a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., \u2013(\u20133) = 3, and that 0 is its own opposite.<\/option><option value=\"6.NS.C.6.b\" data-msa=\"0\" data-wap=\"1\">6.NS.C.6.b: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.<\/option><option value=\"6.NS.C.6.c\" data-msa=\"0\" data-wap=\"1\">6.NS.C.6.c: &lt;p&gt;Find and position &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integers&lt;\/a&gt; and other &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; on a horizontal or vertical &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;; find and position pairs of integers and other rational numbers on a coordinate plane.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.7\" data-msa=\"0\" data-wap=\"1\">6.NS.C.7: &lt;p&gt;Understand ordering and absolute value of &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.7.a\" data-msa=\"0\" data-wap=\"1\">6.NS.C.7.a: &lt;p&gt;Interpret statements of inequality as statements about the relative position of two numbers on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;. For example, interpret &amp;ndash;3 &amp;gt; &amp;ndash;7 as a statement that &amp;ndash;3 is located to the right of &amp;ndash;7 on a number line oriented from left to right.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.7.b\" data-msa=\"0\" data-wap=\"1\">6.NS.C.7.b: &lt;p&gt;Write, interpret, and explain statements of order for &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; in real-world contexts. For example, write &amp;ndash;3 oC &amp;gt; &amp;ndash;7 oC to express the fact that &amp;ndash;3 oC is warmer than &amp;ndash;7 oC.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.7.c\" data-msa=\"0\" data-wap=\"1\">6.NS.C.7.c: &lt;p&gt;Understand the absolute value of a &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt; as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of &amp;ndash;30 dollars, write |&amp;ndash;30| = 30 to describe the size of the debt in dollars.&lt;\/p&gt;\r\n<\/option><option value=\"6.NS.C.7.d\" data-msa=\"0\" data-wap=\"1\">6.NS.C.7.d: Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than \u201330 dollars represents a debt greater than 30 dollars.<\/option><option value=\"6.NS.C.8\" data-msa=\"0\" data-wap=\"1\">6.NS.C.8: &lt;p&gt;Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.1\" data-msa=\"0\" data-wap=\"1\">6.RP.A.1: &lt;p&gt;Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. &lt;em&gt;For example, &amp;ldquo;The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.&amp;rdquo; &amp;ldquo;For every vote candidate A received, candidate C received nearly three votes.&amp;rdquo;&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.D.12\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.D.12: &lt;p&gt;Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.A.1\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.A.1: &lt;p&gt;Interpret expressions that represent a quantity in terms of its context:&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.A.2\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.A.2: &lt;p&gt;Use the structure of an expression to identify ways to rewrite it.&lt;em&gt; For example, see x&lt;sup&gt;4&lt;\/sup&gt; &amp;ndash; y&lt;sup&gt;4&lt;\/sup&gt; as (x&lt;sup&gt;2&lt;\/sup&gt;)&lt;sup&gt;2&lt;\/sup&gt; &amp;ndash; (y&lt;sup&gt;2&lt;\/sup&gt;)&lt;sup&gt;2&lt;\/sup&gt;, thus recognizing it as a difference of squares that can be factored as (x&lt;sup&gt;2&lt;\/sup&gt; &amp;ndash; y&lt;sup&gt;2&lt;\/sup&gt;)(x&lt;sup&gt;2&lt;\/sup&gt; + y&lt;sup&gt;2&lt;\/sup&gt;).&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.B.3\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.B.3: &lt;p&gt;Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.B.3.a\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.B.3.a: &lt;p&gt;Factor a quadratic expression to reveal the zeros of the function it defines.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.B.3.b\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.B.3.b: &lt;p&gt;Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.B.3.c\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.B.3.c: &lt;p&gt;Use the properties of exponents to transform expressions for exponential functions.&lt;em&gt; For example the expression 1.15&lt;sup&gt;t&lt;\/sup&gt; can be rewritten as (1.151\/12)&lt;sup&gt;12t&lt;\/sup&gt; &amp;asymp; 1.012&lt;sup&gt;12t &lt;\/sup&gt;to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.2\" data-msa=\"0\" data-wap=\"1\">6.RP.A.2: &lt;p&gt;Understand the concept of a unit rate a\/b associated with a ratio a:b with b &amp;ne; 0, and use rate language in the context of a ratio relationship. For example, &amp;ldquo;This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3\/4 cup of flour for each cup of sugar.&amp;rdquo; &amp;ldquo;We paid \\$75 for 15 hamburgers, which is a rate of \\$5 per hamburger.&amp;quot;*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Expectations for unit rates in this grade are limited to non-complex fractions.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.3\" data-msa=\"0\" data-wap=\"1\">6.RP.A.3: &lt;p&gt;Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, &lt;a id=&quot;A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.&quot; name=&quot;A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.&quot;&gt;tape diagrams&lt;\/a&gt;, double &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagrams&lt;\/a&gt;, or equations.&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.3.a\" data-msa=\"0\" data-wap=\"1\">6.RP.A.3.a: &lt;p&gt;Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.3.b\" data-msa=\"0\" data-wap=\"1\">6.RP.A.3.b: &lt;p&gt;Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.3.c\" data-msa=\"0\" data-wap=\"1\">6.RP.A.3.c: &lt;p&gt;Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30\/100 times the quantity); solve problems involving finding the whole, given a part and the percent.&lt;\/p&gt;\r\n<\/option><option value=\"6.RP.A.3.d\" data-msa=\"0\" data-wap=\"1\">6.RP.A.3.d: &lt;p&gt;Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.A.1\" data-msa=\"2\" data-wap=\"1\">6.SP.A.1: &lt;p&gt;Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, &amp;ldquo;How old am I?&amp;rdquo; is not a statistical question, but &amp;ldquo;How old are the students in my school?&amp;rdquo; is a statistical question because one anticipates variability in students&amp;rsquo; ages.&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.A.2\" data-msa=\"2\" data-wap=\"1\">6.SP.A.2: &lt;p&gt;Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.A.3\" data-msa=\"2\" data-wap=\"1\">6.SP.A.3: &lt;p&gt;Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.B.4\" data-msa=\"2\" data-wap=\"1\">6.SP.B.4: &lt;p&gt;Display numerical data in plots on a number line, including &lt;a id=&quot;See &amp;quot;line plot:&amp;quot; A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;See &amp;quot;line plot:&amp;quot; A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;dot plots&lt;\/a&gt;, histograms, and &lt;a id=&quot;&amp;quot;A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.&amp;quot;&quot; name=&quot;&amp;quot;A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.&amp;quot;&quot;&gt;box plots&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.B.5\" data-msa=\"2\" data-wap=\"1\">6.SP.B.5: &lt;p&gt;Summarize numerical data sets in relation to their context, such as by:&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.B.5.a\" data-msa=\"2\" data-wap=\"1\">6.SP.B.5.a: Reporting the number of observations.<\/option><option value=\"6.SP.B.5.b\" data-msa=\"2\" data-wap=\"1\">6.SP.B.5.b: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.<\/option><option value=\"6.SP.B.5.c\" data-msa=\"2\" data-wap=\"1\">6.SP.B.5.c: &lt;p&gt;Giving quantitative measures of center (&lt;a id=&quot;&amp;quot;A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list\u2014or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.&amp;quot;&quot; name=&quot;&amp;quot;A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list\u2014or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.&amp;quot;&quot;&gt;median&lt;\/a&gt; and\/or &lt;a id=&quot;&amp;quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. *To be more precise, this defines the arithmetic mean.&amp;quot;&quot; name=&quot;&amp;quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. *To be more precise, this defines the arithmetic mean.&amp;quot;&quot;&gt;mean&lt;\/a&gt;) and variability (&lt;a id=&quot;A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 \u2013 6 = 9. See also: first quartile, third quartile.&quot; name=&quot;A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 \u2013 6 = 9. See also: first quartile, third quartile.&quot;&gt;interquartile range&lt;\/a&gt; and\/or &lt;a id=&quot;&amp;quot;A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.&amp;quot;&quot; name=&quot;&amp;quot;A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.&amp;quot;&quot;&gt;mean absolute deviation&lt;\/a&gt;), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.&lt;\/p&gt;\r\n<\/option><option value=\"6.SP.B.5.d\" data-msa=\"2\" data-wap=\"1\">6.SP.B.5.d: &lt;p&gt;Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.A.1\" data-msa=\"0\" data-wap=\"1\">7.EE.A.1: &lt;p&gt;Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.A.2\" data-msa=\"0\" data-wap=\"1\">7.EE.A.2: &lt;p&gt;Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that &amp;ldquo;increase by 5%&amp;rdquo; is the same as &amp;ldquo;multiply by 1.05.&amp;rdquo;&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.B.3\" data-msa=\"0\" data-wap=\"1\">7.EE.B.3: &lt;p&gt;Solve multi-step real-life and mathematical problems posed with positive and negative &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; in any form (&lt;a id=&quot;The numbers 0, 1, 2, 3, \u2026.&quot; name=&quot;The numbers 0, 1, 2, 3, \u2026.&quot;&gt;whole numbers&lt;\/a&gt;, &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt;, and decimals), using tools strategically. Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1\/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3\/4 inches long in the center of a door that is 27 1\/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.B.4\" data-msa=\"0\" data-wap=\"1\">7.EE.B.4: &lt;p&gt;Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.B.4\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.B.4: &lt;p&gt;Solve quadratic equations in one variable.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.B.4.a\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.B.4.a: &lt;p&gt;Use the method of completing the square to transform any quadratic equation in &lt;em&gt;x&lt;\/em&gt; into an equation of the form &lt;em&gt;(x &amp;ndash; p)&lt;sup&gt;2&lt;\/sup&gt;&lt;\/em&gt; = &lt;em&gt;q&lt;\/em&gt; that has the same solutions. Derive the quadratic formula from this form.&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.B.4.a\" data-msa=\"0\" data-wap=\"1\">7.EE.B.4.a: &lt;p&gt;Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.B.4.b\" data-msa=\"0\" data-wap=\"1\">7.EE.B.4.b: &lt;p&gt;Solve word problems leading to inequalities of the form px + q &amp;gt; r or px + q &amp;lt; r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.&lt;\/p&gt;\r\n<\/option><option value=\"7.G.A.1\" data-msa=\"2\" data-wap=\"1\">7.G.A.1: &lt;p&gt;Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.&lt;\/p&gt;\r\n<\/option><option value=\"7.G.A.2\" data-msa=\"2\" data-wap=\"1\">7.G.A.2: &lt;p&gt;Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.&lt;\/p&gt;\r\n<\/option><option value=\"7.G.A.3\" data-msa=\"2\" data-wap=\"1\">7.G.A.3: &lt;p&gt;Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.&lt;\/p&gt;\r\n<\/option><option value=\"7.G.B.4\" data-msa=\"2\" data-wap=\"1\">7.G.B.4: &lt;p&gt;Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.&lt;\/p&gt;\r\n<\/option><option value=\"7.G.B.5\" data-msa=\"2\" data-wap=\"1\">7.G.B.5: &lt;p&gt;Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.&lt;\/p&gt;\r\n<\/option><option value=\"7.G.B.6\" data-msa=\"2\" data-wap=\"1\">7.G.B.6: &lt;p&gt;Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.1\" data-msa=\"0\" data-wap=\"1\">7.NS.A.1: &lt;p&gt;Apply and extend previous understandings of addition and subtraction to add and subtract &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;; represent addition and subtraction on a horizontal or vertical &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.1.a\" data-msa=\"0\" data-wap=\"1\">7.NS.A.1.a: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.<\/option><option value=\"7.NS.A.1.b\" data-msa=\"0\" data-wap=\"1\">7.NS.A.1.b: &lt;p&gt;Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are &lt;a id=&quot;Two numbers whose sum is 0 are additive inverses of one another. Example: 3\/4 and \u2013 3\/4 are additive inverses of one another because 3\/4 + (\u2013 3\/4) = (\u2013 3\/4) + 3\/4 = 0.&quot; name=&quot;Two numbers whose sum is 0 are additive inverses of one another. Example: 3\/4 and \u2013 3\/4 are additive inverses of one another because 3\/4 + (\u2013 3\/4) = (\u2013 3\/4) + 3\/4 = 0.&quot;&gt;additive inverses&lt;\/a&gt;). Interpret sums of &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; by describing real-world contexts.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.1.c\" data-msa=\"0\" data-wap=\"1\">7.NS.A.1.c: &lt;p&gt;Understand subtraction of &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; as adding the &lt;a id=&quot;Two numbers whose sum is 0 are additive inverses of one another. Example: 3\/4 and \u2013 3\/4 are additive inverses of one another because 3\/4 + (\u2013 3\/4) = (\u2013 3\/4) + 3\/4 = 0.&quot; name=&quot;Two numbers whose sum is 0 are additive inverses of one another. Example: 3\/4 and \u2013 3\/4 are additive inverses of one another because 3\/4 + (\u2013 3\/4) = (\u2013 3\/4) + 3\/4 = 0.&quot;&gt;additive inverse&lt;\/a&gt;, p &amp;ndash; q = p + (&amp;ndash;q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.1.d\" data-msa=\"0\" data-wap=\"1\">7.NS.A.1.d: &lt;p&gt;Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; as strategies to add and subtract &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.2\" data-msa=\"0\" data-wap=\"1\">7.NS.A.2: &lt;p&gt;Apply and extend previous understandings of multiplication and division and of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; to multiply and divide &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.2.a\" data-msa=\"0\" data-wap=\"1\">7.NS.A.2.a: &lt;p&gt;Understand that multiplication is extended from &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt; to &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; by requiring that operations continue to satisfy the &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt;, particularly the distributive property, leading to products such as (&amp;ndash;1)(&amp;ndash;1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.2.b\" data-msa=\"0\" data-wap=\"1\">7.NS.A.2.b: &lt;p&gt;Understand that &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integers&lt;\/a&gt; can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt;. If p and q are integers, then &amp;ndash;(p\/q) = (&amp;ndash;p)\/q = p\/(&amp;ndash;q). Interpret quotients of rational numbers by describing real- world contexts.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.2.c\" data-msa=\"0\" data-wap=\"1\">7.NS.A.2.c: &lt;p&gt;Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;properties of operations&lt;\/a&gt; as strategies to multiply and divide &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.2.d\" data-msa=\"0\" data-wap=\"1\">7.NS.A.2.d: &lt;p&gt;Convert a &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt; to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.&lt;\/p&gt;\r\n<\/option><option value=\"7.NS.A.3\" data-msa=\"0\" data-wap=\"1\">7.NS.A.3: &lt;p&gt;Solve real-world and mathematical problems involving the four operations with &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt;.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Computations with rational numbers extend the rules for manipulating fractions to complex fractions.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"7.RP.A.1\" data-msa=\"0\" data-wap=\"1\">7.RP.A.1: &lt;p&gt;Compute unit rates associated with ratios of &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fractions&lt;\/a&gt;, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1\/2 mile in each 1\/4 hour, compute the unit rate as the &lt;a id=&quot;A fraction A\/B where A and\/or B are fractions (B nonzero).&quot; name=&quot;A fraction A\/B where A and\/or B are fractions (B nonzero).&quot;&gt;complex fraction&lt;\/a&gt; 1\/2\/1\/4 miles per hour, equivalently 2 miles per hour.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.A.1\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.A.1: &lt;p&gt;Understand that polynomials form a system analogous to the &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integers&lt;\/a&gt;, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.B.2\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.B.2: &lt;p&gt;Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x &amp;ndash; a is p(a), so p(a) = 0 if and only if (x &amp;ndash; a) is a factor of p(x).&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.B.3\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.B.3: &lt;p&gt;Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.C.4\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.C.4: &lt;p&gt;Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;+ y&lt;sup&gt;2&lt;\/sup&gt;)&lt;sup&gt;2&lt;\/sup&gt;= (x&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;- y&lt;sup&gt;2&lt;\/sup&gt;)&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;+ (2xy)&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;can be used to generate Pythagorean triples.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-APR.C.5\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.C.5: &lt;p&gt;(+) Know and apply the Binomial Theorem for the expansion of (x + y)&lt;sup&gt;n&lt;\/sup&gt;&amp;nbsp;in powers of x and y for a positive &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integer&lt;\/a&gt; n, where x and y are any numbers, with coefficients determined for example by Pascal&amp;rsquo;s Triangle.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"7.RP.A.2\" data-msa=\"0\" data-wap=\"1\">7.RP.A.2: &lt;p&gt;Recognize and represent proportional relationships between quantities.&lt;\/p&gt;\r\n<\/option><option value=\"7.RP.A.2.a\" data-msa=\"0\" data-wap=\"1\">7.RP.A.2.a: &lt;p&gt;Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.&lt;\/p&gt;\r\n<\/option><option value=\"7.RP.A.2.b\" data-msa=\"0\" data-wap=\"1\">7.RP.A.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.<\/option><option value=\"7.RP.A.2.c\" data-msa=\"0\" data-wap=\"1\">7.RP.A.2.c: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.<\/option><option value=\"7.RP.A.2.d\" data-msa=\"0\" data-wap=\"1\">7.RP.A.2.d: &lt;p&gt;Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.&lt;\/p&gt;\r\n<\/option><option value=\"7.RP.A.3\" data-msa=\"0\" data-wap=\"1\">7.RP.A.3: &lt;p&gt;Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.A.1\" data-msa=\"1\" data-wap=\"1\">7.SP.A.1: &lt;p&gt;Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.A.2\" data-msa=\"1\" data-wap=\"1\">7.SP.A.2: &lt;p&gt;Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the &lt;a id=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.  Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. To be more precise, this defines the arithmetic mean.&quot; name=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.  Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. To be more precise, this defines the arithmetic mean.&quot;&gt;mean&lt;\/a&gt; word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.B.3\" data-msa=\"2\" data-wap=\"1\">7.SP.B.3: &lt;p&gt;Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the &lt;a id=&quot;&amp;quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. *To be more precise, this defines the arithmetic mean.&amp;quot;&quot; name=&quot;&amp;quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. *To be more precise, this defines the arithmetic mean.&amp;quot;&quot;&gt;mean&lt;\/a&gt; height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (&lt;a id=&quot;&amp;quot;A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.&amp;quot;&quot; name=&quot;&amp;quot;A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.&amp;quot;&quot;&gt;mean absolute deviation&lt;\/a&gt;) on either team; on a &lt;a id=&quot;See &amp;quot;line plot:&amp;quot; A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;See &amp;quot;line plot:&amp;quot; A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;dot plot&lt;\/a&gt;, the separation between the two distributions of heights is noticeable.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.B.4\" data-msa=\"2\" data-wap=\"1\">7.SP.B.4: &lt;p&gt;Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.5\" data-msa=\"1\" data-wap=\"1\">7.SP.C.5: &lt;p&gt;Understand that the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1\/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.6\" data-msa=\"1\" data-wap=\"1\">7.SP.C.6: &lt;p&gt;Approximate the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.7\" data-msa=\"1\" data-wap=\"1\">7.SP.C.7: &lt;p&gt;Develop a &lt;a id=&quot;&amp;quot;A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.&amp;quot;&quot; name=&quot;&amp;quot;A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.&amp;quot;&quot;&gt;probability model&lt;\/a&gt; and use it to find &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probabilities&lt;\/a&gt; of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.7.a\" data-msa=\"1\" data-wap=\"1\">7.SP.C.7.a: &lt;p&gt;Develop a &lt;a id=&quot;&amp;quot;A probability model which assigns equal probability to all outcomes. See also: probability model.&amp;quot;&quot; name=&quot;&amp;quot;A probability model which assigns equal probability to all outcomes. See also: probability model.&amp;quot;&quot;&gt;uniform probability model&lt;\/a&gt; by assigning equal &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.7.b\" data-msa=\"1\" data-wap=\"1\">7.SP.C.7.b: &lt;p&gt;Develop a &lt;a id=&quot;&amp;quot;A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.&amp;quot;&quot; name=&quot;&amp;quot;A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.&amp;quot;&quot;&gt;probability model&lt;\/a&gt; (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.8\" data-msa=\"1\" data-wap=\"1\">7.SP.C.8: &lt;p&gt;Find &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probabilities&lt;\/a&gt; of compound events using organized lists, tables, tree diagrams, and simulation.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.8.a\" data-msa=\"1\" data-wap=\"1\">7.SP.C.8.a: &lt;p&gt;Understand that, just as with simple events, the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of a compound event is the &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; of outcomes in the &lt;a id=&quot;In a probability model for a random process, a list of the individual outcomes that are to be considered.&quot; name=&quot;In a probability model for a random process, a list of the individual outcomes that are to be considered.&quot;&gt;sample space&lt;\/a&gt; for which the compound event occurs.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.8.b\" data-msa=\"1\" data-wap=\"1\">7.SP.C.8.b: &lt;p&gt;Represent &lt;a id=&quot;&amp;quot;In a probability model for a random process, a list of the individual outcomes that are to be considered.&amp;quot;&quot; name=&quot;&amp;quot;In a probability model for a random process, a list of the individual outcomes that are to be considered.&amp;quot;&quot;&gt;sample spaces&lt;\/a&gt; for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., &amp;ldquo;rolling double sixes&amp;rdquo;), identify the outcomes in the sample space which compose the event.&lt;\/p&gt;\r\n<\/option><option value=\"7.SP.C.8.c\" data-msa=\"1\" data-wap=\"1\">7.SP.C.8.c: &lt;p&gt;Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; that it will take at least 4 donors to find one with type A blood?&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.A.1\" data-msa=\"0\" data-wap=\"1\">8.EE.A.1: &lt;p&gt;Know and apply the properties of &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integer&lt;\/a&gt; exponents to generate equivalent numerical expressions. For example, 3&lt;sup&gt;2&lt;\/sup&gt; &amp;times; 3&lt;sup&gt;&amp;ndash;5&lt;\/sup&gt; = 3&lt;sup&gt;&amp;ndash;3&lt;\/sup&gt; = 1\/3&lt;sup&gt;3&lt;\/sup&gt; = 1\/27.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.A.2\" data-msa=\"0\" data-wap=\"1\">8.EE.A.2: &lt;p&gt;Use square root and cube root symbols to represent solutions to equations of the form &lt;em&gt;x&lt;sup&gt;2&lt;\/sup&gt; = p&lt;\/em&gt; and &lt;em&gt;x&lt;sup&gt;3&lt;\/sup&gt; = p&lt;\/em&gt;, where &lt;em&gt;p&lt;\/em&gt; is a positive &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt;. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that &amp;radic;2 is irrational.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.A.3\" data-msa=\"0\" data-wap=\"1\">8.EE.A.3: &lt;p&gt;Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.&lt;em&gt; For example, estimate the population of the United States as 3 &amp;times; 10&lt;sup&gt;8&lt;\/sup&gt; and the population of the world as 7 &amp;times; 10&lt;sup&gt;9&lt;\/sup&gt;, and determine that the world population is more than 20 times larger.&lt;\/em&gt;&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.A.4\" data-msa=\"0\" data-wap=\"1\">8.EE.A.4: &lt;p&gt;Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.B.5\" data-msa=\"0\" data-wap=\"1\">8.EE.B.5: &lt;p&gt;Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.B.6\" data-msa=\"0\" data-wap=\"1\">8.EE.B.6: &lt;p&gt;Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.C.7\" data-msa=\"0\" data-wap=\"1\">8.EE.C.7: &lt;p&gt;Solve linear equations in one variable.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.C.7.a\" data-msa=\"0\" data-wap=\"1\">8.EE.C.7.a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).<\/option><option value=\"8.EE.C.7.b\" data-msa=\"0\" data-wap=\"1\">8.EE.C.7.b: &lt;p&gt;Solve linear equations with &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt; coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.C.8\" data-msa=\"0\" data-wap=\"1\">8.EE.C.8: &lt;p&gt;Analyze and solve pairs of simultaneous linear equations.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.C.8.a\" data-msa=\"0\" data-wap=\"1\">8.EE.C.8.a: &lt;p&gt;Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.C.8.b\" data-msa=\"0\" data-wap=\"1\">8.EE.C.8.b: &lt;p&gt;Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.&lt;\/p&gt;\r\n<\/option><option value=\"8.EE.C.8.c\" data-msa=\"0\" data-wap=\"1\">8.EE.C.8.c: &lt;p&gt;Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.&lt;\/p&gt;\r\n<\/option><option value=\"8.F.A.1\" data-msa=\"0\" data-wap=\"1\">8.F.A.1: &lt;p&gt;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.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Function notation is not required in Grade 8.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"8.F.A.2\" data-msa=\"0\" data-wap=\"1\">8.F.A.2: &lt;p&gt;Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.&lt;\/p&gt;\r\n<\/option><option value=\"8.F.A.3\" data-msa=\"0\" data-wap=\"1\">8.F.A.3: &lt;p&gt;Interpret the equation&lt;em&gt; y = mx + b&lt;\/em&gt; as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s&lt;sup&gt;2&lt;\/sup&gt; giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.&lt;\/p&gt;\r\n<\/option><option value=\"8.F.B.4\" data-msa=\"0\" data-wap=\"1\">8.F.B.4: &lt;p&gt;Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.A.1\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.A.1: &lt;p&gt;Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.A.2\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.A.2: &lt;p&gt;Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-REI.B.3\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.B.3: &lt;p&gt;Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.&lt;\/p&gt;\r\n<\/option><option value=\"8.F.B.5\" data-msa=\"0\" data-wap=\"1\">8.F.B.5: &lt;p&gt;Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.A.1\" data-msa=\"0\" data-wap=\"1\">8.G.A.1: &lt;p&gt;Verify experimentally the properties of rotations, reflections, and translations:&lt;\/p&gt;\r\n<\/option><option value=\"8.G.A.1.a\" data-msa=\"0\" data-wap=\"1\">8.G.A.1.a: Lines are taken to lines, and line segments to line segments of the same length.<\/option><option value=\"8.G.A.1.b\" data-msa=\"0\" data-wap=\"1\">8.G.A.1.b: Angles are taken to angles of the same measure.<\/option><option value=\"8.G.A.1.c\" data-msa=\"0\" data-wap=\"1\">8.G.A.1.c: Parallel lines are taken to parallel lines.<\/option><option value=\"8.G.A.2\" data-msa=\"0\" data-wap=\"1\">8.G.A.2: &lt;p&gt;Understand that a two-dimensional figure is &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt; to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.A.3\" data-msa=\"0\" data-wap=\"1\">8.G.A.3: &lt;p&gt;Describe the effect of &lt;a id=&quot;A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot; name=&quot;A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot;&gt;dilations&lt;\/a&gt;, translations, rotations, and reflections on two-dimensional figures using coordinates.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.A.4\" data-msa=\"0\" data-wap=\"1\">8.G.A.4: &lt;p&gt;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 &lt;a id=&quot;A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot; name=&quot;A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot;&gt;dilations&lt;\/a&gt;; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.A.5\" data-msa=\"0\" data-wap=\"1\">8.G.A.5: &lt;p&gt;Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.B.6\" data-msa=\"0\" data-wap=\"1\">8.G.B.6: &lt;p&gt;Explain a proof of the Pythagorean Theorem and its converse.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.B.7\" data-msa=\"0\" data-wap=\"1\">8.G.B.7: &lt;p&gt;Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.B.8\" data-msa=\"0\" data-wap=\"1\">8.G.B.8: &lt;p&gt;Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.&lt;\/p&gt;\r\n<\/option><option value=\"8.G.C.9\" data-msa=\"2\" data-wap=\"1\">8.G.C.9: &lt;p&gt;Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.&lt;\/p&gt;\r\n<\/option><option value=\"8.NS.A.1\" data-msa=\"1\" data-wap=\"1\">8.NS.A.1: &lt;p&gt;Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.&lt;\/p&gt;\r\n<\/option><option value=\"8.NS.A.2\" data-msa=\"1\" data-wap=\"1\">8.NS.A.2: &lt;p&gt;Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a &lt;a id=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot; name=&quot;A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.&quot;&gt;number line diagram&lt;\/a&gt;, and estimate the value of expressions (e.g., &amp;radic;2). For example, by truncating the decimal expansion of &amp;radic;2, show that &amp;radic;2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.&lt;\/p&gt;\r\n<\/option><option value=\"8.SP.A.1\" data-msa=\"1\" data-wap=\"1\">8.SP.A.1: &lt;p&gt;Construct and interpret &lt;a id=&quot;&amp;quot;A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.&amp;quot;&quot; name=&quot;&amp;quot;A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.&amp;quot;&quot;&gt;scatter plots&lt;\/a&gt; for &lt;a id=&quot;Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.&quot; name=&quot;Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.&quot;&gt;bivariate measurement data&lt;\/a&gt; to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.&lt;\/p&gt;\r\n<\/option><option value=\"8.SP.A.2\" data-msa=\"1\" data-wap=\"1\">8.SP.A.2: &lt;p&gt;Know that straight lines are widely used to model relationships between two quantitative variables. For &lt;a id=&quot;&amp;quot;A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.&amp;quot;&quot; name=&quot;&amp;quot;A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.&amp;quot;&quot;&gt;scatter plots&lt;\/a&gt; that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.&lt;\/p&gt;\r\n<\/option><option value=\"8.SP.A.3\" data-msa=\"1\" data-wap=\"1\">8.SP.A.3: &lt;p&gt;Use the equation of a linear model to solve problems in the context of &lt;a id=&quot;Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.&quot; name=&quot;Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.&quot;&gt;bivariate measurement data&lt;\/a&gt;, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm\/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.&lt;\/p&gt;\r\n<\/option><option value=\"8.SP.A.4\" data-msa=\"1\" data-wap=\"1\">8.SP.A.4: &lt;p&gt;Understand that patterns of association can also be seen in &lt;a id=&quot;Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.&quot; name=&quot;Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.&quot;&gt;bivariate categorical data&lt;\/a&gt; by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.A.1\" data-msa=\"0\" data-wap=\"1\">K.CC.A.1: &lt;p&gt;Count to 100 by ones and by tens.&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.A.2\" data-msa=\"0\" data-wap=\"1\">K.CC.A.2: &lt;p&gt;Count forward beginning from a given number within the known sequence (instead of having to begin at 1).&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.A.3\" data-msa=\"0\" data-wap=\"1\">K.CC.A.3: &lt;p&gt;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).&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.B.4\" data-msa=\"0\" data-wap=\"1\">K.CC.B.4: &lt;p&gt;Understand the relationship between numbers and quantities; connect counting to cardinality.&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.B.4.a\" data-msa=\"0\" data-wap=\"1\">K.CC.B.4.a: 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.<\/option><option value=\"K.CC.B.4.b\" data-msa=\"0\" data-wap=\"1\">K.CC.B.4.b: 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.<\/option><option value=\"K.CC.B.4.c\" data-msa=\"0\" data-wap=\"1\">K.CC.B.4.c: Understand that each successive number name refers to a quantity that is one larger.<\/option><option value=\"K.CC.B.5\" data-msa=\"0\" data-wap=\"1\">K.CC.B.5: &lt;p&gt;Count to answer &amp;ldquo;how many?&amp;rdquo; questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1&amp;ndash;20, count out that many objects.&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.C.6\" data-msa=\"0\" data-wap=\"1\">K.CC.C.6: &lt;p&gt;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.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*&amp;nbsp;Include groups with up to ten objects.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"K.CC.C.7\" data-msa=\"0\" data-wap=\"1\">K.CC.C.7: &lt;p&gt;Compare two numbers between 1 and 10 presented as written numerals.&lt;\/p&gt;\r\n<\/option><option value=\"K.G.A.1\" data-msa=\"2\" data-wap=\"1\">K.G.A.1: &lt;p&gt;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.&lt;\/p&gt;\r\n<\/option><option value=\"K.G.A.2\" data-msa=\"2\" data-wap=\"1\">K.G.A.2: &lt;p&gt;Correctly name shapes regardless of their orientations or overall size.&lt;\/p&gt;\r\n<\/option><option value=\"K.G.A.3\" data-msa=\"2\" data-wap=\"1\">K.G.A.3: &lt;p&gt;Identify shapes as two-dimensional (lying in a plane, &amp;ldquo;flat&amp;rdquo;) or three- dimensional (&amp;ldquo;solid&amp;rdquo;).&lt;\/p&gt;\r\n<\/option><option value=\"K.G.B.4\" data-msa=\"1\" data-wap=\"1\">K.G.B.4: &lt;p&gt;Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices\/&amp;ldquo;corners&amp;rdquo;) and other attributes (e.g., having sides of equal length).&lt;\/p&gt;\r\n<\/option><option value=\"K.G.B.5\" data-msa=\"1\" data-wap=\"1\">K.G.B.5: &lt;p&gt;Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.&lt;\/p&gt;\r\n<\/option><option value=\"K.G.B.6\" data-msa=\"1\" data-wap=\"1\">K.G.B.6: &lt;p&gt;Compose simple shapes to form larger shapes. For example, &amp;ldquo;Can you join these two triangles with full sides touching to make a rectangle?&amp;rdquo;&lt;\/p&gt;\r\n<\/option><option value=\"K.MD.A.1\" data-msa=\"2\" data-wap=\"1\">K.MD.A.1: &lt;p&gt;Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.&lt;\/p&gt;\r\n<\/option><option value=\"K.MD.A.2\" data-msa=\"2\" data-wap=\"1\">K.MD.A.2: &lt;p&gt;Directly compare two objects with a measurable attribute in common, to see which object has &amp;ldquo;more of&amp;rdquo;\/&amp;ldquo;less of&amp;rdquo; the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller\/shorter.&lt;\/p&gt;\r\n<\/option><option value=\"K.MD.B.3\" data-msa=\"1\" data-wap=\"1\">K.MD.B.3: &lt;p&gt;Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Limit category counts to be less than or equal to 10.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"K.NBT.A.1\" data-msa=\"0\" data-wap=\"1\">K.NBT.A.1: &lt;p&gt;Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.&lt;\/p&gt;\r\n<\/option><option value=\"K.OA.A.1\" data-msa=\"0\" data-wap=\"1\">K.OA.A.1: &lt;p&gt;Represent addition and subtraction with objects, fingers, mental images, drawings*, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"K.OA.A.2\" data-msa=\"0\" data-wap=\"1\">K.OA.A.2: &lt;p&gt;Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.&lt;\/p&gt;\r\n<\/option><option value=\"K.OA.A.3\" data-msa=\"0\" data-wap=\"1\">K.OA.A.3: &lt;p&gt;Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).&lt;\/p&gt;\r\n<\/option><option value=\"K.OA.A.4\" data-msa=\"0\" data-wap=\"1\">K.OA.A.4: &lt;p&gt;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.&lt;\/p&gt;\r\n<\/option><option value=\"K.OA.A.5\" data-msa=\"0\" data-wap=\"1\">K.OA.A.5: &lt;p&gt;Fluently add and subtract within 5.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.A.4\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.A.4: &lt;p&gt;(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.B.5\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.B.5: &lt;p&gt;Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and &lt;a id=&quot;In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values.&quot; name=&quot;In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values.&quot;&gt;midline&lt;\/a&gt;.&amp;nbsp;&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.B.6\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.B.6: &lt;p&gt;(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.B.7\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.B.7: &lt;p&gt;(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.C.8\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.C.8: &lt;p&gt;Prove the Pythagorean identity sin&lt;sup&gt;2&lt;\/sup&gt;(&amp;theta;) + cos&lt;sup&gt;2&lt;\/sup&gt;(&amp;theta;) = 1 and use it to find sin(&amp;theta;), cos(&amp;theta;), or tan(&amp;theta;) given sin(&amp;theta;), cos(&amp;theta;), or tan(&amp;theta;) and the quadrant of the angle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-TF.C.9\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.C.9: &lt;p&gt;(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-C.A.1\" data-msa=\"0\" data-wap=\"1\">HS.G-C.A.1: &lt;p&gt;Prove that all circles are similar.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-C.A.2\" data-msa=\"0\" data-wap=\"1\">HS.G-C.A.2: &lt;p&gt;Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-C.A.3\" data-msa=\"0\" data-wap=\"1\">HS.G-C.A.3: &lt;p&gt;Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-C.A.4\" data-msa=\"0\" data-wap=\"1\">HS.G-C.A.4: &lt;p&gt;(+) Construct a tangent line from a point outside a given circle to the circle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-C.B.5\" data-msa=\"0\" data-wap=\"1\">HS.G-C.B.5: &lt;p&gt;Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.A.1\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.A.1: &lt;p&gt;Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.A.2\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.A.2: &lt;p&gt;Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.A.3\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.A.3: &lt;p&gt;Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.A.4\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.A.4: &lt;p&gt;Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.A.5\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.A.5: &lt;p&gt;Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.B.6\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.B.6: &lt;p&gt;Use geometric descriptions of &lt;a id=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot; name=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot;&gt;rigid motions&lt;\/a&gt; to transform figures and to predict the effect of a given &lt;a id=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot; name=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot;&gt;rigid motion&lt;\/a&gt; on a given figure; given two figures, use the definition of congruence in terms of &lt;a id=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot; name=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot;&gt;rigid motions&lt;\/a&gt; to decide if they are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent.&lt;\/a&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.B.7\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.B.7: &lt;p&gt;Use the definition of congruence in terms of &lt;a id=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot; name=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot;&gt;rigid motions&lt;\/a&gt; to show that two triangles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt; if and only if corresponding pairs of sides and corresponding pairs of angles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent.&lt;\/a&gt;&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.B.8\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.B.8: &lt;p&gt;Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of &lt;a id=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot; name=&quot;A transformation of points in space consisting of a sequence of one or more translations, reflections, and\/or rotations. Rigid motions are here assumed to preserve distances and angle measures.&quot;&gt;rigid motions&lt;\/a&gt;.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.C.10\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.C.10: &lt;p&gt;Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180&amp;deg;; base angles of isosceles triangles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt;; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the &lt;a id=&quot;A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list\u2014or the  mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.&quot; name=&quot;A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list\u2014or the  mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.&quot;&gt;medians&lt;\/a&gt; of a triangle meet at a point.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.C.11\" data-msa=\"0\" data-wap=\"1\">HS.G-CO.C.11: &lt;p&gt;Prove theorems about parallelograms. Theorems include: opposite sides are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt;, opposite angles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt;, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt; diagonals.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.C.9\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.C.9: &lt;p&gt;Prove theorems about lines and angles. Theorems include: vertical angles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt;; when a transversal crosses parallel lines, alternate interior angles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt; and corresponding angles are &lt;a id=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot; name=&quot;Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations)&quot;&gt;congruent&lt;\/a&gt;; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment&amp;rsquo;s endpoints.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.D.12\" data-msa=\"0\" data-wap=\"1\">HS.G-CO.D.12: &lt;p&gt;Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-CO.D.13\" data-msa=\"0\" data-wap=\"1\">HS.G-CO.D.13: &lt;p&gt;Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GMD.A.1\" data-msa=\"0\" data-wap=\"1\">HS.G-GMD.A.1: &lt;p&gt;Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri&amp;rsquo;s principle, and informal limit arguments.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GMD.A.2\" data-msa=\"0\" data-wap=\"1\">HS.G-GMD.A.2: &lt;p&gt;(+) Give an informal argument using Cavalieri&amp;rsquo;s principle for the formulas for the volume of a sphere and other solid figures.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GMD.A.3\" data-msa=\"0\" data-wap=\"1\">HS.G-GMD.A.3: &lt;p&gt;Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GMD.B.4\" data-msa=\"0\" data-wap=\"1\">HS.G-GMD.B.4: &lt;p&gt;Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.A.1\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.A.1: &lt;p&gt;Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.A.2\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.A.2: &lt;p&gt;Derive the equation of a parabola given a focus and directrix.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.A.3\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.A.3: &lt;p&gt;(+) 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.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.B.4\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.B.4: &lt;p&gt;Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, &amp;radic;3) lies on the circle centered at the origin and containing the point (0, 2).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.B.5\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.B.5: &lt;p&gt;Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.B.6\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.B.6: &lt;p&gt;Find the point on a directed line segment between two given points that partitions the segment in a given ratio.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-GPE.B.7\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.B.7: &lt;p&gt;Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-MG.A.1\" data-msa=\"0\" data-wap=\"1\">HS.G-MG.A.1: &lt;p&gt;Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-MG.A.2\" data-msa=\"0\" data-wap=\"1\">HS.G-MG.A.2: &lt;p&gt;Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-MG.A.3\" data-msa=\"0\" data-wap=\"1\">HS.G-MG.A.3: &lt;p&gt;Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.A.1\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.A.1: &lt;p&gt;Verify experimentally the properties of &lt;a id=&quot;A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot; name=&quot;A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot;&gt;dilations&lt;\/a&gt; given by a center and a scale factor:&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.A.2\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.A.2: &lt;p&gt;Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.A.3\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.A.3: &lt;p&gt;Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.B.4\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.B.4: &lt;p&gt;Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.B.5\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.B.5: &lt;p&gt;Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.C.6\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.C.6: &lt;p&gt;Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.C.7\" data-msa=\"0\" data-wap=\"1\">HS.G-SRT.C.7: &lt;p&gt;Explain and use the relationship between the sine and cosine of complementary angles.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.C.8\" data-msa=\"0\" data-wap=\"1\">HS.G-SRT.C.8: &lt;p&gt;Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.D.10\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.D.10: &lt;p&gt;(+) Prove the Laws of Sines and Cosines and use them to solve problems.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.D.11\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.D.11: &lt;p&gt;(+) Understand and apply the Law of Sines and the Law of Cosines to find uknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.D.9\" data-msa=\"0\" data-wap=\"1\">HS.G-SRT.D.9: &lt;p&gt;(+) 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.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.A.1\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.A.1: &lt;p&gt;Know there is a complex number i such that i&lt;sup&gt; 2&lt;\/sup&gt;&amp;nbsp;= &amp;ndash;1, and every complex number has the form a + bi with a and b real.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.A.2\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.A.2: &lt;p&gt;Use the relation i&lt;sup&gt; 2&lt;\/sup&gt;&amp;nbsp;= &amp;ndash;1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.A.3\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.A.3: &lt;p&gt;(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.B.4\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.B.4: &lt;p&gt;(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.B.5\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.B.5: &lt;p&gt;(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (&amp;ndash;1 + &amp;radic;3 i)&lt;sup&gt;3&lt;\/sup&gt;&amp;nbsp;= 8 because (&amp;ndash;1 + &amp;radic;3 i) has modulus 2 and argument 120&amp;deg;.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.B.6\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.B.6: &lt;p&gt;(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.C.7\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.C.7: &lt;p&gt;Solve quadratic equations with real coefficients that have complex solutions.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.C.8\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.C.8: &lt;p&gt;(+) Extend polynomial identities to the complex numbers. For example, rewrite x&lt;sup&gt;2&lt;\/sup&gt;&amp;nbsp;+ 4 as (x + 2i)(x &amp;ndash; 2i).&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-CN.C.9\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.C.9: &lt;p&gt;(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-Q.A.1\" data-msa=\"0\" data-wap=\"0\">HS.N-Q.A.1: &lt;p&gt;Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-Q.A.2\" data-msa=\"0\" data-wap=\"0\">HS.N-Q.A.2: &lt;p&gt;Define appropriate quantities for the purpose of descriptive modeling.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-Q.A.3\" data-msa=\"0\" data-wap=\"0\">HS.N-Q.A.3: &lt;p&gt;Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-RN.A.1\" data-msa=\"0\" data-wap=\"0\">HS.N-RN.A.1: &lt;p&gt;Explain how the definition of the meaning of rational exponents follows from extending the properties of &lt;a id=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot; name=&quot;A number expressible in the form a or \u2013a for some whole number a.&quot;&gt;integer&lt;\/a&gt; exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5&lt;sup&gt;1\/3&lt;\/sup&gt; to be the cube root of 5 because we want (5&lt;sup&gt;1\/3&lt;\/sup&gt;)&lt;sup&gt;3&lt;\/sup&gt;= 5&lt;sup&gt;(1\/3)3&lt;\/sup&gt;&amp;nbsp;to hold, so (5&lt;sup&gt;1\/3&lt;\/sup&gt;)&lt;sup&gt;3&amp;nbsp;&lt;\/sup&gt;must equal 5.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-RN.A.2\" data-msa=\"0\" data-wap=\"0\">HS.N-RN.A.2: &lt;p&gt;Rewrite expressions involving radicals and rational exponents using the properties of exponents.&lt;\/p&gt;\r\n<\/option><option value=\"HS.N-RN.B.3\" data-msa=\"0\" data-wap=\"0\">HS.N-RN.B.3: &lt;p&gt;Explain why the sum or product of two &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational numbers&lt;\/a&gt; is rational; that the sum of a &lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt;rational number&lt;\/a&gt; and an irrational number is irrational; and that the product of a nonzero&lt;a id=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot; name=&quot;A number expressible in the form a\/b or \u2013 a\/b for some fraction a\/b. The rational numbers include the integers.&quot;&gt; rational number&lt;\/a&gt; and an irrational number is irrational.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.A.1\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.A.1: &lt;p&gt;Describe events as subsets of a &lt;a id=&quot;In a probability model for a random process, a list of the  individual outcomes that are to be considered.&quot; name=&quot;In a probability model for a random process, a list of the  individual outcomes that are to be considered.&quot;&gt;sample space&lt;\/a&gt; (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (&amp;ldquo;or,&amp;rdquo; &amp;ldquo;and,&amp;rdquo; &amp;ldquo;not&amp;rdquo;).&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.A.2\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.A.2: &lt;p&gt;Understand that two events A and B are independent if the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.A.3\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.A.3: &lt;p&gt;Understand the conditional &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of A given B as P(A and B)\/P(B), and interpret independence of A and B as saying that the conditional &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of A given B is the same as the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of A, and the conditional &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of B given A is the same as the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of B.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.A.4\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.A.4: &lt;p&gt;Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a &lt;a id=&quot;In a probability model for a random process, a list of the  individual outcomes that are to be considered.&quot; name=&quot;In a probability model for a random process, a list of the  individual outcomes that are to be considered.&quot;&gt;sample space&lt;\/a&gt; to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.A.5\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.A.5: &lt;p&gt;Recognize and explain the concepts of conditional &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.B.6\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.B.6: &lt;p&gt;Find the conditional &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; of A given B as the &lt;a id=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot; name=&quot;A number expressible in the form a\/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.&quot;&gt;fraction&lt;\/a&gt; of B&amp;rsquo;s outcomes that also belong to A, and interpret the answer in terms of the model.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.B.7\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.B.7: &lt;p&gt;Apply the Addition Rule, P(A or B) = P(A) + P(B) &amp;ndash; P(A and B), and interpret the answer in terms of the model.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.B.8\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.B.8: &lt;p&gt;(+) Apply the general Multiplication Rule in a &lt;a id=&quot;A probability model which assigns equal probability to all outcomes. See also: probability model.&quot; name=&quot;A probability model which assigns equal probability to all outcomes. See also: probability model.&quot;&gt;uniform &lt;\/a&gt;&lt;a id=&quot;A probability model is used to assign probabilities to  outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.&quot; name=&quot;A probability model is used to assign probabilities to  outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.&quot;&gt;probability model&lt;\/a&gt;, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-CP.B.9\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.B.9: &lt;p&gt;(+) Use permutations and combinations to compute probabilities of compound events and solve problems.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-IC.A.1\" data-msa=\"0\" data-wap=\"0\">HS.S-IC.A.1: &lt;p&gt;Understand statistics as a process for making inferences about population parameters based on a random sample from that population.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-IC.A.2\" data-msa=\"0\" data-wap=\"1\">HS.S-IC.A.2: &lt;p&gt;Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with &lt;a id=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot; name=&quot;A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).&quot;&gt;probability&lt;\/a&gt; 0.5. Would a result of 5 tails in a row cause you to question the model?&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-IC.B.4\" data-msa=\"0\" data-wap=\"1\">HS.S-IC.B.4: &lt;p&gt;Use data from a sample survey to estimate a population &lt;a id=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. *To be more precise, this defines the arithmetic mean.&quot; name=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. *To be more precise, this defines the arithmetic mean.&quot;&gt;mean&lt;\/a&gt; or proportion; develop a margin of error through the use of simulation models for random sampling.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-IC.B.5\" data-msa=\"0\" data-wap=\"1\">HS.S-IC.B.5: &lt;p&gt;Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-IC.B.6\" data-msa=\"0\" data-wap=\"1\">HS.S-IC.B.6: &lt;p&gt;Evaluate reports based on data.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.A.1\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.A.1: &lt;p&gt;Represent data with plots on the real number line (&lt;a id=&quot;See &amp;quot;line plot:&amp;quot; A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot; name=&quot;See &amp;quot;line plot:&amp;quot; A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.&quot;&gt;dot plots&lt;\/a&gt;, histograms, and &lt;a id=&quot;A method of visually displaying a distribution of data values by using  the median, quartiles, and extremes of the data set. A box shows the middle  50% of the data&quot; name=&quot;A method of visually displaying a distribution of data values by using  the median, quartiles, and extremes of the data set. A box shows the middle  50% of the data&quot;&gt;box plots&lt;\/a&gt;).&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.A.2\" data-msa=\"0\" data-wap=\"0\">HS.S-ID.A.2: &lt;p&gt;Use statistics appropriate to the shape of the data distribution to compare center (&lt;a id=&quot;A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list\u2014or the  mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.&quot; name=&quot;A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list\u2014or the  mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.&quot;&gt;median&lt;\/a&gt;, &lt;a id=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.  *To be more precise, this defines the arithmetic mean.&quot; name=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.  *To be more precise, this defines the arithmetic mean.&quot;&gt;mean&lt;\/a&gt;) and spread (&lt;a id=&quot;A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 \u2013 6 = 9. See also: first quartile, third quartile.&quot; name=&quot;A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 \u2013 6 = 9. See also: first quartile, third quartile.&quot;&gt;interquartile range&lt;\/a&gt;, standard deviation) of two or more different data sets.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.A.3\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.A.3: &lt;p&gt;Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.A.4\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.A.4: &lt;p&gt;Use the &lt;a id=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.  *To be more precise, this defines the arithmetic mean.&quot; name=&quot;A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.* Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.  *To be more precise, this defines the arithmetic mean.&quot;&gt;mean&lt;\/a&gt; and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.B.5\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.B.5: &lt;p&gt;Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.B.6\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.B.6: &lt;p&gt;Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.B.6.a\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.B.6.a: &lt;p&gt;Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.B.6.b\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.B.6.b: &lt;p&gt;Informally assess the fit of a function by plotting and analyzing residuals.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.B.6.c\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.B.6.c: &lt;p&gt;Fit a linear function for a &lt;a id=&quot;A graph in the coordinate plane representing a set of bivariate  data. For example, the heights and weights of a group of people could be displayed on a scatter plot.&quot; name=&quot;A graph in the coordinate plane representing a set of bivariate  data. For example, the heights and weights of a group of people could be displayed on a scatter plot.&quot;&gt;scatter plot&lt;\/a&gt; that suggests a linear association.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.C.7\" data-msa=\"0\" data-wap=\"0\">HS.S-ID.C.7: &lt;p&gt;Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.C.8\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.C.8: &lt;p&gt;Compute (using technology) and interpret the correlation coefficient of a linear fit.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-ID.C.9\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.C.9: &lt;p&gt;Distinguish between correlation and causation.&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.A.1.b\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.A.1.b: &lt;p&gt;The &lt;a id=&quot;A transformation that moves each point along th eray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot; name=&quot;A transformation that moves each point along th eray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot;&gt;dilation&lt;\/a&gt; of a line segment is longer or shorter in the ratio given by the scale factor.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.1.b\" data-msa=\"0\" data-wap=\"0\">HS.F-LE.A.1.b: &lt;p&gt;Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.1.c\" data-msa=\"0\" data-wap=\"0\">HS.F-LE.A.1.c: &lt;p&gt;Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.4.b\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.4.b: &lt;p&gt;(+) Verify by composition that one function is the inverse of another.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.4.c\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.4.c: &lt;p&gt;(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.4.d\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.4.d: &lt;p&gt;(+) Produce an invertible function from a non-invertible function by restricting the domain.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-BF.B.4.a\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B.4.a: &lt;p&gt;Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x)=2x&lt;sup&gt;3&lt;\/sup&gt;&amp;nbsp;or f(x) = (x+1)\/(x-1) for x &amp;ne;1&lt;\/p&gt;\r\n<\/option><option value=\"HS.G-SRT.A.1.a\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.A.1.a: &lt;p&gt;A &lt;a id=&quot;A transformation that moves each point along th eray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot; name=&quot;A transformation that moves each point along th eray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.&quot;&gt;dilation&lt;\/a&gt; takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.&lt;\/p&gt;\r\n<\/option><option value=\"HS.F-LE.A.1.a\" data-msa=\"0\" data-wap=\"0\">HS.F-LE.A.1.a: &lt;p&gt;Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.A.1.b\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.A.1.b: &lt;p&gt;Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)&lt;sup&gt;n&lt;\/sup&gt;&amp;nbsp;as the product of P and a factor not depending on P.&lt;\/p&gt;\r\n<\/option><option value=\"HS.A-SSE.A.1.a\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.A.1.a: &lt;p&gt;Interpret parts of an expression, such as terms, factors, and coefficients.&lt;\/p&gt;\r\n<\/option><option value=\"HS.S-IC.B.3\" data-msa=\"0\" data-wap=\"1\">HS.S-IC.B.3: &lt;p&gt;Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.&lt;\/p&gt;\r\n<\/option><option value=\"1.G.A\" data-msa=\"2\" data-wap=\"0\">1.G.A: Reason With Shapes And Their Attributes.<\/option><option value=\"1.MD.A\" data-msa=\"0\" data-wap=\"0\">1.MD.A: Measure Lengths Indirectly And By Iterating Length Units.<\/option><option value=\"1.MD.B\" data-msa=\"2\" data-wap=\"0\">1.MD.B: Tell And Write Time.<\/option><option value=\"1.MD.C\" data-msa=\"1\" data-wap=\"0\">1.MD.C: Represent And Interpret Data.<\/option><option value=\"1.NBT.A\" data-msa=\"0\" data-wap=\"0\">1.NBT.A: Extend The Counting Sequence.<\/option><option value=\"1.NBT.B\" data-msa=\"0\" data-wap=\"0\">1.NBT.B: Understand Place Value.<\/option><option value=\"1.NBT.C\" data-msa=\"0\" data-wap=\"0\">1.NBT.C: &lt;p&gt;Use Place Value Understanding And &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;Properties Of Operations&lt;\/a&gt; To Add And Subtract.&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.A\" data-msa=\"0\" data-wap=\"0\">1.OA.A: Represent And Solve Problems Involving Addition And Subtraction.<\/option><option value=\"1.OA.B\" data-msa=\"0\" data-wap=\"0\">1.OA.B: &lt;p&gt;Understand And Apply &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;Properties Of Operations&lt;\/a&gt; And The Relationship Between Addition And Subtraction.&lt;\/p&gt;\r\n<\/option><option value=\"1.OA.C\" data-msa=\"0\" data-wap=\"0\">1.OA.C: Add And Subtract Within 20.<\/option><option value=\"1.OA.D\" data-msa=\"0\" data-wap=\"0\">1.OA.D: Work With Addition And Subtraction Equations.<\/option><option value=\"2.G.A\" data-msa=\"2\" data-wap=\"0\">2.G.A: Reason With Shapes And Their Attributes.<\/option><option value=\"2.MD.A\" data-msa=\"0\" data-wap=\"0\">2.MD.A: Measure And Estimate Lengths In Standard Units.<\/option><option value=\"2.MD.B\" data-msa=\"0\" data-wap=\"0\">2.MD.B: Relate Addition And Subtraction To Length.<\/option><option value=\"2.MD.C\" data-msa=\"1\" data-wap=\"0\">2.MD.C: Work With Time And Money.<\/option><option value=\"2.MD.D\" data-msa=\"1\" data-wap=\"0\">2.MD.D: Represent And Interpret Data.<\/option><option value=\"2.NBT.A\" data-msa=\"0\" data-wap=\"0\">2.NBT.A: Understand Place Value.<\/option><option value=\"2.NBT.B\" data-msa=\"0\" data-wap=\"0\">2.NBT.B: &lt;p&gt;Use Place Value Understanding And &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;Properties Of Operations&lt;\/a&gt; To Add And Subtract.&lt;\/p&gt;\r\n<\/option><option value=\"2.OA.A\" data-msa=\"0\" data-wap=\"0\">2.OA.A: Represent And Solve Problems Involving Addition And Subtraction.<\/option><option value=\"2.OA.B\" data-msa=\"0\" data-wap=\"0\">2.OA.B: Add And Subtract Within 20.<\/option><option value=\"2.OA.C\" data-msa=\"1\" data-wap=\"0\">2.OA.C: Work With Equal Groups Of Objects To Gain Foundations For Multiplication.<\/option><option value=\"3.G.A\" data-msa=\"1\" data-wap=\"0\">3.G.A: &lt;p&gt;Reason With Shapes And Their Attributes.&lt;\/p&gt;\r\n<\/option><option value=\"3.MD.A\" data-msa=\"0\" data-wap=\"0\">3.MD.A: Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects.<\/option><option value=\"3.MD.B\" data-msa=\"1\" data-wap=\"0\">3.MD.B: Represent And Interpret Data.<\/option><option value=\"3.MD.C\" data-msa=\"0\" data-wap=\"0\">3.MD.C: Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.<\/option><option value=\"3.MD.D\" data-msa=\"2\" data-wap=\"0\">3.MD.D: Geometric Measurement: Recognize Perimeter As An Attribute Of Plane Figures And Distinguish Between Linear And Area Measures.<\/option><option value=\"3.NBT.A\" data-msa=\"2\" data-wap=\"0\">3.NBT.A: &lt;p&gt;Use Place Value Understanding And &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;Properties Of Operations&lt;\/a&gt; To Perform Multi-Digit Arithmetic.*&lt;\/p&gt;\r\n\r\n&lt;p&gt;&amp;nbsp;&lt;\/p&gt;\r\n\r\n&lt;p&gt;&lt;sup&gt;*A range of algorithms may be used.&lt;\/sup&gt;&lt;\/p&gt;\r\n<\/option><option value=\"3.NF.A\" data-msa=\"0\" data-wap=\"0\">3.NF.A: Develop Understanding Of Fractions As Numbers.<\/option><option value=\"3.OA.A\" data-msa=\"0\" data-wap=\"0\">3.OA.A: Represent And Solve Problems Involving Multiplication And Division.<\/option><option value=\"3.OA.B\" data-msa=\"0\" data-wap=\"0\">3.OA.B: Understand Properties Of Multiplication And The Relationship Between Multiplication And Division.<\/option><option value=\"3.OA.C\" data-msa=\"0\" data-wap=\"0\">3.OA.C: Multiply And Divide Within 100.<\/option><option value=\"3.OA.D\" data-msa=\"0\" data-wap=\"0\">3.OA.D: Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic.<\/option><option value=\"4.G.A\" data-msa=\"2\" data-wap=\"0\">4.G.A: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles.<\/option><option value=\"4.MD.A\" data-msa=\"1\" data-wap=\"0\">4.MD.A: Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit.<\/option><option value=\"4.MD.B\" data-msa=\"1\" data-wap=\"0\">4.MD.B: Represent And Interpret Data.<\/option><option value=\"4.MD.C\" data-msa=\"2\" data-wap=\"0\">4.MD.C: Geometric Measurement: Understand Concepts Of Angle And Measure Angles.<\/option><option value=\"4.NBT.A\" data-msa=\"0\" data-wap=\"0\">4.NBT.A: &lt;p&gt;Generalize Place Value Understanding For Multi-Digit Whole Numbers.&lt;\/p&gt;\r\n<\/option><option value=\"4.NBT.B\" data-msa=\"0\" data-wap=\"0\">4.NBT.B: &lt;p&gt;Use Place Value Understanding And &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;Properties Of Operations&lt;\/a&gt; To Perform Multi-Digit Arithmetic.&lt;\/p&gt;\r\n<\/option><option value=\"4.NF.A\" data-msa=\"0\" data-wap=\"0\">4.NF.A: Extend Understanding Of Fraction Equivalence And Ordering.<\/option><option value=\"4.NF.B\" data-msa=\"0\" data-wap=\"0\">4.NF.B: Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers.<\/option><option value=\"4.NF.C\" data-msa=\"0\" data-wap=\"0\">4.NF.C: Understand Decimal Notation For Fractions, And Compare Decimal Fractions.<\/option><option value=\"4.OA.A\" data-msa=\"0\" data-wap=\"0\">4.OA.A: Use The Four Operations With Whole Numbers To Solve Problems.<\/option><option value=\"4.OA.B\" data-msa=\"1\" data-wap=\"0\">4.OA.B: Gain Familiarity With Factors And Multiples.<\/option><option value=\"4.OA.C\" data-msa=\"2\" data-wap=\"0\">4.OA.C: Generate And Analyze Patterns.<\/option><option value=\"5.G.A\" data-msa=\"2\" data-wap=\"0\">5.G.A: Graph Points On The Coordinate Plane To Solve Real-World And Mathematical Problems.<\/option><option value=\"5.G.B\" data-msa=\"2\" data-wap=\"0\">5.G.B: Classify Two-Dimensional Figures Into Categories Based On Their Properties.<\/option><option value=\"5.MD.A\" data-msa=\"1\" data-wap=\"0\">5.MD.A: Convert Like Measurement Units Within A Given Measurement System.<\/option><option value=\"5.MD.B\" data-msa=\"1\" data-wap=\"0\">5.MD.B: Represent And Interpret Data.<\/option><option value=\"5.MD.C\" data-msa=\"0\" data-wap=\"0\">5.MD.C: Geometric Measurement: Understand Concepts Of Volume And Relate Volume To Multiplication And To Addition.<\/option><option value=\"5.NBT.A\" data-msa=\"0\" data-wap=\"0\">5.NBT.A: Understand The Place Value System.<\/option><option value=\"5.NBT.B\" data-msa=\"0\" data-wap=\"0\">5.NBT.B: Perform Operations With Multi-Digit Whole Numbers And With Decimals To Hundredths.<\/option><option value=\"5.NF.A\" data-msa=\"0\" data-wap=\"0\">5.NF.A: Use Equivalent Fractions As A Strategy To Add And Subtract Fractions.<\/option><option value=\"5.NF.B\" data-msa=\"0\" data-wap=\"0\">5.NF.B: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions.<\/option><option value=\"5.OA.A\" data-msa=\"2\" data-wap=\"0\">5.OA.A: Write And Interpret Numerical Expressions.<\/option><option value=\"5.OA.B\" data-msa=\"2\" data-wap=\"0\">5.OA.B: Analyze Patterns And Relationships.<\/option><option value=\"6.EE.A\" data-msa=\"0\" data-wap=\"0\">6.EE.A: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.<\/option><option value=\"6.EE.B\" data-msa=\"0\" data-wap=\"0\">6.EE.B: Reason About And Solve One-Variable Equations And Inequalities.<\/option><option value=\"6.EE.C\" data-msa=\"0\" data-wap=\"0\">6.EE.C: Represent And Analyze Quantitative Relationships Between Dependent And Independent Variables.<\/option><option value=\"6.G.A\" data-msa=\"1\" data-wap=\"0\">6.G.A: Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume.<\/option><option value=\"6.NS.A\" data-msa=\"0\" data-wap=\"0\">6.NS.A: Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.<\/option><option value=\"6.NS.B\" data-msa=\"2\" data-wap=\"0\">6.NS.B: Compute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples.<\/option><option value=\"6.NS.C\" data-msa=\"0\" data-wap=\"0\">6.NS.C: Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.<\/option><option value=\"6.RP.A\" data-msa=\"0\" data-wap=\"0\">6.RP.A: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.<\/option><option value=\"6.SP.A\" data-msa=\"2\" data-wap=\"0\">6.SP.A: Develop Understanding Of Statistical Variability.<\/option><option value=\"6.SP.B\" data-msa=\"2\" data-wap=\"0\">6.SP.B: Summarize And Describe Distributions.<\/option><option value=\"7.EE.A\" data-msa=\"0\" data-wap=\"0\">7.EE.A: &lt;p&gt;Use &lt;a id=&quot;[3]&quot; name=&quot;[3]&quot;&gt;Properties Of Operations&lt;\/a&gt; To Generate Equivalent Expressions.&lt;\/p&gt;\r\n<\/option><option value=\"7.EE.B\" data-msa=\"0\" data-wap=\"0\">7.EE.B: Solve Real-Life And Mathematical Problems Using Numerical And Algebraic Expressions And Equations.<\/option><option value=\"7.G.A\" data-msa=\"2\" data-wap=\"0\">7.G.A: Draw, Construct, And Describe Geometrical Figures And Describe The Relationships Between Them.<\/option><option value=\"7.G.B\" data-msa=\"2\" data-wap=\"0\">7.G.B: Solve Real-Life And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume.<\/option><option value=\"7.NS.A\" data-msa=\"0\" data-wap=\"0\">7.NS.A: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers.<\/option><option value=\"7.RP.A\" data-msa=\"0\" data-wap=\"0\">7.RP.A: Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems.<\/option><option value=\"7.SP.A\" data-msa=\"1\" data-wap=\"0\">7.SP.A: Use Random Sampling To Draw Inferences About A Population.<\/option><option value=\"7.SP.B\" data-msa=\"2\" data-wap=\"0\">7.SP.B: Draw Informal Comparative Inferences About Two Populations.<\/option><option value=\"7.SP.C\" data-msa=\"1\" data-wap=\"0\">7.SP.C: Investigate Chance Processes And Develop, Use, And Evaluate Probability Models.<\/option><option value=\"8.EE.A\" data-msa=\"0\" data-wap=\"0\">8.EE.A: Work With Radicals And Integer Exponents.<\/option><option value=\"8.EE.B\" data-msa=\"0\" data-wap=\"0\">8.EE.B: Understand The Connections Between Proportional Relationships, Lines, And Linear Equations.<\/option><option value=\"8.EE.C\" data-msa=\"0\" data-wap=\"0\">8.EE.C: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations.<\/option><option value=\"8.F.A\" data-msa=\"0\" data-wap=\"0\">8.F.A: Define, Evaluate, And Compare Functions.<\/option><option value=\"8.F.B\" data-msa=\"0\" data-wap=\"0\">8.F.B: Use Functions To Model Relationships Between Quantities.<\/option><option value=\"8.G.A\" data-msa=\"0\" data-wap=\"0\">8.G.A: Understand Congruence And Similarity Using Physical Models, Transparencies, Or Geometry Software.<\/option><option value=\"8.G.B\" data-msa=\"0\" data-wap=\"0\">8.G.B: Understand And Apply The Pythagorean Theorem.<\/option><option value=\"8.G.C\" data-msa=\"2\" data-wap=\"0\">8.G.C: Solve Real-World And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres.<\/option><option value=\"8.NS.A\" data-msa=\"1\" data-wap=\"0\">8.NS.A: Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers.<\/option><option value=\"8.SP.A\" data-msa=\"1\" data-wap=\"0\">8.SP.A: Investigate Patterns Of Association In Bivariate Data.<\/option><option value=\"K.CC.A\" data-msa=\"0\" data-wap=\"0\">K.CC.A: Know Number Names And The Count Sequence.<\/option><option value=\"K.CC.B\" data-msa=\"0\" data-wap=\"0\">K.CC.B: Count To Tell The Number Of Objects.<\/option><option value=\"K.CC.C\" data-msa=\"0\" data-wap=\"0\">K.CC.C: Compare Numbers.<\/option><option value=\"K.G.A\" data-msa=\"2\" data-wap=\"0\">K.G.A: Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres).<\/option><option value=\"K.G.B\" data-msa=\"1\" data-wap=\"0\">K.G.B: &lt;p&gt;Analyze, Compare, Create, And Compose Shapes.&lt;\/p&gt;\r\n<\/option><option value=\"K.MD.A\" data-msa=\"2\" data-wap=\"0\">K.MD.A: Describe And Compare Measurable Attributes.<\/option><option value=\"K.MD.B\" data-msa=\"1\" data-wap=\"0\">K.MD.B: Classify Objects And Count The Number Of Objects In Each Category.<\/option><option value=\"K.NBT.A\" data-msa=\"0\" data-wap=\"0\">K.NBT.A: Work With Numbers 11\u201319 To Gain Foundations For Place Value.<\/option><option value=\"K.OA.A\" data-msa=\"0\" data-wap=\"0\">K.OA.A: Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From.<\/option><option value=\"..B\" data-msa=\"0\" data-wap=\"1\">..B: All Five Questions Of A Multiple-Choice Test Where Each Question Has Four Choices, And Find The Expected Grade Under Various Grading Schemes.<\/option><option value=\"HS.F-IF.C\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.C: Analyze Functions Using Different Representations<\/option><option value=\"HS.G-MG.A\" data-msa=\"0\" data-wap=\"1\">HS.G-MG.A: Apply Geometric Concepts In Modeling Situations<\/option><option value=\"HS.G-SRT.D\" data-msa=\"0\" data-wap=\"1\">HS.G-SRT.D: Apply Trigonometry To General Triangles<\/option><option value=\"HS.F-BF.A\" data-msa=\"0\" data-wap=\"0\">HS.F-BF.A: Build A Function That Models A Relationship Between Two Quantities<\/option><option value=\"HS.F-BF.B\" data-msa=\"0\" data-wap=\"1\">HS.F-BF.B: Build New Functions From Existing Functions<\/option><option value=\"..A\" data-msa=\"0\" data-wap=\"1\">..A: Calculate Expected Values And Use Them To Solve Problems<\/option><option value=\"HS.F-LE.A\" data-msa=\"0\" data-wap=\"0\">HS.F-LE.A: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems<\/option><option value=\"HS.A-CED.A\" data-msa=\"0\" data-wap=\"0\">HS.A-CED.A: Create Equations That Describe Numbers Or Relationships<\/option><option value=\"HS.G-SRT.C\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.C: Define Trigonometric Ratios And Solve Problems Involving Right Triangles<\/option><option value=\"HS.G-CO.A\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.A: Experiment With Transformations In The Plane<\/option><option value=\"HS.G-GMD.A\" data-msa=\"0\" data-wap=\"1\">HS.G-GMD.A: Explain Volume Formulas And Use Them To Solve Problems<\/option><option value=\"HS.F-TF.A\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.A: Extend The Domain Of Trigonometric Functions Using The Unit Circle<\/option><option value=\"HS.N-RN.A\" data-msa=\"0\" data-wap=\"0\">HS.N-RN.A: Extend The Properties Of Exponents To Rational Exponents.<\/option><option value=\"HS.G-C.B\" data-msa=\"0\" data-wap=\"1\">HS.G-C.B: Find Arc Lengths And Areas Of Sectors Of Circles<\/option><option value=\"HS.F-LE.B\" data-msa=\"0\" data-wap=\"1\">HS.F-LE.B: Interpret Expressions For Functions In Terms Of The Situation They Model<\/option><option value=\"HS.F-IF.B\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.B: Interpret Functions That Arise In Applications In Terms Of The Context<\/option><option value=\"HS.S-ID.C\" data-msa=\"0\" data-wap=\"0\">HS.S-ID.C: Interpret Linear Models<\/option><option value=\"HS.A-SSE.A\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.A: Interpret The Structure Of Expressions<\/option><option value=\"HS.G-CO.D\" data-msa=\"0\" data-wap=\"1\">HS.G-CO.D: Make Geometric Constructions<\/option><option value=\"HS.S-IC.B\" data-msa=\"0\" data-wap=\"1\">HS.S-IC.B: Make Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational Studies<\/option><option value=\"HS.F-TF.B\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.B: Model Periodic Phenomena With Trigonometric Functions<\/option><option value=\"HS.A-APR.A\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.A: Perform Arithmetic Operations On Polynomials<\/option><option value=\"HS.N-CN.A\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.A: Perform Arithmetic Operations With Complex Numbers.<\/option><option value=\"..C\" data-msa=\"0\" data-wap=\"1\">..C: Perform Operations On Matrices And Use Matrices In Applications.<\/option><option value=\"..B\" data-msa=\"0\" data-wap=\"1\">..B: Perform Operations On Vectors.<\/option><option value=\"HS.F-TF.C\" data-msa=\"0\" data-wap=\"1\">HS.F-TF.C: Prove And Apply Trigonometric Identities<\/option><option value=\"HS.G-CO.C\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.C: Prove Geometric Theorems<\/option><option value=\"HS.G-SRT.B\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.B: Prove Theorems Involving Similarity<\/option><option value=\"HS.N-Q.A\" data-msa=\"0\" data-wap=\"0\">HS.N-Q.A: Reason Quantitatively And Use Units To Solve Problems.<\/option><option value=\"..A\" data-msa=\"0\" data-wap=\"1\">..A: Represent And Model With Vector Quantities.<\/option><option value=\"HS.A-REI.D\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.D: Represent And Solve Equations And Inequalities Graphically<\/option><option value=\"HS.N-CN.B\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.B: Represent Complex Numbers And Their Operations On The Complex Plane.<\/option><option value=\"HS.A-APR.D\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.D: Rewrite Rational Expressions<\/option><option value=\"HS.A-REI.B\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.B: Solve Equations And Inequalities In One Variable<\/option><option value=\"HS.A-REI.C\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.C: Solve Systems Of Equations<\/option><option value=\"HS.S-ID.A\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.A: Summarize, Represent, And Interpret Data On A Single Count Or Measurement Variable<\/option><option value=\"HS.S-ID.B\" data-msa=\"0\" data-wap=\"1\">HS.S-ID.B: Summarize, Represent, And Interpret Data On Two Categorical And Quantitative Variables<\/option><option value=\"HS.G-GPE.A\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.A: Translate Between The Geometric Description And The Equation For A Conic Section<\/option><option value=\"HS.G-C.A\" data-msa=\"0\" data-wap=\"1\">HS.G-C.A: Understand And Apply Theorems About Circles<\/option><option value=\"HS.S-IC.A\" data-msa=\"0\" data-wap=\"0\">HS.S-IC.A: Understand And Evaluate Random Processes Underlying Statistical Experiments<\/option><option value=\"HS.G-CO.B\" data-msa=\"0\" data-wap=\"0\">HS.G-CO.B: Understand Congruence In Terms Of Rigid Motions<\/option><option value=\"HS.S-CP.A\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.A: Understand Independence And Conditional Probability And Use Them To Interpret Data<\/option><option value=\"HS.G-SRT.A\" data-msa=\"0\" data-wap=\"0\">HS.G-SRT.A: Understand Similarity In Terms Of Similarity Transformations<\/option><option value=\"HS.A-REI.A\" data-msa=\"0\" data-wap=\"0\">HS.A-REI.A: Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning<\/option><option value=\"HS.F-IF.A\" data-msa=\"0\" data-wap=\"0\">HS.F-IF.A: Understand The Concept Of A Function And Use Function Notation<\/option><option value=\"HS.A-APR.B\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.B: Understand The Relationship Between Zeros And Factors Of Polynomials<\/option><option value=\"HS.N-CN.C\" data-msa=\"0\" data-wap=\"1\">HS.N-CN.C: Use Complex Numbers In Polynomial Identities And Equations.<\/option><option value=\"HS.G-GPE.B\" data-msa=\"0\" data-wap=\"1\">HS.G-GPE.B: Use Coordinates To Prove Simple Geometric Theorems Algebraically<\/option><option value=\"HS.A-APR.C\" data-msa=\"0\" data-wap=\"0\">HS.A-APR.C: Use Polynomial Identities To Solve Problems<\/option><option value=\"..C\" data-msa=\"0\" data-wap=\"1\">..C: Use Probability To Evaluate Outcomes Of Decisions<\/option><option value=\"HS.N-RN.B\" data-msa=\"0\" data-wap=\"0\">HS.N-RN.B: Use Properties Of Rational And Irrational Numbers.<\/option><option value=\"HS.S-CP.B\" data-msa=\"0\" data-wap=\"1\">HS.S-CP.B: Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability Model<\/option><option value=\"HS.G-GMD.B\" data-msa=\"0\" data-wap=\"1\">HS.G-GMD.B: Visualize Relationships Between Two-Dimensional And Three- Dimensional Objects<\/option><option value=\"HS.A-SSE.B\" data-msa=\"0\" data-wap=\"0\">HS.A-SSE.B: Write Expressions In Equivalent Forms To Solve Problems<\/option><option value=\"MP.1\">MP.1: Make sense of\r\n  problems and persevere in solving them. Mathematically proficient students start by explaining to themselves\r\n  the meaning of a problem and looking for entry points to its solution. They\r\n  analyze givens, constraints, relationships, and goals. They make conjectures\r\n  about the form and meaning of the solution and plan a solution pathway rather\r\n  than simply jumping into a solution attempt. They consider analogous\r\n  problems, and try special cases and simpler forms of the original problem in\r\n  order to gain insight into its solution. They monitor and evaluate their\r\n  progress and change course if necessary. Older students might, depending on\r\n  the context of the problem, transform algebraic expressions or change the viewing\r\n  window on their graphing calculator to get the information they need.\r\n  Mathematically proficient students can explain correspondences between\r\n  equations, verbal descriptions, tables, and graphs or draw diagrams of\r\n  important features and relationships, graph data, and search for regularity\r\n  or trends. Younger students might rely on using concrete objects or pictures\r\n  to help conceptualize and solve a problem. Mathematically proficient students\r\n  check their answers to problems using a different method, and they\r\n  continually ask themselves, \"Does this make sense?\" They can\r\n  understand the approaches of others to solving complex problems and identify\r\n  correspondences between different approaches.<\/option><option value=\"MP.2\">MP.2: Reason abstractly\r\n  and quantitatively. Mathematically\r\n  proficient students make sense of quantities and their relationships in\r\n  problem situations. They bring two complementary abilities to bear on\r\n  problems involving quantitative relationships: the ability to &lt;i&gt;decontextualize&lt;\/i&gt;\u2014to abstract a\r\n  given situation and represent it symbolically and manipulate the representing\r\n  symbols as if they have a life of their own, without necessarily attending to\r\n  their referents\u2014and the ability to &lt;i&gt;contextualize&lt;\/i&gt;, to pause as needed during the manipulation process in order\r\n  to probe into the referents for the symbols involved. Quantitative reasoning\r\n  entails habits of creating a coherent representation of the problem at hand;\r\n  considering the units involved; attending to the meaning of quantities, not\r\n  just how to compute them; and knowing and flexibly using different properties\r\n  of operations and objects.<\/option><option value=\"MP.3\">MP.3: Construct viable\r\n  arguments and critique the reasoning of others. Mathematically proficient students\r\n  understand and use stated assumptions, definitions, and previously\r\n  established results in constructing arguments. They make conjectures and\r\n  build a logical progression of statements to explore the truth of their\r\n  conjectures. They are able to analyze situations by breaking them into cases,\r\n  and can recognize and use counterexamples. They justify their conclusions,\r\n  communicate them to others, and respond to the arguments of others. They\r\n  reason inductively about data, making plausible arguments that take into\r\n  account the context from which the data arose. Mathematically proficient\r\n  students are also able to compare the effectiveness of two plausible\r\n  arguments, distinguish correct logic or reasoning from that which is flawed,\r\n  and\u2014if there is a flaw in an argument\u2014explain what it is. Elementary students\r\n  can construct arguments using concrete referents such as objects, drawings,\r\n  diagrams, and actions. Such arguments can make sense and be correct, even\r\n  though they are not generalized or made formal until later grades. Later,\r\n  students learn to determine domains to which an argument applies. Students at\r\n  all grades can listen or read the arguments of others, decide whether they\r\n  make sense, and ask useful questions to clarify or improve the arguments.<\/option><option value=\"MP.4\">MP.4: Model with\r\n  mathematics. Mathematically proficient\r\n  students can apply the mathematics they know to solve problems arising in\r\n  everyday life, society, and the workplace. In early grades, this might be as\r\n  simple as writing an addition equation to describe a situation. In middle\r\n  grades, a student might apply proportional reasoning to plan a school event\r\n  or analyze a problem in the community. By high school, a student might use\r\n  geometry to solve a design problem or use a function to describe how one\r\n  quantity of interest depends on another. Mathematically proficient students\r\n  who can apply what they know are comfortable making assumptions and\r\n  approximations to simplify a complicated situation, realizing that these may\r\n  need revision later. They are able to identify important quantities in a\r\n  practical situation and map their relationships using such tools as diagrams,\r\n  two-way tables, graphs, flowcharts and formulas. They can analyze those\r\n  relationships mathematically to draw conclusions. They routinely interpret\r\n  their mathematical results in the context of the situation and reflect on\r\n  whether the results make sense, possibly improving the model if it has not\r\n  served its purpose.<\/option><option value=\"MP.5\">MP.5: Use appropriate\r\n  tools strategically. Mathematically\r\n  proficient students consider the available tools when solving a mathematical\r\n  problem. These tools might include pencil and paper, concrete models, a\r\n  ruler, a protractor, a calculator, a spreadsheet, a computer algebra system,\r\n  a statistical package, or dynamic geometry software. Proficient students are\r\n  sufficiently familiar with tools appropriate for their grade or course to\r\n  make sound decisions about when each of these tools might be helpful,\r\n  recognizing both the insight to be gained and their limitations. For example,\r\n  mathematically proficient high school students analyze graphs of functions\r\n  and solutions generated using a graphing calculator. They detect possible\r\n  errors by strategically using estimation and other mathematical knowledge.\r\n  When making mathematical models, they know that technology can enable them to\r\n  visualize the results of varying assumptions, explore consequences, and\r\n  compare predictions with data. Mathematically proficient students at various\r\n  grade levels are able to identify relevant external mathematical resources,\r\n  such as digital content located on a website, and use them to pose or solve\r\n  problems. They are able to use technological tools to explore and deepen\r\n  their understanding of concepts.<\/option><option value=\"MP.6\">MP.6: Attend to\r\n  precision. Mathematically proficient\r\n  students try to communicate precisely to others. They try to use clear\r\n  definitions in discussion with others and in their own reasoning. They state\r\n  the meaning of the symbols they choose, including using the equal sign\r\n  consistently and appropriately. They are careful about specifying units of\r\n  measure, and labeling axes to clarify the correspondence with quantities in a\r\n  problem. They calculate accurately and efficiently, express numerical answers\r\n  with a degree of precision appropriate for the problem context. In the\r\n  elementary grades, students give carefully formulated explanations to each\r\n  other. By the time they reach high school they have learned to examine claims\r\n  and make explicit use of definitions.<\/option><option value=\"MP.7\">MP.7: Look for and make\r\n  use of structure. Mathematically\r\n  proficient students look closely to discern a pattern or structure. Young\r\n  students, for example, might notice that three and seven more is the same\r\n  amount as seven and three more, or they may sort a collection of shapes\r\n  according to how many sides the shapes have. Later, students will see 7 \u00d7 8\r\n  equals the well remembered 7 \u00d7 5 + 7 \u00d7 3, in preparation for learning about\r\n  the distributive property. In the expression &lt;i&gt;x&lt;\/i&gt;&lt;sup&gt;2&lt;\/sup&gt; + 9&lt;i&gt;x&lt;\/i&gt; + 14, older students can see the\r\n  14 as 2 \u00d7 7 and the 9 as 2 + 7. They recognize the significance of an\r\n  existing line in a geometric figure and can use the strategy of drawing an\r\n  auxiliary line for solving problems. They also can step back for an overview\r\n  and shift perspective. They can see complicated things, such as some\r\n  algebraic expressions, as single objects or as being composed of several\r\n  objects. For example, they can see 5 - 3(&lt;i&gt;x&lt;\/i&gt; \u2013 &lt;i&gt;y&lt;\/i&gt;)2\r\n  as 5 minus a positive number times a square and use that to realize that its\r\n  value cannot be more than 5 for any real numbers &lt;i&gt;x&lt;\/i&gt; and &lt;i&gt;y&lt;\/i&gt;.<\/option><option value=\"MP.8\">MP.8: Look for and express\r\n  regularity in repeated reasoning. Mathematically proficient students notice if calculations are\r\n  repeated, and look both for general methods and for shortcuts. Upper\r\n  elementary students might notice when dividing 25 by 11 that they are\r\n  repeating the same calculations over and over again, and conclude they have a\r\n  repeating decimal. By paying attention to the calculation of slope as they\r\n  repeatedly check whether points are on the line through (1, 2) with slope 3,\r\n  middle school students might abstract the equation (&lt;i&gt;y&lt;\/i&gt; \u2013 2)\/(&lt;i&gt;x&lt;\/i&gt;\r\n  \u2013 1) = 3. Noticing the regularity in the way terms cancel when expanding (&lt;i&gt;x&lt;\/i&gt; \u2013 1)(&lt;i&gt;x&lt;\/i&gt; + 1), (&lt;i&gt;x&lt;\/i&gt; \u2013 1)(&lt;i&gt;x&lt;\/i&gt;&lt;sup&gt;2&lt;\/sup&gt; + &lt;i&gt;x&lt;\/i&gt; +\r\n  1), and (&lt;i&gt;x&lt;\/i&gt; \u2013 1)(&lt;i&gt;x&lt;\/i&gt;&lt;sup&gt;3&lt;\/sup&gt; + &lt;i&gt;x&lt;\/i&gt;&lt;sup&gt;2&lt;\/sup&gt; + &lt;i&gt;x&lt;\/i&gt; +\r\n  1) might lead them to the general formula for the sum of a geometric series.\r\n  As they work to solve a problem, mathematically proficient students maintain\r\n  oversight of the process, while attending to the details. They continually\r\n  evaluate the reasonableness of their intermediate results.<\/option><\/select>";