PBS LearningMedia
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Pros
Vast library of rich digital resources are appropriate for a wide age and subject range.Cons
Not all pieces come with lesson plans.Bottom Line
Excellent free site has thousands of valuable, highquality digital resources for students and teachers.Free
A Basic account allows teachers to browse and save content, organize folders of saved content, and share collections of resources with students via email.
Dashboard features available with a Custom account include robust user management tools, comprehensive analytics tools, state standards alignment, content management tools including sharing within state/district/school, content personalization by grade/subject, and option to purchase full length video media packs
Ageappropriate resources are stimulating and inviting.
Learning is integral to the experience with indepth lessons that promote critical thinking skills.
Multidimensional resources offer demos, extensions, and access to student tracking information.
PBS LearningMedia provides Common Core and state standards alignment, student access, class accounts, a robust user management system, comprehensive analytics, and a content management system. There's so much content on the site that accessing all materials for a certain topic may seem a bit cumbersome, but it's well worth the navigation.
The professional development component is of particular note. A new Middle School Literacy piece is an excellent resource for all teachers of tweens. Other PD materials are available in a variety of areas, including how to support Englishlanguage learners, implementing literature circles, contemporary issues in the classroom, and phonemic assessment. Educators can access strategies, tools, and learning resources.
Read More Read LessPBS LearningMedia contains tens of thousands of digital resources aligned to Common Core standards and ready for classroom use. Topics cover English language arts, math, professional development, science and health, and social studies with resources for grades PreK through college. The selfpaced lessons are interactive, engage students, and include a variety of digital media. In most cases, students learn content by reading and writing. Resources range from short video and audio clips to interactives, lesson plans, and much more.
Teachers can search by grade level, subject, and standard. You can also browse more than 100 resource collections such as Middle School Literacy Initiative, High School Math, Cyberlearning on STEM, Art and Science of Growing Food, and Culture and Identity. In addition to more than 80 PBS member stations, content contributors include the National Archives, the Jim Henson Company, Annenberg Media, and the Library of Congress.
Read More Read LessGenerally, the videos embedded throughout the site are welldone and concise, and feature master educators. Videos showcasing teachermodeled best practices are truly excellent. Navigation is easy after an initial self orientation, yet it still requires you to go through several steps before you can access content.
Units range from slavery to adaptation to financial fitness and include objectives, lessons, related materials, and alignment to standards. The selfpaced computer resources are cool and relevant and can really hook kids. Students can work independently on a computer (or collaboratively with a peer) at a selfdirected pace, allowing the teacher to visit students individually and provide timely feedback.
Read More Read LessKey Standards Supported
Language  
L.K: Conventions of Standard English  
L.K.1  Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. 
L.K.2  Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. 
Vocabulary Acquisition and Use  
L.K.4  Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on kindergarten reading and content. 
L.K.5  With guidance and support from adults, explore word relationships and nuances in word meanings. 
L.K.6  Use words and phrases acquired through conversations, reading and being read to, and responding to texts. 
L.1: Conventions of Standard English  
L.1.2  Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. 
L.1.2a  Capitalize dates and names of people. 
L.1.2b  Use end punctuation for sentences. 
L.1.2c  Use commas in dates and to separate single words in a series. 
L.1.2d  Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words. 
L.1.2e  Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions. 
Vocabulary Acquisition and Use  
L.1.4  Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 1 reading and content, choosing flexibly from an array of strategies. 
L.1.4a  Use sentencelevel context as a clue to the meaning of a word or phrase. 
L.1.5  With guidance and support from adults, demonstrate understanding of figurative language, word relationships and nuances in word meanings. 
L.1.5a  Sort words into categories (e.g., colors, clothing) to gain a sense of the concepts the categories represent. 
L.1.5b  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). 
L.1.5d  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. 
L.2: Conventions of Standard English  
L.2.2b  Use commas in greetings and closings of letters. 
L.2.2c  Use an apostrophe to form contractions and frequently occurring possessives. 
L.2.2d  Generalize learned spelling patterns when writing words (e.g., cage → badge; boy → boil). 
Vocabulary Acquisition and Use  
L.2.4a  Use sentencelevel context as a clue to the meaning of a word or phrase. 
L.3: Conventions of Standard English  
L.3.1c  Use abstract nouns (e.g., childhood). 
L.3.1e  Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses. 
L.3.1g  Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified. 
L.3.2e  Use conventional spelling for highfrequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). 
L.3.2f  Use spelling patterns and generalizations (e.g., word families, positionbased spellings, syllable patterns, ending rules, meaningful word parts) in writing words. 
L3.2c  Use commas and quotation marks in dialogue. 
Vocabulary Acquisition and Use  
L.3.4a  Use sentencelevel context as a clue to the meaning of a word or phrase. 
L.3.5a  Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps). 
L.5: Vocabulary acquisition and Use  
L.5.4a  Use context (e.g., cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase. 
L.5.4b  Use common, gradeappropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis). 
L.5.5a  Interpret figurative language, including similes and metaphors, in context. 
L.5.5c  Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words. 
L.6: Conventions of Standard English  
L.6.2  Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. 
Vocabulary Acquisition and Use  
L.6.4  Determine or clarify the meaning of unknown and multiplemeaning words and phrases based on grade 6 reading and content, choosing flexibly from a range of strategies. 
L.6.5  Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. 
L.6.6  Acquire and use accurately gradeappropriate general academic and domainspecific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. 
L.7: Conventions of Standard English  
L.7.2b  Spell correctly. 
Vocabulary Acquisition and Use  
L.7.4a  Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. 
L.7.4b  Use common, gradeappropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., belligerent, bellicose, rebel). 
L.7.4d  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). 
L.7.5b  Use the relationship between particular words (e.g., synonym/antonym, analogy) to better understand each of the words. 
L.7.6  Acquire and use accurately gradeappropriate general academic and domainspecific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. 
L.8: Conventions of Standard English  
L.8.1b  Form and use verbs in the active and passive voice. 
L.8.1c  Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood. 
L.8.2c  Spell correctly. 
Vocabulary Acquisition and Use  
L.8.4a  Use context (e.g., the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. 
L.8.4b  Use common, gradeappropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede). 
L.8.4d  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). 
L.8.5b  Use the relationship between particular words to better understand each of the words. 
L.8.6  Acquire and use accurately gradeappropriate general academic and domainspecific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. 
L.910: Conventions of Standard English  
L.910.2c  Spell correctly. 
Vocabulary Acquisition and Use  
L.910.4a  Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. 
L.910.4d  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). 
L.1112: Conventions of Standard English  
L.1112.2.b  Spell correctly. 
Knowledge of Language  
L.1112.3a  Vary syntax for effect, consulting references (e.g., Tufte’s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading. 
Vocabulary Acquisition and Use  
L.1112.4a  Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. 
L.1112.4d  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). 
Reading Foundational Skills  
RF.1: Fluency  
RF.1.4a  Read onlevel text with purpose and understanding. 
RF.1.4b  Read onlevel text orally with accuracy, appropriate rate, and expression on successive readings. 
RF.1.4c  Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
Phonics and Word recognition  
RF.1.3a  Know the spellingsound correspondences for common consonant digraphs. 
RF.1.3b  Decode regularly spelled onesyllable words. 
RF.1.3c  Know final e and common vowel team conventions for representing long vowel sounds. 
RF.1.3f  Read words with inflectional endings. 
Phonological awareness  
RF.1.2a  Distinguish long from short vowel sounds in spoken singlesyllable words. 
RF.1.2b  Orally produce singlesyllable words by blending sounds (phonemes), including consonant blends. 
RF.2: Fluency  
RF.2.4  Read with sufficient accuracy and fluency to support comprehension. 
RF.2.4a  Read onlevel text with purpose and understanding. 
RF.2.4c  Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
Phonics and Word recognition  
RF.2.3a  Distinguish long and short vowels when reading regularly spelled onesyllable words. 
RF.2.3b  Know spellingsound correspondences for additional common vowel teams. 
RF.2.3d  Decode words with common prefixes and suffixes. 
RF.3: Fluency  
RF.3.4a  Read onlevel text with purpose and understanding. 
RF.3.4b  Read onlevel prose and poetry orally with accuracy, appropriate rate, and expression on successive readings 
RF.3.4c  Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
Phonics and Word recognition  
RF.3.3a  Identify and know the meaning of the most common prefixes and derivational suffixes. 
RF.4: Fluency  
RF.4.4a  Read onlevel text with purpose and understanding. 
RF.4.4b  Read onlevel prose and poetry orally with accuracy, appropriate rate, and expression on successive readings. 
RF.4.4c  Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
RF.5: Fluency  
RF.5.4a  Read onlevel text with purpose and understanding. 
RF.5.4b  Read onlevel prose and poetry orally with accuracy, appropriate rate, and expression on successive readings. 
RF.5.4c  Use context to confirm or selfcorrect word recognition and understanding, rereading as necessary. 
RF.K: Phonics and Word recognition  
RF.K.3  Know and apply gradelevel phonics and word analysis skills in decoding words. 
Phonological awareness  
RF.K.2  Demonstrate understanding of spoken words, syllables, and sounds (phonemes). 
Print Concepts  
RF.K.1  Demonstrate understanding of the organization and basic features of print. 
Reading History/Social Studies  
RH.68: Craft and Structure  
RH.68.4  Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies. 
RH.68.6  Identify aspects of a text that reveal an author’s point of view or purpose (e.g., loaded language, inclusion or avoidance of particular facts). 
Integration of Knowledge and Ideas  
RH.68.7  Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts. 
RH.68.8  Distinguish among fact, opinion, and reasoned judgment in a text. 
RH.68.9  Analyze the relationship between a primary and secondary source on the same topic. 
Key Ideas and Details  
RH.68.1  Cite specific textual evidence to support analysis of primary and secondary sources. 
RH.68.2  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. 
Range of Reading and Level of Text Complexity  
RH.68.10  By the end of grade 8, read and comprehend history/social studies texts in the grades 6–8 text complexity band independently and proficiently. 
RH.910: Craft and Structure  
RH.910.4  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. 
Integration of Knowledge and Ideas  
RH.910.8  Assess the extent to which the reasoning and evidence in a text support the author’s claims. 
RH.910.9  Compare and contrast treatments of the same topic in several primary and secondary sources. 
Key Ideas and Details  
RH.910.2  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. 
RH.910.3  Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them. 
Range of Reading and Level of Text Complexity  
RH.910.10  By the end of grade 10, read and comprehend history/social studies texts in the grades 9–10 text complexity band independently and proficiently. 
RH.1112: Integration of Knowledge and Ideas  
RH.1112.7  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. 
RH.1112.8  Evaluate an author’s premises, claims, and evidence by corroborating or challenging them with other information. 
Key Ideas and Details  
RH.1112.1  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. 
RH.1112.2  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. 
RH.1112.3  Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain. 
Range of Reading and Level of Text Complexity  
RH.1112.10  By the end of grade 12, read and comprehend history/social studies texts in the grades 11–CCR text complexity band independently and proficiently. 
Reading Informational  
RI.K: Craft and Structure  
RI.K.4  With prompting and support, ask and answer questions about unknown words in a text. 
RI.K.6  Name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text. 
Integration of Knowledge and Ideas  
RI.K.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). 
RI.K.8  With prompting and support, identify the reasons an author gives to support points in a text. 
RI.K.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). 
Key Ideas and Details  
RI.K.1  With prompting and support, ask and answer questions about key details in a text. 
RI.K.2  With prompting and support, identify the main topic and retell key details of a text. 
RI.K.3  With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text. 
Range of Reading and Level of Text Complexity  
RI.K.10  Actively engage in group reading activities with purpose and understanding. 
RI.1: Craft and Structure  
RI.1.4  Ask and answer questions to help determine or clarify the meaning of words and phrases in a text. 
RI.1.6  Distinguish between information provided by pictures or other illustrations and information provided by the words in a text. 
Integration of Knowledge and Ideas  
RI.1.7  Use the illustrations and details in a text to describe its key ideas. 
RI.1.8  Identify the reasons an author gives to support points in a text. 
RI.1.9  Identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures). 
Key Ideas and Details  
RI.1.1  Ask and answer questions about key details in a text. 
RI.1.2  Identify the main topic and retell key details of a text. 
RI.1.3  Describe the connection between two individuals, events, ideas, or pieces of information in a text. 
Range of Reading and Level of Text Complexity  
RI.1.10  With prompting and support, read informational texts appropriately complex for grade 1. 
RI.2: Craft and Structure  
RI.2.4  Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area. 
Integration of Knowledge and Ideas  
RI.2.7  Explain how specific images (e.g., a diagram showing how a machine works) contribute to and clarify a text. 
Key Ideas and Details  
RI.2.1  Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. 
Range of Reading and Level of Text Complexity  
RI.2.10  By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RI.3: Craft and Structure  
RI.3.4  Determine the meaning of general academic and domainspecific words and phrases in a text relevant to a grade 3 topic or subject area. 
RI.3.6  Distinguish their own point of view from that of the author of a text. 
Integration of Knowledge and Ideas  
RI.3.7  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). 
RI.3.8  Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence). 
Key Ideas and Details  
RI.3.1  Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. 
RI.3.2  Determine the main idea of a text; recount the key details and explain how they support the main idea. 
RI.3.3  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. 
Range of Reading and Level of Text Complexity  
RI.3.10  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 2–3 text complexity band independently and proficiently. 
RI.4: Craft and Structure  
RI.4.4  Determine the meaning of general academic and domainspecific words or phrases in a text relevant to a grade 4 topic or subject area. 
RI.4.5  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. 
RI.4.6  Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided. 
Integration of Knowledge and Ideas  
RI.4.7  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. 
RI.4.9  Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably. 
Key Ideas and Details  
RI.4.1  Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. 
RI.4.2  Determine the main idea of a text and explain how it is supported by key details; summarize the text. 
RI.4.3  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. 
Range of Reading and Level of Text Complexity  
RI.4.10  By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RI.5: Craft and Structure  
RI.5.4  Determine the meaning of general academic and domainspecific words and phrases in a text relevant to a grade 5 topic or subject area. 
RI.5.5  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. 
RI.5.6  Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent. 
Integration of Knowledge and Ideas  
RI.5.7  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. 
RI.5.8  Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s). 
RI.5.9  Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. 
Key Ideas and Details  
RI.5.2  Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text. 
RI.5.3  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. 
Range of Reading and Level of Text Complexity  
RI.5.10  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 4–5 text complexity band independently and proficiently. 
RI.6: Craft and Structure  
RI.6.4  Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. 
RI.6.6  Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text. 
Integration of Knowledge and Ideas  
RI.6.7  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. 
RI.6.8  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. 
RI.6.9  Compare and contrast one author’s presentation of events with that of another (e.g., a memoir written by and a biography on the same person). 
Key Ideas and Details  
RI.6.1  Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.6.2  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. 
RI.6.3  Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes). 
Range of Reading and Level of Text Complexity  
RI.6.10  By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RI.7: Craft and Structure  
RI.7.4  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. 
RI.7.6  Determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others. 
Integration of Knowledge and Ideas  
RI.7.7  Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium’s portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words). 
RI.7.8  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. 
RI.7.9  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. 
Key Ideas and Details  
RI.7.1  Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.7.2  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. 
RI.7.3  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). 
Range of Reading and Level of Text Complexity  
RI.7.10  By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RI.8: Craft and Structure  
RI.8.4  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. 
RI.8.5  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. 
RI.8.6  Determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. 
Integration of Knowledge and Ideas  
RI.8.7  Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. 
RI.8.8  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. 
RI.8.9  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. 
Key Ideas and Details  
RI.8.1  Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.8.2  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. 
RI.8.3  Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories). 
Range of Reading and Level of Text Complexity  
RI.8.10  By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6–8 text complexity band independently and proficiently. 
RI.910: Craft and Structure  
RI.910.4  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). 
RI.910.5  Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter). 
RI.910.6  Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose. 
Integration of Knowledge and Ideas  
RI.910.7  Analyze various accounts of a subject told in different mediums (e.g., a person’s life story in both print and multimedia), determining which details are emphasized in each account. 
Key Ideas and Details  
RI.910.1  Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RI.910.2  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. 
RI.910.3  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. 
Range of Reading and Level of Text Complexity  
RI.910.10  By the end of grade 9, read and comprehend literary nonfiction in the grades 9–10 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RI.1112: Craft and Structure  
RI.1112.6  Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness or beauty of the text. 
Integration of Knowledge and Ideas  
RI.1112.7  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. 
RI.1112.8  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). 
Key Ideas and Details  
RI.1112.1  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. 
RI.1112.2  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. 
RI.1112.3  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. 
Range of Reading and Level of Text Complexity  
RI.1112.10  By the end of grade 11, read and comprehend literary nonfiction in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. 
Reading Literature  
RL.K: Craft and Structure  
RL.K.4  Ask and answer questions about unknown words in a text. 
RL.K.6  With prompting and support, name the author and illustrator of a story and define the role of each in telling the story. 
Integration of Knowledge and Ideas  
RL.K.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). 
RL.K.9  With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories. 
Key Ideas and Details  
RL.K.1  With prompting and support, ask and answer questions about key details in a text. 
RL.K.2  With prompting and support, retell familiar stories, including key details. 
RL.K.3  With prompting and support, identify characters, settings, and major events in a story. 
Range of Reading and Level of Text Complexity  
RL.K.10  Actively engage in group reading activities with purpose and understanding. 
RL.1: Craft and Structure  
RL.1.4  Identify words and phrases in stories or poems that suggest feelings or appeal to the senses. 
RL.1.5  Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types. 
RL.1.6  Identify who is telling the story at various points in a text. 
Integration of Knowledge and Ideas  
RL.1.7  Use illustrations and details in a story to describe its characters, setting, or events. 
Rl.1.9  Compare and contrast the adventures and experiences of characters in stories. 
Key Ideas and Details  
RL.1.1  Ask and answer questions about key details in a text. 
RL.1.2  Retell stories, including key details, and demonstrate understanding of their central message or lesson. 
RL.1.3  Describe characters, settings, and major events in a story, using key details. 
Range of Reading and Level of Text Complexity  
RL.1.10  With prompting and support, read prose and poetry of appropriate complexity for grade 1. 
RL.2: Craft and Structure  
RL.2.4  Describe how words and phrases (e.g., regular beats, alliteration, rhymes, repeated lines) supply rhythm and meaning in a story, poem, or song. 
RL.2.5  Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action. 
Integration of Knowledge and Ideas  
RL.2.7  Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot. 
RL.2.9  Compare and contrast two or more versions of the same story (e.g., Cinderella stories) by different authors or from different cultures. 
Key Ideas and Details  
RL.2.2  Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral. 
RL.2.3  Describe how characters in a story respond to major events and challenges. 
Range of Reading and Level of Text Complexity  
RL.2.10  By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RL.3: Craft and Structure  
RL.3.4  Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliteral language. 
RL.3.5  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. 
RL.3.6  Distinguish their own point of view from that of the narrator or those of the characters. 
Integration of Knowledge and Ideas  
RL.3.7  Explain how specific aspects of a text’s illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting). 
RL.3.9  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). 
Key Ideas and Details  
RL.3.1  Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. 
RL.3.2  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. 
RL.3.3  Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. 
Range of Reading and Complexity of Text  
RL.3.10  By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently. 
RL.4: Craft and Structure  
RL.4.5  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. 
RL.4.6  Compare and contrast the point of view from which different stories are narrated, including the difference between first and thirdperson narrations. 
Integration of Knowledge and Ideas  
RL.4.7  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. 
RL.4.9  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. 
Key Ideas and Details  
RL.4.1  Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. 
RL.4.2  Determine a theme of a story, drama, or poem from details in the text; summarize the text. 
RL.4.3  Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character’s thoughts, words, or actions). 
Range of Reading and Complexity of Text  
RL.4.10  By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RL.5: Craft and Structure  
RL.5.4  Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes. 
RL.5.5  Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem. 
RL.5.6  Describe how a narrator’s or speaker’s point of view influences how events are described. 
Integration of Knowledge and Ideas  
RL.5.7  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). 
RL.5.9  Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics. 
Key Ideas and Details  
RL.5.2  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. 
RL.5.3  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). 
Range of Reading and Complexity of Text  
RL.5.10  By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently. 
RL.6: Craft and Structure  
RL.6.4  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. 
RL.6.5  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. 
RL.6.6  Explain how an author develops the point of view of the narrator or speaker in a text. 
Integration of Knowledge and Ideas  
RL.6.7  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 “see” and “hear” when reading the text to what they perceive when they listen or watch. 
RL.6.9  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. 
Key Ideas and Details  
RL.6.1  Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.6.3  Describe how a particular story’s or drama’s plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution. 
Range of Reading and Level of Text Complexity  
RL.6.10  By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RL.7: Craft and Structure  
RL.7.4  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. 
RL.7.5  Analyze how a drama’s or poem’s form or structure (e.g., soliloquy, sonnet) contributes to its meaning. 
RL.7.6  Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. 
Integration of Knowledge and Ideas  
RL.7.7  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). 
RL.7.9  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. 
Key Ideas and Details  
RL.7.1  Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.7.3  Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot). 
Range of Reading and Level of Text Complexity  
RL.7.10  By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. 
RL.8: Craft and Structure  
RL.8.4  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. 
RL.8.5  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. 
Integration of Knowledge and Ideas  
RL.8.7  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. 
Key Ideas and Details  
RL.8.1  Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.8.2  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. 
RL.8.3  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. 
Range of Reading and Level of Text Complexity  
RL.8.10  By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6–8 text complexity band independently and proficiently. 
RL.910: Craft and Structure  
RL.910.4  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). 
RL.910.5  Analyze how an author’s 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. 
RL.910.6  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. 
Integration of Knowledge and Ideas  
RL.910.7  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’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus). 
RL.910.9  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). 
Key Ideas and Details  
RL.910.1  Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. 
RL.910.2  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. 
RL.910.3  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. 
RL.1112: Craft and Structure  
RL.1112.4  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.) 
RL.1112.5  Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact. 
RL.1112.6  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). 
Integration of Knowledge and Ideas  
RL.1112.7  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.) 
Key Ideas and Details  
RL.1112.1  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. 
RL.1112.2  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. 
RL.1112.3  Analyze the impact of the author’s choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed). 
Range of Reading and Level of Text Complexity  
RL.1112.10  By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11–CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. 
Reading Science/Technical  
RST.68: Craft and Structure  
RST.68.4  Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. 
Integration of Knowledge and Ideas  
RST.68.9  Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic. 
Key Ideas and Details  
RST.68.2  Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions. 
Range of Reading and Level of Text Complexity  
RST.68.10  By the end of grade 8, read and comprehend science/technical texts in the grades 6–8 text complexity band independently and proficiently. 
RST.910: Craft and Structure  
RST.910.4  Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. 
Key Ideas and Details  
RST.910.1  Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions. 
RST.910.2  Determine the central ideas or conclusions of a text; trace the text’s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text. 
RST.1112: Craft and Structure  
RST.1112.4  Determine the meaning of symbols, key terms, and other domainspecific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics. 
Integration of Knowledge and Ideas  
RST.1112.7  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. 
Range of Reading and Level of Text Complexity  
RST.1112.10  By the end of grade 12, read and comprehend science/technical texts in the grades 11–12 text complexity band independently and proficiently. 
Speaking & Listening  
SL.K: Continue a conversation through multiple exchanges.  
SL.K.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. 
Presentation of Knowledge and Ideas  
SL.K.4  Describe familiar people, places, things, and events and, with prompting and support, provide additional detail. 
SL.K.5  Add drawings or other visual displays to descriptions as desired to provide additional detail. 
SL.1: Comprehension and Collaboration  
SL.1.1  Participate in collaborative conversations with diverse partners about grade 1 topics and texts with peers and adults in small and larger groups. 
SL.1.1c  Ask questions to clear up any confusion about the topics and texts under discussion. 
SL.1.2  Ask and answer questions about key details in a text read aloud or information presented orally or through other media. 
Presentation of Knowledge and Ideas  
SL.1.4  Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly. 
SL.1.5  Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings. 
SL.2: Presentation of Knowledge and Ideas  
SL.2.4  Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences. 
SL.3: Comprehension and Collaboration  
SL.3.1d  Explain their own ideas and understanding in light of the discussion. 
SL.3.2  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. 
SL.3.3  Ask and answer questions about information from a speaker, offering appropriate elaboration and detail. 
Presentation of Knowledge and Ideas  
SL.3.4  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. 
SL.5: Comprehension and Collaboration  
SL.5.1b  Follow agreedupon rules for discussions and carry out assigned roles. 
SL.5.1c  Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. 
SL.5.1d  Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. 
SL.5.2  Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. 
SL.5.3  Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. 
Presentation of Knowledge and Ideas  
SL.5.5  Include multimedia components (e.g., graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes. 
SL.6: Comprehension and Collaboration  
SL.6.1b  Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed. 
SL.6.1c  Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion. 
SL.6.1d  Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing. 
SL.8: Comprehension and Collaboration  
SL.8.2  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. 
SL.910: Comprehension and Collaboration  
SL.910.1a  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, wellreasoned exchange of ideas. 
SL.910.1b  Work with peers to set rules for collegial discussions and decisionmaking (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. 
SL.910.1c  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. 
SL.910.1d  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. 
SL.910.2  Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. 
Presentation of Knowledge and Ideas  
SL.910.5  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. 
SL.1112: Comprehension and Collaboration  
SL.1112.1a  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, wellreasoned exchange of ideas. 
SL.1112.1b  Work with peers to promote civil, democratic discussions and decisionmaking, set clear goals and deadlines, and establish individual roles as needed. 
SL.1112.1c  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. 
SL.1112.1d  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. 
Writing  
W.K: Production and Distribution of Writing  
W.K.5  With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed. 
Research to Build and Present Knowledge  
W.K.7  Participate in shared research and writing projects (e.g., explore a number of books by a favorite author and express opinions about them). 
W.K.8  With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question. 
Text Types and Purposes  
W.K.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...). 
W.K.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. 
W.K.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. 
W.1: Production and Distribution of Writing  
W.1.5  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. 
Research to Build and Present Knowledge  
W.1.7  Participate in shared research and writing projects (e.g., explore a number of “howto” books on a given topic and use them to write a sequence of instructions). 
W.1.8  With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question. 
W.2: Research to Build and Present Knowledge  
W.2.7  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). 
W.2.8  Recall information from experiences or gather information from provided sources to answer a question. 
Text Types and Purposes  
W.2.1  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. 
W.2.3  Write narratives in which they recount a wellelaborated 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. 
W.3: Production and Distribution of Writing  
W.3.4  With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.3.5  With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. 
Range of Writing  
W.3.10  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 disciplinespecific tasks, purposes, and audiences. 
Research to Build and Present Knowledge  
W.3.7  Conduct short research projects that build knowledge about a topic. 
W.3.8  Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories. 
Text Types and Purposes  
W.3.1a  Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons. 
W.3.1b  Provide reasons that support the opinion. 
W.3.1d  Provide a concluding statement or section. 
W.3.2a  Introduce a topic and group related information together; include illustrations when useful to aiding comprehension. 
W.3.2b  Develop the topic with facts, definitions, and details. 
W.3.3a  Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally. 
W.3.3b  Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations. 
W.4: Production and Distribution of Writing  
W.4.4  Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.4.5  With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. 
W.4.6  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. 
Range of Writing  
W.4.10  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 disciplinespecific tasks, purposes, and audiences. 
Research to Build and Present Knowledge  
W.4.7  Conduct short research projects that build knowledge through investigation of different aspects of a topic. 
W.4.8  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. 
W.4.9a  Apply grade 4 Reading standards to literature (e.g., “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character’s thoughts, words, or actions].”). 
W.4.9b  Apply grade 4 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text”). 
Text Types and Purposes  
W.4.1a  Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose. 
W.4.1b  Provide reasons that are supported by facts and details. 
W.4.1d  Provide a concluding statement or section related to the opinion presented. 
W.4.2b  Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. 
W.4.2d  d.Use precise language and domainspecific vocabulary to inform about or explain the topic. 
W.4.3a  Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. 
W.4.3b  Use dialogue and description to develop experiences and events or show the responses of characters to situations. 
W.5: Production and Distribution of Writing  
W.5.4  Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.5.5  With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. 
W.5.6  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. 
Range of Writing  
W.5.10  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 disciplinespecific tasks, purposes, and audiences. 
Research to Build and Present Knowledge  
W.5.7  Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. 
W.5.8  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. 
W.5.9a  Apply grade 5 Reading standards to literature (e.g., “Compare 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]”). 
W.5.9b  Apply grade 5 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]”). 
Text Types and Purposes  
W.5.1a  Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose. 
W.5.1b  Provide logically ordered reasons that are supported by facts and details. 
W.5.1d  Provide a concluding statement or section related to the opinion presented. 
W.5.2b  Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. 
W.5.2d  Use precise language and domainspecific vocabulary to inform about or explain the topic. 
W.5.3a  Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. 
W.5.3b  Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations. 
W.5.3d  Use concrete words and phrases and sensory details to convey experiences and events precisely. 
W.6: Production and Distribution of Writing  
W.6.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.6.5  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. 
W.6.6  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. 
Range of Writing  
W.6.10  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 disciplinespecific tasks, purposes, and 
Research to Build and Present Knowledge  
W.6.7  Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate. 
W.6.9  Draw evidence from literary or informational texts to support analysis, reflection, and research. 
W.6.9a  Apply grade 6 Reading standards to literature (e.g., “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”). 
W.6.9b  Apply grade 6 Reading standards to literary nonfiction (e.g., “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”). 
Text Types and Purposes  
W.6.1a  Introduce claim(s) and organize the reasons and evidence clearly. 
W.6.1b  Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text. 
W.6.1c  Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons. 
W.6.1d  Establish and maintain a formal style. 
W.6.1e  Provide a concluding statement or section that follows from the argument presented. 
W.6.2a  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. 
W.6.2b  Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. 
W.6.2d  Use precise language and domainspecific vocabulary to inform about or explain the topic. 
W.6.2f  Provide a concluding statement or section that follows from the information or explanation presented. 
W.6.3a  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. 
W.6.3b  Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters. 
W.6.3d  Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events. 
W.7: Production and Distribution of Writing  
W.7.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.7.5  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. 
W.7.6  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. 
Range of Writing  
W.7.10  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 disciplinespecific tasks, purposes, and audiences. 
Research to Build and Present Knowledge  
W.7.7  Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation. 
W.7.9b  Apply grade 7 Reading standards to literary nonfiction (e.g. “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”). 
Text Types and Purposes  
W.7.1a  Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically. 
W.7.1b  Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. 
W.7.1c  Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence. 
W.7.1d  Establish and maintain a formal style. 
W.7.1e  Provide a concluding statement or section that follows from and supports the argument presented. 
W.7.2a  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. 
W.7.2b  Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. 
W.7.2d  Use precise language and domainspecific vocabulary to inform about or explain the topic. 
W.7.3a  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. 
W.7.3b  Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters. 
W.7.3c  Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another. 
W.7.3d  Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. 
W.8: Production and Distribution of Writing  
W.8.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.8.5  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. 
W.8.6  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. 
Range of Writing  
W.8.10  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 disciplinespecific tasks, purposes, and audiences. 
Research to Build and Present Knowledge  
W.8.7  Conduct short research projects to answer a question (including a selfgenerated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. 
Text Types and Purposes  
W.8.1a  Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. 
W.8.1b  Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. 
W.8.1c  Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. 
W.8.1d  Establish and maintain a formal style. 
W.8.1e  Provide a concluding statement or section that follows from and supports the argument presented. 
W.8.2a  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. 
W.8.2b  Develop the topic with relevant, wellchosen facts, definitions, concrete details, quotations, or other information and examples. 
W.8.2d  Use precise language and domainspecific vocabulary to inform about or explain the topic. 
W.8.3a  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. 
W.8.3b  Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters. 
W.8.3c  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. 
W.8.3d  Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. 
W.910: Production and Distribution of Writing  
W.910.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.910.5  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. 
W.910.6  Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. 
Range of Writing  
W.910.10  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. 
Research to Build and Present Knowledge  
W.910.7  Conduct short as well as more sustained research projects to answer a question (including a selfgenerated 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. 
W.910.8  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. 
W.910.9  Draw evidence from literary or informational texts to support analysis, reflection, and research. 
Text Types and Purposes  
W.910.1b  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’s knowledge level and concerns. 
W.910.1c  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. 
W.910.1d  Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. 
W.910.1e  Provide a concluding statement or section that follows from and supports the argument presented. 
W.910.2a  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. 
W.910.2b  Develop the topic with wellchosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. 
W.910.2d  Use precise language and domainspecific vocabulary to manage the complexity of the topic. 
W.910.2e  Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. 
W.910.3a  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. 
W.910.3b  Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. 
W.910.3d  Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. 
W.910.3e  Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. 
W.1112: Production and Distribution of Writing  
W.1112.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Gradespecific expectations for writing types are defined in standards 1–3 above.) 
W.1112.5  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. 
Range of Writing  
W.1112.10  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 
Research to Build and Present Knowledge  
W.1112.7  Conduct short as well as more sustained research projects to answer a question (including a selfgenerated 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. 
W.1112.8  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. 
Text Types and Purposes  
W.1112.1a  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. 
W.1112.1b  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’s knowledge level, concerns, values, and possible biases. 
W.1112.1d  Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. 
W.1112.1e  Provide a concluding statement or section that follows from and supports the argument presented. 
W.1112.2a  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. 
W.1112.2b  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’s knowledge of the topic. 
W.1112.2d  Use precise language, domainspecific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic. 
W.1112.2e  Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. 
W.1112.3a  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. 
W.1112.3b  Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. 
W.1112.3d  Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. 
W.1112.3e  Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. 
Writing HS/S/T  
WHST.68: Production and Distribution of Writing  
WHST.68.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 
WHST.68.6  Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently. 
Research to Build and Present Knowledge  
WHST.68.7  Conduct short research projects to answer a question (including a selfgenerated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. 
WHST.68.9  Draw evidence from informational texts to support analysis reflection, and research. 
WHST.910: Production and Distribution of Writing  
WHST.910.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 
Range of Writing  
WHST.910.10  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 disciplinespecific tasks, purposes, and audiences. 
Research to Build and Present Knowledge  
WHST.910.7  Conduct short as well as more sustained research projects to answer a question (including a selfgenerated 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. 
WHST.910.9  Draw evidence from informational texts to support analysis, reflection, and research. 
Text Types and Purposes  
WHST.910.2a  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. 
WHST.910.2b  Develop the topic with wellchosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. 
WHST.910.2e  Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. 
WHST.910.2f  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). 
WHST.1112: Production and Distribution of Writing  
WHST.1112.4  Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 
Research to Build and Present Knowledge  
WHST.1112.7  Conduct short as well as more sustained research projects to answer a question (including a selfgenerated 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. 
WHST.1112.9  Draw evidence from informational texts to support analysis, reflection, and research. 
Text Types and Purposes  
WHST.1112.2a  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. 
WHST.1112.2b  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’s knowledge of the topic. 
WHST.1112.2d  Use precise language, domainspecific 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. 
WHST.1112.2e  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). 
Circles  
HSG.C: Find Arc Lengths And Areas Of Sectors Of Circles  
HSG.C.5  Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. 
Understand And Apply Theorems About Circles  
HSG.C.2  Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. 
Conditional Probability And The Rules Of Probability  
HSS.CP: Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability Model  
HSS.CP.9  (+) Use permutations and combinations to compute probabilities of compound events and solve problems. 
Congruence  
HSG.CO: Experiment With Transformations In The Plane  
HSG.CO.1  Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 
HSG.CO.2  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). 
HSG.CO.4  Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 
HSG.CO.5  Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 
Prove Geometric Theorems  
HSG.CO.10  Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. 
HSG.CO.11  Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. 
HSG.CO.9  Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. 
Understand Congruence In Terms Of Rigid Motions  
HSG.CO.6  Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. 
HSG.CO.7  Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. 
Counting And Cardinality  
K.CC: Count To Tell The Number Of Objects.  
K.CC.4  Understand the relationship between numbers and quantities; connect counting to cardinality. 
K.CC.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. 
Know Number Names And The Count Sequence.  
K.CC.1  Count to 100 by ones and by tens. 
K.CC.3  Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). 
Creating Equations  
HSA.CED: Create Equations That Describe Numbers Or Relationships  
HSA.CED.1  Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 
HSA.CED.2  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 
HSA.CED.4  Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. 
Expressing Geometric Properties With Equations  
HSG.GPE: Translate Between The Geometric Description And The Equation For A Conic Section  
HSG.GPE.2  Derive the equation of a parabola given a focus and directrix. 
Use Coordinates To Prove Simple Geometric Theorems Algebraically  
HSG.GPE.6  Find the point on a directed line segment between two given points that partitions the segment in a given ratio. 
Expressions And Equations  
6.EE: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions.  
6.EE.1  Write and evaluate numerical expressions involving wholenumber exponents. 
6.EE.2  Write, read, and evaluate expressions in which letters stand for numbers. 
6.EE.2.a  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. 
6.EE.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. 
6.EE.2.c  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld 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). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. 
6.EE.3  Apply the properties of operations to generate equivalent expressions. 
Reason About And Solve OneVariable Equations And Inequalities.  
6.EE.5  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. 
6.EE.6  Use variables to represent numbers and write expressions when solving a realworld 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. 
Represent And Analyze Quantitative Relationships Between Dependent And Independent Variables.  
6.EE.9  Use variables to represent two quantities in a realworld 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. 
8.EE: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations.  
8.EE.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). 
8.EE.8.b  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. 
8.EE.8.c  Solve realworld 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. 
Understand The Connections Between Proportional Relationships, Lines, And Linear Equations.  
8.EE.5  Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed. 
Work With Radicals And Integer Exponents.  
8.EE.4  Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 
Functions  
8.F: Define, Evaluate, And Compare Functions.  
8.F.1  Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1 
8.F.3  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 
Use Functions To Model Relationships Between Quantities.  
8.F.4  Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 
8.F.5  Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 
Geometric Measurement And Dimension  
HSG.GMD: Explain Volume Formulas And Use Them To Solve Problems  
HSG.GMD.1  Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. 
HSG.GMD.3  Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★ 
Geometry  
1.G: Reason With Shapes And Their Attributes.  
1.G.2  Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional 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.4 
1.G.3  Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 
2.G: Reason With Shapes And Their Attributes.  
2.G.1  Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 
3.G: Reason With Shapes And Their Attributes.  
3.G.1  Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 
4.G: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles.  
4.G.1  Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 
4.G.2  Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 
4.G.3  Recognize a line of symmetry for a twodimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry. 
5.G: Classify TwoDimensional Figures Into Categories Based On Their Properties.  
5.G.3  Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. 
Graph Points On The Coordinate Plane To Solve RealWorld And Mathematical Problems.  
5.G.1  Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line 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., xaxis and xcoordinate, yaxis and ycoordinate). 
5.G.2  Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 
6.G: Solve RealWorld And Mathematical Problems Involving Area, Surface Area, And Volume.  
6.G.1  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld and mathematical problems. 
6.G.2  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 
6.G.3  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. 
6.G.4  Represent threedimensional 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 realworld and mathematical problems. 
7.G: Draw, Construct, And Describe Geometrical Figures And Describe The Relationships Between Them.  
7.G.2  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. 
7.G.3  Describe the twodimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 
Solve RealLife And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume.  
7.G.4  Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 
7.G.5  Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. 
7.G.6  Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 
8.G: Solve RealWorld And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres.  
8.G.9  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. 
Understand And Apply The Pythagorean Theorem.  
8.G.7  Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. 
8.G.8  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 
Understand Congruence And Similarity Using Physical Models, Trans Parencies, Or Geometry Software.  
8.G.1.a  Lines are taken to lines, and line segments to line segments of the same length. 
8.G.1.b  Angles are taken to angles of the same measure. 
8.G.1.c  Parallel lines are taken to parallel lines. 
8.G.2  Understand that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 
8.G.4  Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. 
K.G: Analyze, Compare, Create, And Compose Shapes.  
K.G.4  Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). 
K.G.5  Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. 
K.G.6  Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” 
Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres).  
K.G.1  Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. 
K.G.3  Identify shapes as twodimensional (lying in a plane, “flat”) or three dimensional (“solid”). 
Interpreting Functions  
HSF.IF: Interpret Functions That Arise In Applications In Terms Of The Context  
HSF.IF.5  Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★ 
HSF.IF.6  Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ 
Linear, Quadratic, And Exponential Models  
HSF.LE: Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems  
HSF.LE.2  Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). 
Making Inferences And Justifying Conclusions  
HSS.IC: Understand And Evaluate Random Processes Underlying Statistical Experiments  
HSS.IC.1  Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 
Measurement And Data  
1.MD: Represent And Interpret Data.  
1.MD.4  Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 
Tell And Write Time.  
1.MD.3  Tell and write time in hours and halfhours using analog and digital clocks. 
2.MD: Measure And Estimate Lengths In Standard Units.  
2.MD.1  Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 
2.MD.2  Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 
2.MD.3  Estimate lengths using units of inches, feet, centimeters, and meters. 
2.MD.4  Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 
Represent And Interpret Data.  
2.MD.10  Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple put together, takeapart, and compare problems4 using information presented in a bar graph. 
2.MD.9  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 line plot, where the horizontal scale is marked off in wholenumber units. 
Work With Time And Money.  
2.MD.8  Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 
3.MD: Geometric Measurement: Recognize Perimeter As An Attribute Of Plane Figures And Distinguish Between Linear And Area Measures.  
3.MD.8  Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 
Geometric Measurement: Understand Concepts Of Area And Relate Area To Multiplication And To Addition.  
3.MD.5  Recognize area as an attribute of plane figures and understand concepts of area measurement. 
3.MD.5.a  A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. 
3.MD.6  Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 
3.MD.7.a  Find the area of a rectangle with wholenumber side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. 
3.MD.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 wholenumber products as rectangular areas in mathematical reasoning. 
3.MD.7.c  Use tiling to show in a concrete case that the area of a rectangle with wholenumber side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. 
3.MD.7.d  Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. 
Represent And Interpret Data.  
3.MD.3  Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 
Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects.  
3.MD.1  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 number line diagram. 
3.MD.2  Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve onestep 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.7 
4.MD: Geometric Measurement: Understand Concepts Of Angle And Measure Angles.  
4.MD.5.a  An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “onedegree angle,” and can be used to measure angles. 
4.MD.5.b  An angle that turns through n onedegree angles is said to have an angle measure of n degrees. 
4.MD.6  Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 
4.MD.7  Recognize angle measure as additive. When an angle is decomposed into nonoverlapping 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. 
Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit.  
4.MD.1  Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... 
4.MD.2  Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 
4.MD.3  Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. 
5.MD: Convert Like Measurement Units Within A Given Measurement System.  
5.MD.1  Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real world problems. 
Geometric Measurement: Understand Concepts Of Volume And Relate Volume To Multiplication And To Addition.  
5.MD.5.b  Apply the formulas V=l×w×handV=b×h 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. 
Represent And Interpret Data.  
5.MD.2  Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. 
K.MD: Classify Objects And Count The Number Of Objects In Each Category.  
K.MD.3  Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3 
Describe And Compare Measurable Attributes.  
K.MD.1  Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. 
Modeling With Geometry  
HSG.MG: Apply Geometric Concepts In Modeling Situations  
HSG.MG.1  Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★ 
HSG.MG.3  Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★ 
Number And Operations In Base Ten  
1.NBT: Use Place Value Understanding And Properties Of Operations To Add And Subtract.  
1.NBT.4  Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 
1.NBT.6  Subtract multiples of 10 in the range 1090 from multiples of 10 in the range 1090 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 
2.NBT: Understand Place Value.  
2.NBT.1.a  100 can be thought of as a bundle of ten tens — called a “hundred.” 
2.NBT.2  Count within 1000; skipcount by 5s, 10s, and 100s. 
2.NBT.4  Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 
Use Place Value Understanding And Properties Of Operations To Add And Subtract.  
2.NBT.5  Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 
2.NBT.6  Add up to four twodigit numbers using strategies based on place value and properties of operations. 
2.NBT.7  Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 
3.NBT: Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.4  
3.NBT.1  Use place value understanding to round whole numbers to the nearest 10 or 100. 
3.NBT.2  Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 
3.NBT.3  Multiply onedigit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 
5.NBT: Perform Operations With MultiDigit Whole Numbers And With Decimals To Hundredths.  
5.NBT.5  Fluently multiply multidigit whole numbers using the standard algorithm. 
5.NBT.7  Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 
Understand The Place Value System.  
5.NBT.1  Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 
5.NBT.2  Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. 
5.NBT.3.a  Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). 
5.NBT.3.b  Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 
5.NBT.4  Use place value understanding to round decimals to any place. 
4.NBT: Generalize Place Value Understanding For MultiDigit Whole Numbers.  
4.NBT.2  Read and write multidigit whole numbers using baseten numerals, number names, and expanded form. Compare two multidigit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 
4.NBT.3  Use place value understanding to round multidigit whole numbers to any place. 
Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.  
4.NBT.4  Fluently add and subtract multidigit whole numbers using the standard algorithm. 
4.NBT.5  Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 
Number And Operations—Fractions  
5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions.  
5.NF.3  Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 
5.NF.4  Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 
5.NF.5.a  Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 
5.NF.5.b  Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. 
Use Equivalent Fractions As A Strategy To Add And Subtract Fractions.  
5.NF.1  Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 
5.NF.2  Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions 
4.NF: Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers.  
4.NF.4.a  Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). 
4.NF.4.c  Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? 
Understand Decimal Notation For Fractions, And Compare Decimal Fractions.  
4.NF.5  Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 
4.NF.6  Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 
4.NF.7  Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 
3.NF: Develop Understanding Of Fractions As Numbers.  
3.NF.1  Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 
3.NF.2  Understand a fraction as a number on the number line; represent fractions on a number line diagram. 
3.NF.2.a  Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 
3.NF.2.b  Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 
3.NF.3  Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 
3.NF.3.a  Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 
3.NF.3.c  Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. 
3.NF.3.d  Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 
Operations And Algebraic Thinking  
1.OA: Add And Subtract Within 20.  
1.OA.5  Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 
1.OA.6  Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 
2.OA: Add And Subtract Within 20.  
2.OA.2  Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two onedigit numbers. 
Work With Equal Groups Of Objects To Gain Foundations For Multiplication.  
2.OA.4  Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 
3.OA: Multiply And Divide Within 100.  
3.OA.7  Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers. 
Represent And Solve Problems Involving Multiplication And Division.  
3.OA.1  Interpret products of whole numbers, e.g., interpret 5 × 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 × 7. 
3.OA.3  Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 
3.OA.4  Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?. 
Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic.  
3.OA.9  Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 
Understand Properties Of Multiplication And The Relationship Between Multiplication And Division.  
3.OA.5  Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) 
4.OA: Gain Familiarity With Factors And Multiples.  
4.OA.4  Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1–100 is prime or composite. 
Generate And Analyze Patterns.  
4.OA.5  Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. 
Use The Four Operations With Whole Numbers To Solve Problems.  
4.OA.3  Solve multistep word problems posed with whole numbers and having wholenumber 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. 
5.OA: Analyze Patterns And Relationships.  
5.OA.3  Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. 
Write And Interpret Numerical Expressions.  
5.OA.1  Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 
5.OA.2  Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. 
K.OA: Understand Addition As Putting Together And Adding To, And Under Stand Subtraction As Taking Apart And Taking From.  
K.OA.1  Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. 
Quantities  
HSN.Q: Reason Quantitatively And Use Units To Solve Problems.  
HSN.Q .1  Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. 
HSN.Q .2  Define appropriate quantities for the purpose of descriptive modeling. 
HSN.Q .3  Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 
Ratios And Proportional Relationships  
6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.  
6.RP.1  Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 
6.RP.3.c  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 
6.RP.3.d  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 
7.RP: Analyze Proportional Relationships And Use Them To Solve RealWorld And Mathematical Problems.  
7.RP.1  Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 
7.RP.2.b  Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 
7.RP.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. 
7.RP.2.d  Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 
7.RP.3  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. 
Reasoning With Equations And Inequalities  
HSA.REI: Represent And Solve Equations And Inequalities Graphically  
HSA.REI.10  Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 
Solve Equations And Inequalities In One Variable  
HSA.REI.3  Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. 
Solve Systems Of Equations  
HSA.REI.5  Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. 
HSA.REI.6  Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. 
HSA.REI.7  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 = –3x and the circle x2 + y2 = 3. 
Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning  
HSA.REI.1  Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 
HSA.REI.2  Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. 
Seeing Structure In Expressions  
HSA.SSE: Interpret The Structure Of Expressions  
HSA.SSE.1  Interpret expressions that represent a quantity in terms of its context. 
Write Expressions In Equivalent Forms To Solve Problems  
HSA.SSE.3.c  Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 
Similarity, Right Triangles, And Trigonometry  
HSG.SRT: Define Trigonometric Ratios And Solve Problems Involving Right Triangles  
HSG.SRT.6  Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 
HSG.SRT.7  Explain and use the relationship between the sine and cosine of complementary angles. 
HSG.SRT.8  Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★ 
Prove Theorems Involving Similarity  
HSG.SRT.4  Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. 
HSG.SRT.5  Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 
Understand Similarity In Terms Of Similarity Transformations  
HSG.SRT.2  Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. 
HSG.SRT.3  Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 
Statistics And Probability  
6.SP: Develop Understanding Of Statistical Variability.  
6.SP.1  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 
6.SP.2  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. 
6.SP.3  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 
Summarize And Describe Distributions.  
6.SP.4  Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 
6.SP.5.a  Reporting the number of observations. 
6.SP.5.b  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. 
6.SP.5.c  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 
6.SP.5.d  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. 
7.SP: Draw Informal Comparative Inferences About Two Populations.  
7.SP.3  Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 
7.SP.4  Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book. 
Investigate Chance Processes And Develop, Use, And Evaluate Probability Models.  
7.SP.5  Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 
7.SP.6  Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 
7.SP.7.a  Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. 
7.SP.7.b  Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land openend down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 
7.SP.8.c  Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 
8.SP: Investigate Patterns Of Association In Bivariate Data.  
8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 
8.SP.2  Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 
8.SP.3  Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 
The Complex Number System  
HSN.CN: Use Complex Numbers In Polynomial Identities And Equations.  
HSN.CN.9  (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. 
The Number System  
6.NS: Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.  
6.NS.1  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4cup 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? 
Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.  
6.NS.5  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. 
6.NS.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., –(–3) = 3, and that 0 is its own opposite. 
6.NS.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. 
6.NS.6.c  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 
6.NS.7.b  Write, interpret, and explain statements of order for rational numbers in realworld contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC. 
6.NS.8  Solve realworld 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. 
Compute Fluently With MultiDigit Numbers And Find Common Factors And Multiples.  
6.NS.3  Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation. 
7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers.  
7.NS.1.c  Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts. 
7.NS.1.d  Apply properties of operations as strategies to add and subtract rational numbers. 
7.NS.2.a  Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing realworld contexts. 
7.NS.2.c  Apply properties of operations as strategies to multiply and divide rational numbers. 
7.NS.3  Solve realworld and mathematical problems involving the four operations with rational numbers. 
Vector And Matrix Quantities  
HSN.VM: Perform Operations On Matrices And Use Matrices In Applications.  
HSN.VM.6  (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. 
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