Ohio. PracticePlanet Correlation to the Ohio Achievement Tests CORRELATIONS

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1 Ohio PracticePlanet Correlation to the Ohio Achievement Tests CORRELATIONS

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3 Introduction PracticePlanet is a dynamic online test practice program that helps students practice test taking strategies and continuously refresh their memory on the skills that will appear on their high stakes state tests. To accomplish this, Ohio PracticePlanet assessment questions are aligned to the:! Ohio Academic Content s Language Arts (2001) and Mathematics (2001) o Ohio Achievement Tests (OH TESTS) o Identified as such within the Blueprints for Ohio Achievement Tests Specifically, these Ohio PracticePlanet assessment questions are focused on:! Language Arts Grade 3-8! Mathematics Grades 3-8 As a result of this powerful alignment, working through Ohio PracticePlanet assessment questions can help prepare students for the Ohio Achievement Tests (OH TESTS) by helping them become familiar with the content of the questions found on these Ohio state tests. How to use this PracticePlanet Correlation Book As you can see in the example below, the information in this book is presented in two columns. The left column contains the details of the Ohio Academic Content s represented on the Ohio Achievement Tests (OH TESTS) while the right column lists the PracticePlanet Assessment Skill(s) that are correlated with these standards. By examining this correlation, educators can gain a better understanding of the breadth of content covered by PracticePlanet assessment items. 9/22/2008 Introduction v.1.0

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5 Table of Contents Language Arts Grade Grade Grade Grade Grade Grade Mathematics Grade Grade Grade Grade Grade Grade /19/2008 Introduction v.1.0

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7 Language Arts Grade Acquisition of Vocabulary Contextual Understanding: Determine the meaning of unknown words using a variety of context clues, including word, sentence and paragraph clues. 3,B,2: Vocabulary & Context Clues I 3,B,3: Vocabulary & Context Clues II 2.. Acquisition of Vocabulary Contextual Understanding: Use context clues to determine the meaning of homophones, homonyms and homographs. 3,B,24: Synonyms, Antonyms, Homophones, & Word Categories 3.. Acquisition of Vocabulary Conceptual Understanding: Apply the meaning of the terms synonyms and antonyms. 3,B,24: Synonyms, Antonyms, Homophones, & Word Categories 4.. Acquisition of Vocabulary Conceptual Understanding: Read accurately highfrequency sight words. 5.. Acquisition of Vocabulary Structural Understanding: Apply knowledge of individual words in unknown compound words to determine their meanings. 6.. Acquisition of Vocabulary Structural Understanding: Use knowledge of contractions and common abbreviations to identify whole words. 3,A,9: Contractions & Possessives 7.. Acquisition of Vocabulary Structural Understanding: Apply knowledge of prefixes, including un-, re-, pre- and suffixes, including -er, -est, - ful and -less to determine meaning of words. 3,B,1: Prefixes & Suffixes 8.. Acquisition of Vocabulary Structural Understanding: Decode and determine the meaning of words by using knowledge of root words and their various inflections. 3,B,1: Prefixes & Suffixes 9/19/ v.1.0

8 Language Arts Grade Acquisition of Vocabulary Tools and Resources: Determine the meanings and pronunciations of unknown words by using dictionaries, glossaries, technology and textual features, such as definitional footnotes or sidebars. 3,B,14: Using Resource Materials 3,B,15: Dictionary Skills 1.. Reading Process: Concepts of Comprehension Strategies: Establish a purpose for reading, for example, to be informed, to follow directions or to be entertained. 2.. Reading Process: Concepts of Comprehension Strategies: Predict content, events and outcomes by using chapter titles, section headers, illustrations and story topics, and support those predictions with examples from the text. 3,B,11: Predicting 3.. Reading Process: Concepts of Comprehension Strategies: Compare and contrast information between texts and across areas. 4.. Reading Process: Concepts of Comprehension Strategies: Summarize texts, sequencing information accurately and include main ideas and details as appropriate. 3,B,9: Summarizing 5.. Reading Process: Concepts of Comprehension Strategies: Make inferences regarding events and possible outcomes from information in text. 3,B,17: Reading & Responding to Varied Texts & Genre 3,B,25: Drawing Conclusions 3,B,28: Inference 6.. Reading Process: Concepts of Comprehension Strategies: Create and use graphic organizers, such as Venn diagrams and webs, to demonstrate comprehension. 9/19/ v.1.0

9 Language Arts Grade Reading Process: Concepts of Comprehension Strategies: Answer literal, inferential and evaluative questions to demonstrate comprehension of grade-appropriate print texts and electronic and visual media. 3,B,4: Facts & s 7.. Reading Process: Concepts of Answer literal, inferential and 3,B,13: Factual Recall evaluative questions to demonstrate comprehension of grade-appropriate print texts and electronic and visual media. 3,B,17: Reading & Responding to Varied Texts & Genre 8.. Reading Process: Concepts of Self-Monitoring Strategies: Monitor own comprehension by adjusting speed to fit the purpose, or by skimming, scanning, reading on or looking back. 9.. Reading Process: Concepts of Self-Monitoring Strategies: Use criteria to choose independent reading materials, for example, personal interest, knowledge of authors and genres or recommendations from others Reading Process: Concepts of Independent Reading: Independently read books for various purposes, for example, for enjoyment, for literary experience, to gain information or to perform a task. 1.. Reading Applications: Informational, Technical and Use the table of contents, chapter headings, glossary, index, captions and illustrations to locate information and comprehend texts. 9/19/ v.1.0

10 Language Arts Grade Reading Applications: Informational, Technical and List questions about essential elements, for example, why, who, where, what, when and how, from informational text and identify answers. 3.. Reading Applications: Identify and list the important 3,B,4: Facts & s Informational, Technical and central ideas and supporting 3,B,8: Main Idea details of informational text. 3,B,13: Factual Recall 4.. Reading Applications: Draw conclusions from 3,B,22: Graphics Informational, Technical and information in maps, charts, 3,B,25: Drawing Conclusions graphs and diagrams. 3,B,28: Inference 5.. Reading Applications: Analyze a set of directions for 3,B,6: Following Directions Informational, Technical and proper sequencing, clarity and completeness. 1.. Reading Applications: Literary Text Recognize and describe similarities and differences of plot across literary works. 2.. Reading Applications: Literary Text Use concrete details from the text to describe characters and setting. 3,B,7: Story Setting 3,B,12: Recognizing Emotional Reactions 3,B,13: Factual Recall 3,B,17: Reading & Responding to Varied Texts & Genre 3,B,23: Main Character 3.. Reading Applications: Literary Text Retell the plot sequence. 3,B,5: Sequencing 4.. Reading Applications: Literary Text Identify and explain the defining characteristics of literary forms and genres, including fairy tales, folk tales, poetry, fiction and non-fiction. 3,B,19: Appreciating Various Genre 3,B,26: Fact & Fiction 5.. Reading Applications: Literary Text Explain how an author's choice of words appeals to the senses. 6.. Reading Applications: Literary Text Identify stated and implied themes. 9/19/ v.1.0

11 Language Arts Grade Reading Applications: Literary Text Describe methods authors use to influence readers' feelings and attitudes, for example, appeal of characters in a picture book; use of figurative language. 3,B,21: Figurative Language 1.. Acquisition of Vocabulary Contextual Understanding: Determine the meaning of unknown words by using a variety of context clues, including word, sentence and paragraph clues. 4,B,2: Vocabulary & Context Clues I 4,B,3: Vocabulary & Context Clues II 2.. Acquisition of Vocabulary Contextual Understanding: Use context clues to determine the meaning of synonyms, antonyms, homophones, homonyms and homographs. 4,B,23: Synonyms, Antonyms, & Homophones 3.. Acquisition of Vocabulary Conceptual Understanding: Recognize the difference between the meanings of connotation and denotation. 4.. Acquisition of Vocabulary Conceptual Understanding: Identify and apply the meaning of the terms synonym, antonym, homophone and homograph. 4,B,23: Synonyms, Antonyms, & Homophones 5.. Acquisition of Vocabulary Conceptual Understanding: Identify and understand new uses of words and phrases in text, such as similes and metaphors. 4,B,22: Figurative Language 6.. Acquisition of Vocabulary Structural Understanding: Identify word origins to determine the meaning of unknown words and phrases. 4,B,1: Prefixes & Suffixes 9/19/ v.1.0

12 Language Arts Grade Acquisition of Vocabulary Structural Understanding: Identify the meanings of prefixes, suffixes and roots and their various forms to determine the meanings of words. 4,B,1: Prefixes & Suffixes 8.. Acquisition of Vocabulary Structural Understanding: Identify the meanings of abbreviations. 9.. Acquisition of Vocabulary Tools and Resources: Determine the meanings and pronunciations of unknown words by using dictionaries, glossaries, technology and textual features, such as definitional footnotes or sidebars. 4,B,17: Using Resource Materials 4,B,18: Dictionary Skills 1.. Reading Process: Concepts of Comprehension Strategies: Establish and adjust purposes for reading, including to find out, to understand, to interpret, to enjoy and to solve problems. 2.. Reading Process: Concepts of Comprehension Strategies: Predict and support predictions using an awareness of new vocabulary, text structures and familiar plot patterns. 4,B,13: Predicting 3.. Reading Process: Concepts of Comprehension Strategies: Compare and contrast information on a single topic or theme across different text and non-text resources. 4.. Reading Process: Concepts of Comprehension Strategies: Summarize important information in texts to demonstrate comprehension. 4,B,10: Summarizing 9/19/ v.1.0

13 Language Arts Grade Reading Process: Concepts of Comprehension Strategies: Make inferences or draw conclusions about what has been read and support those conclusions with textual evidence. 4,B,14: Drawing Conclusions 4,B,24: Drawing Conclusions 6.. Reading Process: Concepts of Comprehension Strategies: Select, create and use graphic organizers to interpret textual information. 4,B,26: Outlines, Timelines, & Graphic Organizers 7.. Reading Process: Concepts of Comprehension Strategies: 4,B,4: Facts & s Answer literal, inferential and evaluative questions to demonstrate comprehension of grade-appropriate print texts and electronic and visual media. 4,B,14: Drawing Conclusions 4,B,19: Reading & Responding to Varied Texts and Genre 8.. Reading Process: Concepts of Self-Monitoring Strategies: Monitor own comprehension by adjusting speed to fit the purpose, or by skimming, scanning, reading on or looking back. 9.. Reading Process: Concepts of Self-Monitoring Strategies: List questions and search for answers within the text to construct meaning Reading Process: Concepts of Independent Reading: Use criteria to choose independent reading materials, for example, personal interest, knowledge of authors and genres or recommendations from others Reading Process: Concepts of Independent Reading: Independently read books for various purposes, for example, for enjoyment, for literary experience, to gain information or to perform a task. 9/19/ v.1.0

14 Language Arts Grade Reading Applications: Informational, Technical and Make inferences about informational text from the title page, table of contents and chapter headings. 4,B,14: Drawing Conclusions 4,B,17: Using Resource Materials 4,B,24: Drawing Conclusions 2.. Reading Applications: Informational, Technical and Summarize main ideas in informational text, using supporting details as appropriate. 4,B,4: Facts & s 4,B,8: Stated Main Idea 4,B,9: Implied Main Idea 3.. Reading Applications: Informational, Technical and Locate important details about a topic using different sources of information including books, magazines, newspapers and online resources. 4,B,4: Facts & s 4.. Reading Applications: Identify examples of cause 4,B,11: Cause & Effect Informational, Technical and and effect used in informational text. 5.. Reading Applications: Draw conclusions from 4,B,12: Graphics Informational, Technical and information in maps, charts, 4,B,24: Drawing Conclusions graphs and diagrams. 6.. Reading Applications: Clarify steps in a set of 4,B,6: Following Directions Informational, Technical and instructions or procedures for completeness. 7.. Reading Applications: Distinguish fact from opinion. 4,B,16: Fact & Opinion Informational, Technical and 1.. Reading Applications: Literary Text Describe the thoughts, words 4,B,15: Recognizing Emotional Reactions and interactions of characters. 2.. Reading Applications: Literary Text Identify the influence of 4,B,7: Story Setting setting on the selection. 3.. Reading Applications: Literary Text Identify the main incidents of a plot sequence, identifying the major conflict and its resolution. 4,B,5: Sequencing 4,B,8: Stated Main Idea 4,B,9: Implied Main Idea 9/19/ v.1.0

15 Language Arts Grade Reading Applications: Literary Text Identify the speaker and recognize the difference between first- and thirdperson narration. 5.. Reading Applications: Literary Text Determine the theme and whether it is implied or stated directly. 6.. Reading Applications: Literary Text Identify and explain the defining characteristics of literary forms and genres, including poetry, drama, fables, fantasies, chapter books, fiction and non-fiction. 4,B,20: Appreciating Various Genres 7.. Reading Applications: Literary Text Explain how an author's choice of words appeals to the senses and suggests mood. 8.. Reading Applications: Literary Text Identify figurative language in literary works, including idioms, similes and metaphors. 4,B,22: Figurative Language 1.. Writing Processes Prewriting: Generate writing ideas through discussions with others and from printed material. 4,A,11: Writing Process 2.. Writing Processes Prewriting: State and develop 4,A,11: Writing Process a clear main idea for writing. 3.. Writing Processes Prewriting: Develop a purpose 4,A,11: Writing Process and audience for writing. 4.. Writing Processes Prewriting: Use organizational strategies, for example, brainstorming, lists, webs and Venn diagrams, to plan writing. 4,A,11: Writing Process 9/19/ v.1.0

16 Language Arts Grade Writing Processes Drafting, Revising and Editing: Organize writing, beginning with an introduction, body and a resolution of plot, followed by a closing statement or a summary of important ideas and details. 4,A,11: Writing Process 6.. Writing Processes Drafting, Revising and Editing: 4,A,12: Sentence Structure II Vary simple, compound and complex sentence structures. 7.. Writing Processes Drafting, Revising and Editing: Create paragraphs with topic sentences and supporting sentences that are marked by indentation) and are linked by transitional words and phrases. 4,A,11: Writing Process 8.. Writing Processes Drafting, Revising and Editing: Vary language and style as appropriate to audience and purpose. 4,A,11: Writing Process 9.. Writing Processes Drafting, Revising and Editing: 4,A,11: Writing Process Use available technology to compose text Writing Processes Drafting, Revising and Editing: Reread and assess writing for clarity, using a variety of methods, for example, writer's circle or author's chair. 4,A,11: Writing Process 11.. Writing Processes Drafting, Revising and Editing: Add descriptive words and details and delete extraneous information. 4,A,11: Writing Process 12.. Writing Processes Drafting, Revising and Editing: Rearrange words, sentences and paragraphs to clarify meaning. 4,A,11: Writing Process 9/19/ v.1.0

17 Language Arts Grade Writing Processes Drafting, Revising and Editing: Use resources and reference materials, including dictionaries, to select more effective vocabulary. 4,B,17: Using Resource Materials 4,B,18: Dictionary Skills 14.. Writing Processes Drafting, Revising and Editing: Proofread writing and edit to improve conventions, for example, grammar, spelling, punctuation and capitalization, and identify and correct fragments and run-ons. 4,A,1: Capitalization 4,A,3: Spelling 4,A,4: Editing 4,A,5: English Usage 4,A,6: Sentence Structure 4,A,8: Spelling Strategies 4,A,11: Writing Process 15.. Writing Processes Drafting, Revising and Editing: Apply tools, for example, rubric, checklist and feedback, to judge the quality of writing Writing Processes Publishing: Prepare for publication, for display or for sharing with others, writing that follows a format appropriate to the purpose using techniques such as electronic resources and graphics to enhance the final product. 1.. Writing Applications Write narratives that sequence events, including descriptive details and vivid language to develop plot, characters and setting and to establish a point of view. 2.. Writing Applications Write responses to novels, stories and poems that include a simple interpretation of a literary work and support judgments with specific references to the original text and to prior knowledge. 9/19/ v.1.0

18 Language Arts Grade Writing Applications Write formal and informal letters, for example, thank you notes, letters of request, that follow letter format, for example, date, proper salutation, body, closing and signature, include important information and demonstrate a sense of closure. 4.. Writing Applications Write informational reports that include facts and examples and present important details in a logical order. 5.. Writing Applications Produce informal writings, for example, messages, journals, notes and poems, for various purposes. 1.. Writing Conventions Handwriting: Write legibly in cursive, spacing letters, words and sentences appropriately. 2.. Writing Conventions Spelling: Spell high-frequency 4,A,3: Spelling words correctly. 4,A,4: Editing 4,A,8: Spelling Strategies 3.. Writing Conventions Spelling: Spell plurals and 4,A,3: Spelling inflectional endings correctly. 4,A,4: Editing 4,A,8: Spelling Strategies 4.. Writing Conventions Spelling: Spell roots, suffixes 4,A,3: Spelling and prefixes correctly. 4,A,4: Editing 4,A,8: Spelling Strategies 5.. Writing Conventions Punctuation and Capitalization: Use commas, end marks, apostrophes and quotation marks correctly. 4,A,2: Punctuation 4,A,4: Editing 4,A,9: Contractions & Possessives 6.. Writing Conventions Punctuation and 4,A,1: Capitalization Capitalization: Use correct 4,A,4: Editing capitalization. 9/19/ v.1.0

19 Language Arts Grade Writing Conventions Grammar and Usage: Use various parts of speech such as nouns, pronouns and verbs, for example, regular and irregular, past, present and future. 4,A,5: English Usage 4,A,10: Parts of Speech 8.. Writing Conventions Grammar and Usage: Use 4,A,5: English Usage conjunctions and interjections. 4,A,10: Parts of Speech 9.. Writing Conventions Grammar and Usage: Use 4,A,5: English Usage adverbs. 4,A,10: Parts of Speech 10.. Writing Conventions Grammar and Usage: Use 4,A,5: English Usage prepositions and prepositional 4,A,10: Parts of Speech phrases. 4,A,15: Prepositional Phrases 11.. Writing Conventions Grammar and Usage: Use 4,A,5: English Usage objective and nominative case 4,A,10: Parts of Speech pronouns Writing Conventions Grammar and Usage: Use 4,A,5: English Usage subjects and verbs that are in 4,A,10: Parts of Speech agreement. 4,A,13: Subject/Verb Agreement 13.. Writing Conventions Grammar and Usage: Use 4,A,5: English Usage irregular plural nouns. 4,A,10: Parts of Speech 5.. Acquisition of Vocabulary Structural Understanding: Use word origins to determine the meaning of unknown words and phrases. 5,B,1: Prefixes & Suffixes 6.. Acquisition of Vocabulary Structural Understanding: Apply the knowledge of prefixes, suffixes and roots and their various inflections to analyze the meanings of words. 5,B,1: Prefixes & Suffixes 2.. Reading Applications: Literary Text Explain the influence of 5,B,10: Setting setting on the selection. 9/19/ v.1.0

20 Language Arts Grade Reading Applications: Literary Text Identify the main incidents of a plot sequence and explain how they influence future action. 5,B,11: Sequencing 2.. Reading Applications: Informational, Technical and Identify, distinguish between and explain examples of cause and effect in informational text. 5,B,13: Cause & Effect 2.. Reading Process: Concepts of Comprehension Strategies: Predict and support predictions with specific references to textual examples that may be in widely separated sections of text. 5,B,14: Predicting 5.. Reading Process: Concepts of Comprehension Strategies: Make inferences based on implicit information in texts, and provide justifications for those inferences. 5,B,15: Drawing Conclusions 5,B,17: Making Generalizations 1.. Reading Applications: Literary Text Explain how a character's 5,B,16: Recognizing Emotional Reactions thoughts, words and actions 5,B,17: Making Generalizations reveal his or her motivations. 1.. Reading Applications: Informational, Technical and Use text features, such as chapter titles, headings and subheadings; parts of books including the index and table of contents and online tools (search engines) to locate information. 5,B,18: Using Resource Materials 8.. Acquisition of Vocabulary Tools and Resources: Determine the meanings and pronunciations of unknown words by using dictionaries, thesauruses, glossaries, technology and textual features, such as definitional footnotes or sidebars. 5,B,18: Using Resource Materials 5,B,19: Dictionary Skills 9/19/ v.1.0

21 Language Arts Grade Acquisition of Vocabulary Contextual Understanding: Define the meaning of unknown words by using context clues and the author's use of definition, restatement and example. 5,B,2: Vocabulary & Context Clues I 5,B,3: Vocabulary & Context Clues II 9.. Reading Process: Concepts of Self-Monitoring Strategies: List questions and search for answers within the text to construct meaning. 5,B,20: Reading & Responding to Varied Texts & Genre 8.. Reading Applications: Informational, Technical and Distinguish relevant from irrelevant information in a text and identify possible points of confusion for the reader. 5,B,20: Reading & Responding to Varied Texts & Genre 6.. Reading Applications: Literary Text Describe the defining characteristics of literary forms and genres, including poetry, drama, chapter books, biographies, fiction and nonfiction. 5,B,21: Appreciating Various Genre 9.. Reading Applications: Informational, Technical and Identify and understand an author's purpose for writing, including to explain, to entertain or to inform. 5,B,22: Audience & Purpose 4.. Acquisition of Vocabulary Conceptual Understanding: Identify and understand new uses of words and phrases in text, such as similes and metaphors. 5,B,23: Figurative Language 8.. Reading Applications: Literary Text Identify and explain the use of figurative language in literary works, including idioms, similes, hyperboles, metaphors and personification. 5,B,23: Figurative Language 9/19/ v.1.0

22 Language Arts Grade Acquisition of Vocabulary Contextual Understanding: Use context clues to determine the meaning of synonyms, antonyms, homophones, homonyms and homographs. 5,B,24: Synonyms, Antonyms, Homophones 6.. Reading Process: Concepts of Comprehension Strategies: Select, create and use graphic organizers to interpret textual information. 5,B,26: Outlines, Timelines, & Graphic Organizers 7.. Reading Applications: Literary Text Interpret how an author's choice of words appeals to the senses and suggests mood. 5,B,28: Literary Devices 7.. Reading Process: Concepts of Comprehension Strategies: 5,B,4: Facts & s Answer literal, inferential and evaluative questions to demonstrate comprehension of grade-appropriate print texts and electronic and visual media. 5,B,15: Drawing Conclusions 5,B,20: Reading & Responding to Varied Texts & Genre 4.. Reading Applications: Informational, Technical and Summarize the main ideas and supporting details. 5,B,4: Facts & s 5,B,6: Main Idea 5,B,9: Factual Recall 5,B,12: Implied Main Idea 6.. Reading Applications: Informational, Technical and Clarify steps in a set of instructions or procedures for proper sequencing and completeness and revise if necessary. 5,B,5: Following Directions 4.. Reading Process: Concepts of Comprehension Strategies: Summarize the information in texts, recognizing that there may be several important ideas rather than just one main idea and identifying details that support each. 5,B,7: Summarizing 5.. Reading Applications: Literary Text Summarize stated and implied 5,B,7: Summarizing themes. 9/19/ v.1.0

23 Language Arts Grade Reading Applications: Analyze information found in 5,B,8: Graphic Aids Informational, Technical and maps, charts, tables, graphs and diagrams. 7.. Reading Applications: Analyze the difference 5,B,9: Factual Recall Informational, Technical and between fact and opinion. 5,B,27: Fact & Opinion 10.. Reading Process: Concepts of Independent Reading: Use criteria to choose independent reading materials, for example, personal interest, knowledge of authors and genres or recommendations from others Reading Process: Concepts of Independent Reading: Independently read books for various purposes, for example, for enjoyment, for literary experience, to gain information or to perform a task. Not currently assessed at this grade level 4.. Reading Applications: Literary Text Identify the speaker and Not currently assessed at this grade level explain how point of view affects the text. 3.. Acquisition of Vocabulary Conceptual Understanding: Identify the connotation and denotation of new words. 7.. Acquisition of Vocabulary Structural Understanding: Identify the meanings of abbreviations. 1.. Reading Process: Concepts of Comprehension Strategies: Establish and adjust purposes for reading, including to find out, to understand, to interpret, to enjoy and to solve problems. 3.. Reading Process: Concepts of Comprehension Strategies: Make critical comparisons across texts. 9/19/ v.1.0

24 Language Arts Grade Reading Process: Concepts of Self-Monitoring Strategies: Monitor own comprehension by adjusting speed to fit the purpose, or by skimming, scanning, reading on, looking back or summarizing what has been read so far in text. 3.. Reading Applications: Informational, Technical and Compare important details about a topic, using different sources of information, including books, magazines, newspapers and online resources. 1.. Acquisition of Vocabulary Contextual Understanding: Define the meaning of unknown words by using context clues and the author's use of definition, restatement and example. 6,B,2: Vocabulary & Context Clues I 6,B,3: Vocabulary & Context Clues II 2.. Acquisition of Vocabulary Conceptual Understanding: Apply knowledge of connotation and denotation to determine the meaning of words. 3.. Acquisition of Vocabulary Conceptual Understanding: Identify analogies and other word relationships, including synonyms and antonyms, to determine the meaning of words. 6,B,26: Synonyms, Antonyms, & Homophones 4.. Acquisition of Vocabulary Conceptual Understanding: Interpret metaphors and similes to understand new uses of words and phrases in text. 6,B,25: Figurative Language 6,B,30: Literary Devices 5.. Acquisition of Vocabulary Conceptual Understanding: Recognize and use words from other languages that have been adopted into the English language. 6,B,1: Prefixes & Suffixes 9/19/ v.1.0

25 Language Arts Grade Acquisition of Vocabulary Structural Understanding: Apply the knowledge of prefixes, suffixes and roots and their various inflections to analyze the meanings of words. 6,B,1: Prefixes & Suffixes 7.. Acquisition of Vocabulary Structural Understanding: Identify symbols and acronyms and connect them to whole words. 8.. Acquisition of Vocabulary Tools and Resources: Determine the meanings and pronunciations of unknown words by using dictionaries, thesauruses, glossaries, technology and textual features, such as definitional footnotes or sidebars. 6,B,21: Using Resource Materials 6,B,33: Referencing 1.. Reading Process: Concepts of Comprehension Strategies: Establish and adjust purposes for reading, including to find out, to understand, to interpret, to enjoy and to solve problems. 6,B,18: Point of View & Purpose 2.. Reading Process: Concepts of Comprehension Strategies: Predict or hypothesize as appropriate from information in the text, substantiating with specific references to textual examples that may be in widely separated sections of text. 6,B,12: Predicting 3.. Reading Process: Concepts of Comprehension Strategies: Make critical comparisons across texts, noting author's style as well as literal and implied content of text. 9/19/ v.1.0

26 Language Arts Grade Reading Process: Concepts of Comprehension Strategies: Summarize the information in texts, recognizing important ideas and supporting details, and noting gaps or contradictions. 6,B,4: Facts & s 6,B,7: Stated Main Idea 6,B,8: Implied Main Idea 6,B,20: Factual Recall 5.. Reading Process: Concepts of Comprehension Strategies: Select, create and use graphic organizers to interpret textual information. 6,B,28: Outlines, Timelines, & Graphic Organizers 6.. Reading Process: Concepts of Comprehension Strategies: Answer literal, inferential, evaluative and synthesizing questions to demonstrate comprehension of gradeappropriate print texts and electronic and visual media. 6,B,22: Reading & Responding to Varied Texts & Genres 7.. Reading Process: Concepts of Comprehension Strategies: Monitor own comprehension by adjusting speed to fit the purpose, or by skimming, scanning, reading on, looking back, note taking or summarizing what has been read so far in text. 8.. Reading Process: Concepts of Comprehension Strategies: List questions and search for answers within the text to construct meaning. 9.. Reading Process: Concepts of Independent Reading: Use criteria to choose independent reading materials, for example, personal interest, knowledge of authors and genres, or recommendations from others. 9/19/ v.1.0

27 Language Arts Grade Reading Process: Concepts of Independent Reading: Independently read books for various purposes, for example, for enjoyment, for literary experience, to gain information or to perform a task. 1.. Reading Applications: Informational, Technical and Use text features, such as chapter titles, headings and subheading; parts of books, including index, appendix, table of contents and online tools (search engines) to locate information. 6,B,21: Using Resource Materials 2.. Reading Applications: Analyze examples of cause 6,B,11: Cause & Effect Informational, Technical and and effect and fact and 6,B,20: Factual Recall opinion. 6,B,29: Fact & Opinion 3.. Reading Applications: Informational, Technical and Compare and contrast important details about a topic, using different sources of information, including books, magazines, newspapers and online resources 4.. Reading Applications: Informational, Technical and Compare original text to a summary to determine the extent to which the summary adequately reflects the main ideas and critical details of the original text. 6,B,4: Facts & s 6,B,7: Stated Main Idea 6,B,8: Implied Main Idea 6,B,20: Factual Recall 5.. Reading Applications: Analyze information found in 6,B,10: Graphic Aids Informational, Technical and maps, charts, tables, graphs, diagramsand cutaways. 6.. Reading Applications: Informational, Technical and Identify an author's argument or viewpoint and assess the adequacy and accuracy of details used. 6,B,18: Point of View & Purpose 6,B,31: Point of View 9/19/ v.1.0

28 Language Arts Grade Reading Applications: Informational, Technical and Identify and understand an author's purpose for writing, including to explain, entertain, persuade or inform. 6,B,18: Point of View & Purpose 6,B,19: Persuasion 6,B,24: Audience & Purpose 8.. Reading Applications: Informational, Technical and Summarize information from informational text, identifying the treatment, scope and organization of ideas. 6,B,9: Summarizing 1.. Reading Applications: Literary Text Analyze the techniques authors use to describe characters, including narrator or other characters' point of view; character's own thoughts, words or actions. 6,B,15: Making Judgments 6,B,17: Recognizing Emotions 2.. Reading Applications: Literary Text Identify the features of setting 6,B,16: Setting and explain their importance in literary text. 3.. Reading Applications: Literary Text Identify the main and minor events of the plot, and explain how each incident gives rise to the next. 6,B,5: Sequencing 4.. Reading Applications: Literary Text Explain first, third and omniscient points of view, and explain how voice affects the text. 5.. Reading Applications: Literary Text Identify recurring themes, patterns and symbols found in literature from different eras and cultures. 6.. Reading Applications: Literary Text Explain the defining characteristics of literary forms and genres, including poetry, drama, myths, biographies, autobiographies, fiction and non-fiction. 6,B,23: Appreciating Various Genres 9/19/ v.1.0

29 Language Arts Grade Reading Applications: Literary Text Distinguish how an author establishes mood and meaning through word choice, figurative language and syntax. 6,B,25: Figurative Language 6,B,30: Literary Devices 6,B,32: Tone, Mood, & Style 1.. Acquisition of Vocabulary Contextual Understanding: Define the meaning of unknown words through context clues and the author's use of comparison, contrast, definition, restatement and example. 7,B,2: Vocabulary & Context Clues I 7,B,3: Vocabulary & Context Clues II 2.. Acquisition of Vocabulary Contextual Understanding: Apply knowledge of connotation and denotation to determine the meaning of words. 7,B,31: Denotative & Connotative Meaning 3.. Acquisition of Vocabulary Conceptual Understanding: Infer word meanings through the identification of analogies and other word relationships, including synonyms and antonyms. 7,B,4: Multiple Meaning Words 7,B,24: Synonyms & Antonyms 7,B,28: Literary Devices 4.. Acquisition of Vocabulary Conceptual Understanding: Interpret metaphors and similes to understand new uses of words and phrases in text. 7,B,23: Figurative Language 7,B,32: Descriptive Language 5.. Acquisition of Vocabulary Conceptual Understanding: Recognize and use words from other languages that have been adopted into the English language. 7,B,1: Prefixes, Suffixes 6.. Acquisition of Vocabulary Structural Understanding: Use knowledge of Greek, Latin and Anglo-Saxon roots and affixes to understand vocabulary. 7,B,1: Prefixes, Suffixes 9/19/ v.1.0

30 Language Arts Grade Acquisition of Vocabulary Structural Understanding: Use knowledge of symbols and acronyms to identify whole words. 8.. Acquisition of Vocabulary Tools and Resources: Determine the meanings and pronunciations of unknown words by using dictionaries, thesauruses, glossaries, technology and textual features, such as definitional footnotes or sidebars. 7,B,21: Resource Materials 1.. Reading Process: Concepts of Comprehension Strategies: Establish and adjust purposes for reading, including to find out, to understand, to interpret, to enjoy and to solve problems. 2.. Reading Process: Concepts of Comprehension Strategies: Predict or hypothesize as appropriate from information in the text, substantiating with specific references to textual examples that may be in widely separated sections of text. 7,B,13: Predicting 3.. Reading Process: Concepts of Comprehension Strategies: Make critical comparisons across text, noting author's style as well as literal and implied content of text. 7,B,29: Tone, Mood, & Style 4.. Reading Process: Concepts of Comprehension Strategies: Summarize the information in texts, using key ideas, supporting details and referencing gaps or contradictions. 7,B,11: Summarizing 5.. Reading Process: Concepts of Comprehension Strategies: Select, create and use graphic organizers to interpret textual information. 7,B,26: Outlines, Timelines, & Graphic Organizers 9/19/ v.1.0

31 Language Arts Grade Reading Process: Concepts of Comprehension Strategies: 7,B,5: Facts & s Answer literal, inferential, evaluative and synthesizing questions to demonstrate comprehension of gradeappropriate print texts and electronic and visual media. 7,B,15: Making Inferences & Drawing Conclusions 7.. Reading Process: Concepts of Self-Monitoring Strategies: Monitor own comprehension by adjusting speed to fit the purpose, or by skimming, scanning, reading on, looking back, note taking or summarizing what has been read so far in text. 8.. Reading Process: Concepts of Independent Reading: Use criteria to choose independent reading materials, for example, personal interest, knowledge of authors and genres or recommendations from others. 9.. Reading Process: Concepts of Independent Reading: Independently read books for various purposes, for example, for enjoyment, for literary experience, to gain information or to perform a task. 1.. Reading Applications: Informational, Technical and Use text features, such as chapter titles, headings and subheadings; parts of books including index, appendix, table of contents and online tools (search engines) to locate information. 7,B,21: Resource Materials 2.. Reading Applications: Analyze examples of cause 7,B,12: Cause & Effect Informational, Technical and and effect and fact and 7,B,19: Factual Recall opinion. 7,B,27: Fact & Opinion 9/19/ v.1.0

32 Language Arts Grade Reading Applications: Informational, Technical and Compare and contrast different sources of information, including books, magazines, newspapers and online resources, to draw conclusions about a topic. 4.. Reading Applications: Informational, Technical and Compare original text to a summary to determine the extent to which the summary adequately reflects the main ideas, critical details and underlying meaning of the original text. 7,B,9: Stated Main Idea 7,B,10: Implied Main Idea 5.. Reading Applications: Informational, Technical and Analyze information found in maps, charts, tables, graphs, diagrams, cutaways and overlays. 7,B,14: Graphic Aids 6.. Reading Applications: Informational, Technical and Assess the adequacy, accuracy and appropriateness of an author???s details, identifying persuasive techniques and examples of bias and stereotyping. 7,B,34: Persuasion, Bias, Propaganda, & Stereotyping 7.. Reading Applications: Informational, Technical and Identify an author's purpose for writing and explain an author's argument, perspective or viewpoint in text. 7,B,18: Point of View & Purpose 8.. Reading Applications: Informational, Technical and Compare the treatment, scope and organization of ideas from different texts on the same topic. 1.. Reading Applications: Literary Text Explain interactions and conflicts between main and minor characters in literary text and how the interactions affect the plot. 7,B,17: Making Judgments 2.. Reading Applications: Literary Text Analyze the features of the 7,B,8: Setting setting and their importance in a text. 9/19/ v.1.0

33 Language Arts Grade Reading Applications: Literary Text Identify the main and minor events of the plot, and explain how each incident gives rise to the next. 7,B,6: Sequencing 4.. Reading Applications: Literary Text Identify and compare subjective and objective points of view and how they affect the overall body of a work. 5.. Reading Applications: Literary Text Identify recurring themes, patterns and symbols found in literature from different eras and cultures. 7,B,28: Literary Devices 7,B,33: Literary Elements 6.. Reading Applications: Literary Text Explain the defining characteristics of literary forms and genres, including poetry, drama, myths, biographies, autobiographies, science fiction, fiction and non-fiction. 7,B,20: Analyzing Poetry 7,B,22: Appreciating Various Genres 7.. Reading Applications: Literary Text Interpret how mood or meaning is conveyed through word choice, figurative language and syntax. 7,B,23: Figurative Language 7,B,28: Literary Devices 7,B,29: Tone, Mood, & Style 7,B,33: Literary Elements 1.. Writing Processes Prewriting: Generate writing ideas through discussions with others and from printed material, and keep a list of writing ideas. 7,A,12: Writing Process 2.. Writing Processes Prewriting: Conduct background reading, interviews or surveys when appropriate. 7,A,12: Writing Process 3.. Writing Processes Prewriting: Establish a thesis statement for informational writing or a plan for narrative writing. 7,A,12: Writing Process 9/19/ v.1.0

34 Language Arts Grade Writing Processes Prewriting: Determine a 7,A,7: Audience & Purpose purpose and audience. 7,A,12: Writing Process 5.. Writing Processes Prewriting: Use organizational strategies, for example, rough outlines, diagrams, maps, webs and Venn diagrams, to plan writing. 7,A,12: Writing Process 6.. Writing Processes Drafting, Revising and Editing: Organize writing with an effective and engaging introduction, body and a conclusion that summarizes, extends or elaborates on points or ideas in the writing. 7,A,12: Writing Process 7.. Writing Processes Drafting, Revising and Editing: 7,A,12: Writing Process Vary simple, compound and 7,A,13: Sentence Structure II complex sentence structures. 8.. Writing Processes Drafting, Revising and Editing: Group related ideas into paragraphs, including topic sentences following paragraph form, and maintain a consistent focus across paragraphs. 7,A,12: Writing Process 9.. Writing Processes Drafting, Revising and Editing: Use precise language, action verbs, sensory details, colorful modifiers and style as appropriate to audience and purpose. 7,A,5: English Usage 7,A7: Audience & Purpose 7,A,12: Writing Process 10.. Writing Processes Drafting, Revising and Editing: 7,A,12: Writing Process Use available technology to compose text Writing Processes Drafting, Revising and Editing: 7,A,12: Writing Process Reread and analyze clarity of writing. 9/19/ v.1.0

35 Language Arts Grade Writing Processes Drafting, Revising and Editing: Add and delete information and details to better elaborate on a stated central idea and to more effectively accomplish purpose. 7,A,7: Audience & Purpose 7,A,12: Writing Process 13.. Writing Processes Drafting, Revising and Editing: Rearrange words, sentences and paragraphs, and add transitional words and phrases to clarify meaning. 7,A,12: Writing Process 7,A,16: Transitions 14.. Writing Processes Drafting, Revising and Editing: Use resources and reference materials, for example, dictionaries and thesauruses, to select more effective vocabulary. 7,A,12: Writing Process 7,B,21: Resource Materials 15.. Writing Processes Drafting, Revising and Editing: Proofread writing, edit to improve conventions, for example, grammar, spelling, punctuation and capitalization, and identify and correct fragments and run-ons. 7,A,1: Capitalization 7,A,2: Punctuation 7,A,3: Spelling 7,A,4: Editing 7,A,6: Sentence Structure 7,A,9: Spelling Strategies 7,A,12: Writing Process 16.. Writing Processes Drafting, Revising and Editing: Apply tools, for example, rubric, checklist and feedback, to judge the quality of writing Writing Processes Publishing: Prepare for publication (for display or for sharing with others) writing that follows a format appropriate to the purpose, using such techniques as electronic resources, principles of design (margins, tabs, spacing and columns, and graphics) (drawings, charts and graphs, to enhance the final product). 7,A,12: Writing Process 9/19/ v.1.0

36 Language Arts Grade Writing Applications Write narratives that maintain a clear focus and point of view and use sensory details and dialogue to develop plot, character and a specific setting. 2.. Writing Applications Write responses to novels, stories, poems and plays that provide an interpretation, a critique or a reflection and support judgments with specific references to the text. 3.. Writing Applications Write business letters that are formatted to convey ideas, state problems, make requests or give compliments. 4.. Writing Applications Write informational essays or reports, including research, that present a literal understanding of the topic, include specific facts, details and examples from multiple sources, and create an organizing structure appropriate to the purpose, audience and context. 7,A,7: Audience & Purpose 5.. Writing Applications Write persuasive essays that establish a clear position and include relevant information to support ideas. 6.. Writing Applications Produce informal writings, for 7,A,7: Audience & Purpose example, journals, notes and poems, for various purposes. 1.. Writing Conventions Spelling: Spell high-frequency 7,A,3: Spelling words correctly. 7,A,4: Editing 7,A,9: Spelling Strategies 2.. Writing Conventions Punctuation and Capitalization: Use commas, end marks, apostrophes and quotation marks correctly. 7,A,2: Punctuation 7,A,4: Editing 9/19/ v.1.0

37 Language Arts Grade Writing Conventions Punctuation and Capitalization: Use semicolons, colons, hyphens, dashes and brackets correctly. 7,A,2: Punctuation 7,A,4: Editing 4.. Writing Conventions Punctuation and 7,A,1: Capitalization Capitalization: Use correct 7,A,4: Editing capitalization. 5.. Writing Conventions Grammar and Usage: Use all eight parts of speech, for example, noun, pronoun, verb, adverb, adjective, conjunction, preposition, interjection. 7,A,5: English Usage 7,A,11: Parts of Speech 6.. Writing Conventions Grammar and Usage: Use 7,A,5: English Usage dependent and independent clauses. 7.. Writing Conventions Grammar and Usage: Use subject-verb agreement with collective nouns, indefinite pronouns, compound subjects and prepositional phrases. 7,A,5: English Usage 7,A,15: Phrases 8.. Writing Conventions Grammar and Usage: Conjugate regular and irregular verbs in all tenses correctly. 7,A,5: English Usage 1.. Acquisition of Vocabulary Contextual Understanding: Define unknown words through context clues and the author's use of comparison, contrast and cause and effect. 8,B,3: Vocabulary & Context Clues I 8,B,4: Vocabulary & Context Clues II 2.. Acquisition of Vocabulary Conceptual Understanding: Apply knowledge of connotation and denotation to determine the meaning of words. 8,B,32: Denotative & Connotative Meaning 9/19/ v.1.0

38 Language Arts Grade Acquisition of Vocabulary Conceptual Understanding: Identify the relationships of pairs of words in analogical statements, for example, synonyms and antonyms, and infer word meanings from these relationships. 8,B,24: Figurative Language 8,B,25: Synonyms & Antonyms 8,B,29: Literary Devices 8,B,33: Descriptive Language 4.. Acquisition of Vocabulary Conceptual Understanding: Infer the literal and figurative meaning of words and phrases and discuss the function of figurative language, including metaphors, similes and idioms. 8,B,24: Figurative Language 8,B,29: Literary Devices 8,B,33: Descriptive Language 5.. Acquisition of Vocabulary Conceptual Understanding: Examine and discuss the ways that different events, for example, cultural, political, social, technological, and scientific events, impact and change the English language. 6.. Acquisition of Vocabulary Structural Understanding: Use knowledge of Greek, Latin and Anglo-Saxon roots, prefixes and suffixes to understand complex words and new subject-area vocabulary 8,B,2: Prefixes, Suffixes 7.. Acquisition of Vocabulary Tools and Resources: Determine the meanings and pronunciations of unknown words by using dictionaries, thesauruses, glossaries, technology and textual features, such as definitional footnotes or sidebars. 8,B,22: Resource Materials 9/19/ v.1.0

39 Language Arts Grade Reading Process: Concepts of Comprehension Strategies: 8,B,10: Summarizing Apply reading comprehension strategies, including making predictions, comparing and contrasting, recalling and summarizing and making inferences and drawing conclusions. 8,B,12: Predicting 8,B,14: Making Inferences & Drawing Conclusions 8,B,16: Judgments 8,B,21: Comparisons 2.. Reading Process: Concepts of Comprehension Strategies: 8,B,5: Facts & s Answer literal, inferential, evaluative and synthesizing questions to demonstrate comprehension of gradeappropriate print texts and electronic and visual media. 8,B,14: Making Inferences & Drawing Conclusions 3.. Reading Process: Concepts of Self-Monitoring Strategies: Monitor own comprehension by adjusting speed to fit the purpose, or by skimming, scanning, reading on, looking back, note taking or summarizing what has been read so far in text. 4.. Reading Process: Concepts of Independent Reading: Use criteria to choose independent reading materials, for example, personal interest, knowledge of authors and genres or recommendations from others. 5.. Reading Process: Concepts of Independent Reading: Independently read books for various purposes, for example, for enjoyment, for literary experience, to gain information or to perform a task. 1.. Reading Applications: Informational, Technical and Compare and contrast text features, including format and headers of various informational texts in terms of their structure and purpose. 8,B,21: Comparisons 9/19/ v.1.0

40 Language Arts Grade Reading Applications: Informational, Technical and Identify and use the organizational structure of a text, such as chronological, compare-contrast, causeeffect, problem-solution, and evaluate its effectiveness. 8,B,6: Sequencing 8,B,11: Cause & Effect 8,B,21: Comparisons 3.. Reading Applications: Informational, Technical and Compare and contrast the treatment, scope and organization of ideas from different sources on the same topic. 8,B,21: Comparisons 4.. Reading Applications: Informational, Technical and Analyze information found in maps, charts, tables, graphs, diagrams, cutaways and overlays. 8,B,13: Graphic Aids 5.. Reading Applications: Assess the adequacy, 8,B,19: Propaganda Informational, Technical and accuracy and appropriateness of an author's, details, identifying persuasive techniques, for example, bandwagon, testimonial and emotional word repetition, and examples of bias and stereotyping. 8,B,34: Persuasion, Bias, Propaganda, & Stereotyping 6.. Reading Applications: Identify the author's purpose 8,B,18: Point of View & Purpose Informational, Technical and and intended audience for the text. 7.. Reading Applications: Analyze an author's 8,B,18: Point of View & Purpose Informational, Technical and argument, perspective or viewpoint and explain the development of key points. 8,B,19: Propaganda 8,B,34: Persuasion, Bias, Propaganda, & Stereotyping 8.. Reading Applications: Informational, Technical and Recognize how writers cite facts, draw inferences and present opinions in informational text. 8,B,20: Factual Recall 8,B,28: Fact & Opinion 9/19/ v.1.0

41 Language Arts Grade Reading Applications: Informational, Technical and Distinguish the characteristics of consumer materials (for example, warranties, product information, instructional materials) functional or workplace documents (for example, job-related materials, memoranda, instructions) and public documents )for example speeches or newspaper editorials). 1.. Reading Applications: Literary Text Identify and explain various types of characters and how their interactions and conflicts affect the plot. 8,B,15: Generalizations 8,B,16: Judgments 8,B,17: Plot, Setting, Character, & Mood 2.. Reading Applications: Literary Text Analyze the influence of 8,B,17: Plot, Setting, Character, & Mood setting in relation to other literary elements. 3.. Reading Applications: Literary Text Explain how authors pace 8,B,6: Sequencing action and use subplots, 8,B,17: Plot, Setting, Character, & Mood parallel episodes and climax. 4.. Reading Applications: Literary Text Compare and contrast different points of view,for example, first person and third person limited, omniscient, objective and subjective, and explain how voice affects literary text. 5.. Reading Applications: Literary Text Identify and explain universal themes across different works by the same author and by different authors. 6.. Reading Applications: Literary Text Explain how an author's choice of genre affects the expression of a theme or topic. 8,B,17: Plot, Setting, Character, & Mood 8,B,23: Appreciating Various Genre 9/19/ v.1.0

42 Language Arts Grade Reading Applications: Literary Text Explain how an author's choice of genre affects the expression of a theme or topic. 8,B,17: Plot, Setting, Character, & Mood 8,B,23: Appreciating Various Genre 8.. Reading Applications: Literary Text Explain ways in which the author conveys mood and tone through word choice, figurative language, and syntax. 8,B,17: Plot, Setting, Character, & Mood 8,B,24: Figurative Language 8,B,29: Literary Devices 8,B,30: Tone, Mood, & Style 9.. Reading Applications: Literary Text Examine symbols used in 8,B,17: Plot, Setting, Character, & Mood literary texts. 8,B,29: Literary Devices 1 Number, Number Sense and Operations: Number and Number Systems Identify and generate equivalent forms of whole numbers; e.g., 36, , 9 x 4, 46-10, number of inches in a yard. 3,C,25: & Expanded Number Forms 3,C,41: & Expanded Number Forms II 2.a.. Number, Number Sense and Operations: Number and Number Systems Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example: Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games. 3,C,25: & Expanded Number Forms 3,C,41: & Expanded Number Forms II 2.b.. Number, Number Sense and Operations: Number and Number Systems Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example: Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games. 3,C,2: Place Value 3,C,25: & Expanded Number Forms 3,C,41: & Expanded Number Forms II 9/19/ v.1.0

43 Mathematics Grade 3 2.c.. Number, Number Sense and Operations: Number and Number Systems Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example: Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games. 2.d.. Number, Number Sense and Operations: Number and Number Systems Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example: Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games. 3,C,26: Decimal Place Value Models 3 Number, Number Sense and Operations: Number and Number Systems Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, greater than or = to, less than or = to. 3,C,1: Whole Number Comparisons 4 Number, Number Sense and Count money and make 3,C,28: Money Applications Operations: Number and Number change using coins and paper Systems bills to ten dollars. 5 Number, Number Sense and Operations: Number and Number Systems Represent fractions and mixed numbers using words, numerals and physical models. 3,C,4: Fraction Models 6 Number, Number Sense and Operations: Number and Number Systems Compare and order commonly used fractions and mixed numbers using number lines, models (such as fraction circles or bars), points of reference (such as more or less than 1/2), and equivalent forms using physical or visual models. 3,C,38: Fractions & Decimals Ordering 9/19/ v.1.0

44 Mathematics Grade 3 7 Number, Number Sense and Operations: Number and Number Systems Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red. 3,C,4: Fraction Models 3,C,26: Decimal Place Value Models 8.a.. Number, Number Sense and Operations: Meaning of Operations Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example: Use conventional mathematical symbols to write equations for word problems involving multiplication. 3,C,16: Multiplication Problems 3,C,33: Word Problems 8.b.. Number, Number Sense and Operations: Meaning of Operations Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example: Use conventional mathematical symbols to write equations for word problems involving multiplication. 9.a.. Number, Number Sense and Operations: Meaning of Operations Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model. For example: Translate contextual situations involving division into conventional mathematical symbols. 9.b.. Number, Number Sense and Operations: Meaning of Operations Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model. For example: Translate contextual situations involving division into conventional mathematical symbols. 9/19/ v.1.0

45 Mathematics Grade 3 10.a.. Number, Number Sense and Operations: Meaning of Operations Explain and use relationships between operations, such as: Relate addition and subtraction as inverse operations. 10.b.. Number, Number Sense and Operations: Meaning of Operations Explain and use relationships between operations, such as: Relate addition and subtraction as inverse operations. 10.c.. Number, Number Sense and Operations: Meaning of Operations Explain and use relationships between operations, such as: Relate addition and subtraction as inverse operations. 10.d.. Number, Number Sense and Operations: Meaning of Operations Explain and use relationships between operations, such as: Relate addition and subtraction as inverse operations. 11 Number, Number Sense and Operations: Meaning of Operations Model and use the commutative and associative properties for addition and multiplication. 3,C,5: Number Sentences: Missing Elements 12 Number, Number Sense and Operations: Computation and Estimation Add and subtract whole numbers with and without regrouping. 3,C,19: Number Sentences I 3,C,20: Number Sentences II 3,C,29: Addition (Computation) 3,C,30: Subtraction (Computation) 13 Number, Number Sense and Operations: Computation and Estimation Demonstrate fluency in multiplication facts through 10 and corresponding division facts. 3,C,31: Multiplication (Computation) 14 Number, Number Sense and Operations: Computation and Estimation Multiply and divide 2- and 3- digit numbers by a single-digit number, without remainders for division. 3,C,31: Multiplication (Computation) 9/19/ v.1.0

46 Mathematics Grade 3 15 Number, Number Sense and Operations: Computation and Estimation Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates. 3,C,24: Determining Reasonable Solutions 1.a.. Measurement: Measurement Units Identify and select appropriate units for measuring: Length - miles, kilometers and other units of measure as appropriate. 3,C,11: Using Measurement 3,C,12: Metric & Customary Measurement 1.b.. Measurement: Measurement Units Identify and select appropriate units for measuring: Length - miles, kilometers and other units of measure as appropriate. 3,C,11: Using Measurement 3,C,12: Metric & Customary Measurement 1.c.. Measurement: Measurement Units Identify and select appropriate units for measuring: Length - miles, kilometers and other units of measure as appropriate. 3,C,11: Using Measurement 3,C,12: Metric & Customary Measurement 1.d.. Measurement: Measurement Units Identify and select appropriate units for measuring: Length - miles, kilometers and other units of measure as appropriate. 2 Measurement: Measurement Units Establish personal or common referents to include additional units; e.g., a gallon container of milk; a postage stamp is about a square inch. 3,C,11: Using Measurement 3,C,12: Metric & Customary Measurement 3 Measurement: Measurement Units Tell time to the nearest minute 3,C,11: Using Measurement and find elapsed time using a 3,C,34: Elapsed Time calendar or a clock. 3,C,40: Elapsed Time II 4 Measurement: Measurement Units Read thermometers in both Fahrenheit and Celsius scales. 9/19/ v.1.0

47 Mathematics Grade 3 5 Measurement: Use Measurement Techniques and Tools Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest 1/2 or 1/4 unit as appropriate. 3,C,11: Using Measurement 3,C,12: Metric & Customary Measurement 6 Measurement: Use Measurement Techniques and Tools Use appropriate measurement tools and techniques to construct a figure or approximate an amount of specified length, weight or volume (capacity); e.g., construct a rectangle with length 2 1/2 inches and width 3 inches, fill a measuring cup to the 3/4 cup mark. 3,C,11: Using Measurement 3,C,12: Metric & Customary Measurement 7 Measurement: Use Measurement Make estimates for perimeter, Techniques and Tools area and volume using links, tiles, cubes and other models. 1 Geometry and Spatial Sense: Characteristics and Properties Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face. 3,C,8: Classifying Objects 3,C,9: 2-D & 3-D Figures 2.a.. Geometry and Spatial Sense: Characteristics and Properties Identify and describe the relative size of angles with respect to right angles as follows: Use physical models, like straws, to make different sized angles by opening and closing the sides, not by changing the side lengths. 2.b.. Geometry and Spatial Sense: Characteristics and Properties Identify and describe the relative size of angles with respect to right angles as follows: Use physical models, like straws, to make different sized angles by opening and closing the sides, not by changing the side lengths. 9/19/ v.1.0

48 Mathematics Grade 3 3 Geometry and Spatial Sense: Find and name locations on a 3,C,35 Geometry Spatial Sense Spatial Relationships labeled grid or coordinate system; e.g., a map or graph. 4 Geometry and Spatial Sense: Draw lines of symmetry to Transformations and Symmetry verify symmetrical twodimensional shapes. 5 Geometry and Spatial Sense: Visualization and Geometric Models Build a three-dimensional model of an object composed of cubes; e.g., construct a model based on an illustration or actual object. 1 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Extend multiplicative and growing patterns, and describe the pattern or rule in words. 2 Patterns, Functions and Algebra: Analyze and replicate 3,C,3: Skip Counting Use Patterns, Relations and arithmetic sequences with and 3,C,6: Patterning Functions without a calculator. 3 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Use patterns to make predictions, identify relationships, and solve problems. 3,C,3: Skip Counting 3,C,6: Patterning 4 Patterns, Functions and Algebra: Use Algebraic Representations Model problem situations using objects, pictures, tables, numbers, letters and other symbols. 3,C,3: Skip Counting 3,C,5: Number Sentences: Missing Elements 3,C,6: Patterning 3,C,21: Number Sentences Using Graphics 3,C,36: Missing Information 5 Patterns, Functions and Algebra: Use Algebraic Representations Write, solve and explain simple mathematical statements, such as 7 + x > 8 or y + 8 = 10. 3,C,5: Number Sentences: Missing Elements 3,C,21: Number Sentences Using Graphics 3,C,36: Missing Information 6 Patterns, Functions and Algebra: Express mathematical Use Algebraic Representations relationships as equations and inequalities. 7 Patterns, Functions and Algebra: Create tables to record, 3,C,13: Bar & Picture Graphs Analyze Change organize and analyze data to 3,C,22: Charts & Graphs discover patterns and rules. 9/19/ v.1.0

49 Mathematics Grade 3 8 Patterns, Functions and Algebra: Analyze Change Identify and describe quantitative changes, especially those involving addition and subtraction; e.g., the height of water in a glass becoming 1 centimeter lower each week due to evaporation. 1 Data Analysis and Probability: Data Collection Collect and organize data from an experiment, such as recording and classifying observations or measurements, in response to a question posed. 2 Data Analysis and Probability: Data Collection Draw and interpret picture graphs in which a symbol or picture represents more than one object. 3,C,13: Bar & Picture Graphs 3,C,22: Charts & Graphs 3 Data Analysis and Probability: Data Read, interpret and construct 3,C,13: Bar & Picture Graphs Collection bar graphs with intervals greater than one. 4 Data Analysis and Probability: Data Collection Support a conclusion or prediction orally and in writing, using information in a table or graph. 3,C,13: Bar & Picture Graphs 3,C,22: Charts & Graphs 5 Data Analysis and Probability: Data Match a set of data with a 3,C,13: Bar & Picture Graphs Collection graphical representation of 3,C,22: Charts & Graphs the data. 6 Data Analysis and Probability: Data Collection Translate information freely among charts, tables, line plots, picture graphs and bar graphs; e.g., create a bar graph from the information in a chart. 3,C,13: Bar & Picture Graphs 3,C,22: Charts & Graphs 7 Data Analysis and Probability: Data Analyze and interpret Collection information represented on a timeline. 9/19/ v.1.0

50 Mathematics Grade 3 8 Data Analysis and Probability: Identify the mode of a data set Statistical Methods and describe the information it gives about a data set. 9 Data Analysis and Probability: Probability Conduct a simple experiment or simulation of a simple event, record the results in a chart, table or graph, and use the results to draw conclusions about the likelihood of possible outcomes. 10 Data Analysis and Probability: Probability Use physical models, pictures, diagrams and lists to solve problems involving possible arrangements or combinations of two to four objects. 1.a.. Number, Number Sense and Operations: Number and Number Systems Identify and generate equivalent forms of fractions and decimals. For example: Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10, "five tenths, " 0.5, shaded rectangles with half, and five tenths. 1.b.. Number, Number Sense and Operations: Number and Number Systems Identify and generate equivalent forms of fractions and decimals. For example: Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10, "five tenths, " 0.5, shaded rectangles with half, and five tent 9/19/ v.1.0

51 Mathematics Grade 4 2 Number, Number Sense and Operations: Number and Number Systems Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths. 4,C,1: & Expanded Number Forms: Decimals 4,C,2: Comparing Whole Numbers 4,C,28: & Expanded Number Forms: Whole Numbers 3 Number, Number Sense and Round whole numbers to a 4,C,4: Rounding Operations: Number and Number given place value. Systems 4 Number, Number Sense and Operations: Number and Number Systems Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite. 4,C,39: Number Properties: Prime, Composite, Factor, or Multiple 5 Number, Number Sense and Use models and points of 4,C,7: Fraction Models Operations: Number and Number reference to compare 4,C,10: Using Number Lines Systems commonly used fractions. 6 Number, Number Sense and Operations: Meaning of Operations Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as 5 x 47 = 5 x x 7 = = Number, Number Sense and Operations: Meaning of Operations Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money. 4,C,21: Division Applications: Whole Numbers 4,C,23: Problem Solving 4,C,25: Problem Solving 4,C,32: Problem Solving 8 Number, Number Sense and Operations: Computation and Estimation Solve problems involving counting money and making change, using both coins and paper bills. 9/19/ v.1.0

52 Mathematics Grade 4 9 Number, Number Sense and Estimate the results of 4,C,22: Estimation Operations: Computation and Estimation computations involving whole numbers, fractions and decimals, using a variety of strategies. 4,C,27: Determining Reasonableness of Answers 4,C,31: Reasonable Estimations 10 Number, Number Sense and Operations: Computation and Estimation Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators. 4,C,18: Addition Applications: Decimals 4,C,19: Subtraction Applications: Decimals 4,C,33: Fractions: Addition & Subtraction 11 Number, Number Sense and Develop and explain Operations: Computation and strategies for performing Estimation computations mentally. 12 Number, Number Sense and Operations: Computation and Estimation Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem. 4,C,18: Addition Applications: Decimals 4,C,19: Subtraction Applications: Decimals 4,C,20: Multiplication Applications: Whole Numbers 4,C,21: Division Applications: Whole Numbers 4,C,23: Problem Solving 4,C,25: Problem Solving 4,C,32: Problem Solving 4,C,33: Fractions: Addition & Subtraction 4,C,34: Fractions: Multiplication & Division 4,C,35: Addition 4,C,36: Subtraction 13 Number, Number Sense and Operations: Computation and Estimation Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator. 4,C,18: Addition Applications: Decimals 4,C,19: Subtraction Applications: Decimals 4,C,20: Multiplication Applications: Whole Numbers 4,C,21: Division Applications: Whole Numbers 4,C,23: Problem Solving 4,C,25: Problem Solving 4,C,32: Problem Solving 4,C,33: Fractions: Addition & Subtraction 4,C,34: Fractions: Multiplication & Division 4,C,35: Addition 4,C,36: Subtraction 9/19/ v.1.0

53 Mathematics Grade 4 14 Number, Number Sense and Operations: Computation and Estimation Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten. 4,C,20: Multiplication Applications: Whole Numbers 4,C,21: Division Applications: Whole Numbers 4,C,35: Addition 4,C,36: Subtraction 1 Measurement: Measurement Units Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher. 4,C,13: Metric & Customary Measurement 4,C,30: Measurement 2 Measurement: Measurement Units Demonstrate and describe perimeter as surrounding and area as covering a twodimensional shape, and volume as filling a threedimensional object. 3.a.. Measurement: Measurement Units Identify and select appropriate units to measure: Perimeter - string or links (inches or centimeters). 4,C,14: Perimeter 3.b.. Measurement: Measurement Units Identify and select appropriate units to measure: Perimeter - string or links (inches or centimeters). 4,C,15: Area 4,C,24: Geometric Problem Solving 3.c.. Measurement: Measurement Units Identify and select appropriate units to measure: Perimeter - string or links (inches or centimeters). 4 Measurement: Use Measurement Techniques and Tools Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume. 4,C,14: Perimeter 9/19/ v.1.0

54 Mathematics Grade 4 5 Measurement: Use Measurement Techniques and Tools Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons. 4,C,13: Metric & Customary Measurement 4,C,30: Measurement 6 Measurement: Use Measurement Techniques and Tools Write, solve and verify solutions to multi-step problems involving measurement. 1 Geometry and Spatial Sense: Characteristics and Properties Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines. 2 Geometry and Spatial Sense: Characteristics and Properties Describe, classify, compare and model two- and threedimensional objects using their attributes. 4,C,11: 2-D & 3-D Figures 3 Geometry and Spatial Sense: Characteristics and Properties Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids. 4,C,11: 2-D & 3-D Figures 4 Geometry and Spatial Sense: Characteristics and Properties Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles). 4,C,29: Geometry & Spatial Sense 4,C,38: Angles: Acute, Obtuse, Right, & Straight 5 Geometry and Spatial Sense: Describe points, lines and Spatial Relationships planes, and identify models in the environment. 6 Geometry and Spatial Sense: Spatial Relationships Specify locations and plot ordered pairs on a coordinate plane, using first quadrant points. 4,C,40: Ordered Pairs 9/19/ v.1.0

55 Mathematics Grade 4 7 Geometry and Spatial Sense: Transformations and Symmetry Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if 2 shapes are congruent. 4,C,29: Geometry & Spatial Sense 8 Geometry and Spatial Sense: Use geometric models to 4,C,14: Perimeter Visualization and Geometric Models solve problems in other areas of mathematics, such as number (multiplication/ division) and measurement (area, perimeter, border). 4,C,15: Area 4,C,24: Geometric Problem Solving 1 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications. 4,C,6: Skip Counting 4,C,9: Patterning 2 Patterns, Functions and Algebra: Represent and analyze Use Patterns, Relations and patterns and functions using Functions words, tables and graphs. 3 Patterns, Functions and Algebra: Use Algebraic Representation Construct a table of values to solve problems associated with a mathematical relationship. 4 Patterns, Functions and Algebra: Use rules and variables to 4,C,6: Skip Counting Use Algebraic Representation describe patterns and other 4,C,9: Patterning relationships. 5 Patterns, Functions and Algebra: Represent mathematical Use Algebraic Representation relationships with equations or inequalities. 6 Patterns, Functions and Algebra: Analyze Change Describe how a change in one variable affects the value of a related variable; e.g., as one increases the other increases or as one increases the other decreases. 9/19/ v.1.0

56 Mathematics Grade 4 1 Data Analysis and Probability: Data Create a plan for collecting Collection data for a specific purpose. 2 Data Analysis and Probability: Data Represent and interpret data 4,C,17: Interpreting Graphs Collection using tables, bar graphs, line 4,C,26: Charts & Graphs plots and line graphs. 3 Data Analysis and Probability: Data Interpret and construct Venn Collection diagrams to sort and describe data. 4 Data Analysis and Probability: Data Collection Compare different representations of the same data to evaluate how well each representation shows important aspects of the data, and identify appropriate ways to display the data. 5 Data Analysis and Probability: Data Collection Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs. 6 Data Analysis and Probability: Statistical Methods Describe the characteristics of a set of data based on a graphical representation, such as range of the data, clumps of data, and holes in the data. 7 Data Analysis and Probability: Identify the median of a set of Statistical Methods data and describe what it indicates about the data. 8 Data Analysis and Probability: Use range, median and mode Statistical Methods to make comparisons among related sets of data. 9 Data Analysis and Probability: Probability Conduct simple probability experiments and draw conclusions from the results; e.g., rolling number cubes or drawing marbles from a bag. 4,C,16: Possible Outcomes 9/19/ v.1.0

57 Mathematics Grade 4 10 Data Analysis and Probability: Probability Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles. 4,C,16: Possible Outcomes 11 Data Analysis and Probability: Probability Relate the concepts of impossible and certain-tohappen events to the numerical values of 0 (impossible) and 1 (certain). 4,C,16: Possible Outcomes 12 Data Analysis and Probability: Probability Place events in order of likelihood and use a diagram or appropriate language to compare the chance of each event occurring; e.g., impossible, unlikely, equal, likely, certain. 4,C,16: Possible Outcomes 13 Data Analysis and Probability: Probability List and count all possible combinations using one member from each of several sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3 shirts, 2 shorts and 2 pairs of shoes. 4,C,16: Possible Outcomes 1 Number, Number Sense and Operations: Number and Number Systems Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-towhole. 2 Number, Number Sense and Operations: Number and Number Systems Use various forms of one" to demonstrate the equivalence of fractions; e.g.18/24 = 9/12 x 2/2 = 3/4 x 6/6." 5,C,3: Fractions I 5,C,4: Fractions II 3 Number, Number Sense and Identify and generate Operations: Number and Number equivalent forms of fractions, Systems decimals and percents. 9/19/ v.1.0

58 Mathematics Grade 5 4 Number, Number Sense and Operations: Number and Number Systems Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. 5,C,2: Rounding 5 Number, Number Sense and Recognize and identify perfect Operations: Number and Number squares and their roots. Systems 6 Number, Number Sense and Operations: Meaning of Operations Represent and compare numbers less than 0 by extending the number line and using familiar applications; e. g., temperature, owing money. 5,C,1: Compare & Order Numbers 5,C,8: Number Lines 5,C,41: Money Applications 7 Number, Number Sense and Operations: Meaning of Operations Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 8 Number, Number Sense and Identify and use relationships Operations: Meaning of Operations between operations to solve problems. 9 Number, Number Sense and Operations: Meaning of Operations Use order of operations, including use of parentheses, to simplify numerical expressions. 5,C,6: Algebraic Expressions 5,C,32: Algebraic Solution Sentences 10 Number, Number Sense and Justify why fractions need Operations: Meaning of Operations common denominators to be added or subtracted. 11 Number, Number Sense and Operations: Meaning of Operations Explain how place value is related to addition and subtraction of decimals; e.g., ; the two tenths is added to the one tenth because they are both tenths. 9/19/ v.1.0

59 Mathematics Grade 5 12 Number, Number Sense and Operations: Computation and Estimation Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 5,C,24: Subtraction Problems I 5,C,44: Addition Problems II 5,C,45: Subtraction Problems II 13 Number, Number Sense and Estimate the results of 5,C,27: Estimation Operations: Computation and Estimation computations involving whole numbers, fractions and decimals, using a variety of strategies. 5,C,28: Whole Numbers: Problem Solving Strategies 5,C,40: Estimation of Operations 5,C,48: Logic Problems 1 Measurement: Measurement Units Identify and select appropriate units to measure angles; i.e., degrees. 2 Measurement: Measurement Units Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. 5,C,9: Ordered Pairs 3 Measurement: Measurement Units Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects. 5,C,15: Area & Volume 4 Measurement: Measurement Units Demonstrate understanding of the differences among linear units, square units and cubic units. 5,C,13: Metric & Customary Measurement 5,C,14: Perimeter & Circumference 5,C,15: Area & Volume 5 Measurement: Use Measurement Techniques and Tools Make conversions within the same measurement system while performing computations. 5,C,16: Metric Conversions 5,C,17: Customary Conversions 6 Measurement: Use Measurement Techniques and Tools Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 5,C,14: Perimeter & Circumference 5,C,15: Area & Volume 5,C,29: Geometric Problem Solving I 9/19/ v.1.0

60 Mathematics Grade 5 7 Measurement: Use Measurement Techniques and Tools Use benchmark angles (e.g.; 45 degrees, 90 degrees, 120 degrees) to estimate the measure of angles, and use a tool to measure and draw angles. 1 Geometry and Spatial Sense: Characteristics and Properties Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e. g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of pi. 5,C,10: Geometry: 2-D & 3-D Figures 5,C,14: Perimeter & Circumference 2 Geometry and Spatial Sense: Characteristics and Properties Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. 3 Geometry and Spatial Sense: Label vertex, rays, interior and Characteristics and Properties exterior for an angle. 4 Geometry and Spatial Sense: Describe and use properties 5,C,11: Congruence & Symmetry Characteristics and Properties of congruent figures to solve problems. 5 Geometry and Spatial Sense: Characteristics and Properties Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. 6 Geometry and Spatial Sense: Spatial Relationships Extend understanding of coordinate system to include points whose x or y values may be negative numbers. 5,C,9: Ordered Pairs 7 Geometry and Spatial Sense: Visualization and Geometric Models Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. 9/19/ v.1.0

61 Mathematics Grade 5 8 Geometry and Spatial Sense: Visualization and Geometric Models Predict what threedimensional object will result from folding a twodimensional net, then confirm the prediction by folding the net. 1 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 2 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Use calculators or computers to develop patterns, and generalize them using tables and graphs. 5,C,7: Patterning 3 Patterns, Functions and Algebra: Use Algebraic Representations Use variables as unknown quantities in general rules when describing patterns and other relationships. 5,C,7: Patterning 4 Patterns, Functions and Algebra: Use Algebraic Representations Create and interpret the meaning of equations and inequalities representing problem situations. 5 Patterns, Functions and Algebra: Use Algebraic Representations Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 6 Patterns, Functions and Algebra: Analyze Change Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph. 1 Data Analysis and Probability: Data Read, construct and interpret Collection frequency tables, circle graphs and line graphs. 9/19/ v.1.0

62 Mathematics Grade 5 2 Data Analysis and Probability: Data Collection Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 3 Data Analysis and Probability: Data Collection Read and interpret increasingly complex displays of data, such as double bar graphs. 4 Data Analysis and Probability: Data Collection Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 5 Data Analysis and Probability: Data Collection Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. 6, Data Analysis and Probability: Statistical Methods Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 5,C,22: Determining Mean 7 Data Analysis and Probability: List and explain all possible 5,C,18: Probability: Possible Outcomes Probability outcomes in a given situation. 8 Data Analysis and Probability: Probability Identify the probability of events within a simple experiment, such as three chances out of eight. 5,C,21: Probability I 5,C,31: Probability II 9 Data Analysis and Probability: Probability Use 0, 1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. 5,C,21: Probability I 9/19/ v.1.0

63 Mathematics Grade 5 10 Data Analysis and Probability: Probability Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. 11 Data Analysis and Probability: Make predictions based on 5,C,18: Probability: Possible Outcomes Probability experimental and theoretical 5,C,21: Probability I probabilities. 5,C,31: Probability II 1 Number, Number Sense and Operations: Number and Number Systems Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 25 ), and explain why squared" means "second power" and "cubed" means "third power." 6,C,4: Exponents & Notation 2.a.. Number, Number Sense and Operations: Number and Number Systems Find and use the prime factorization of composite numbers. For example: Use the prime factorization to recognize the greatest common factor (GCF). 6,C,6: Least Common Multiple & Greatest Common Factor 2.b.. Number, Number Sense and Operations: Number and Number Systems Find and use the prime factorization of composite numbers. For example: Use the prime factorization to recognize the greatest common factor (GCF). 6,C,6: Least Common Multiple & Greatest Common Factor 2.c.. Number, Number Sense and Operations: Number and Number Systems Find and use the prime factorization of composite numbers. For example: Use the prime factorization to recognize the greatest common factor (GCF). 6,C,5: Factoring 6,C,6: Least Common Multiple & Greatest Common Factor 3 Number, Number Sense and Operations: Number and Number Systems Explain why a number is referred to as being "rational" and recognize that the expression a/b can mean a parts of size 1/b each, a divided by b, or the ratio of a to b. 9/19/ v.1.0

64 Mathematics Grade 6 4 Number, Number Sense and Operations: Number and Number Systems Describe what it means to find a specific percent of a number, using real-life examples. 5, Number, Number Sense and Operations: Number and Number Systems Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than Number, Number Sense and Operations: Meaning of Operations Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions. 7 Number, Number Sense and Operations: Meaning of Operations Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 yards on the first carry but gains 8 yards on the second carry, what is the net gain/loss? 6,C,26: Addition: Word Problems 6,C,27: Subtraction: Word Problems 6,C,28: Multiplication: Word Problems 6,C,29: Division: Word Problems 8 Number, Number Sense and Operations: Meaning of Operations Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take 2 2/3 divided by 1/6. 9 Number, Number Sense and Operations: Meaning of Operations Give examples of how ratios are used to represent comparisons; e.g., part-topart, part-to-whole, whole-topart. 6,C,9: Ratios 10 Number, Number Sense and Operations: Meaning of Operations Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 divided by 1/2 = 12. 6,C,29: Division: Word Problems 6,C,46: Division 9/19/ v.1.0

65 Mathematics Grade 6 11, Number, Number Sense and Operations: Computation and Estimation Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. 6,C,42: Multiplication 6,C,44: Subtraction 6,C,45: Addition 6,C,46: Division 12 Number, Number Sense and Operations: Computation and Estimation Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. 6,C,42: Multiplication 6,C,44: Subtraction 6,C,45: Addition 6,C,46: Division 13 Number, Number Sense and Estimate reasonable solutions 6,C,30: Estimation I Operations: Computation and Estimation to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 approximately = 2 and 4.23 x 5.8 approximately = Number, Number Sense and Operations: Computation and Estimation Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. 6,C,9: Ratios 6,C,37: Determining Reasonable Solutions 6,C,43: Estimation II 6,C,51: Logic Problems 15 Number, Number Sense and Operations: Computation and Estimation Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100. 6,C,37: Determining Reasonable Solutions 1 Measurement: Measurement Units Understand and describe the 6,C,20: Area & Volume difference between surface area and volume. 2 Measurement: Use Measurement Techniques and Tools Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4 circle. 6,C,19: Perimeter & Circumference 6,C,20: Area & Volume 9/19/ v.1.0

66 Mathematics Grade 6 3.a.. Measurement: Use Measurement Techniques and Tools Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: Estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; 3.b.. Measurement: Use Measurement Techniques and Tools Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: Estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; 6,C,19: Perimeter & Circumference 6,C,20: Area & Volume 6,C,32: Geometric Problem Solving I 4 Measurement: Use Measurement Techniques and Tools Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room. 6,C,19: Perimeter & Circumference 6,C,20: Area & Volume 6,C,32: Geometric Problem Solving I 5 Measurement: Use Measurement Techniques and Tools Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters. 6,C,19: Perimeter & Circumference 6,C,20: Area & Volume 6,C,32: Geometric Problem Solving I 6 Measurement: Use Measurement Techniques and Tools Describe what happens to the perimeter and area of a twodimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled. 6,C,19: Perimeter & Circumference 6,C,20: Area & Volume 6,C,32: Geometric Problem Solving I 9/19/ v.1.0

67 Mathematics Grade 6 1 Geometry and Spatial Sense: Characteristics and Properties Classify and describe twodimensional and threedimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/ parallel sides, congruent angles/sides. 6,C,13: Geometry I: 2-D & 3-D Figures 6,C,15: Similar, Congruent, & Symmetrical Figures I 6,C,33: Similar, Congruent, & Symmetrical Figures II 6,C,41: Geometric Problem Solving II: Shapes & Angles 2 Geometry and Spatial Sense: Characteristics and Properties Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate. 6,C,41: Geometric Problem Solving II: Shapes & Angles 6,C,50: Faces, Vertices, & Edges 3 Geometry and Spatial Sense: Use multiple classification 6,C,41: Geometric Problem Solving II: Characteristics and Properties criteria to classify triangles; e. Shapes & Angles g., right scalene triangle. 4 Geometry and Spatial Sense: Characteristics and Properties Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting. 5 Geometry and Spatial Sense: Spatial Relationships Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations. 6,C,14: Transformations 6 Geometry and Spatial Sense: Transformations and Symmetry Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other. 7 Geometry and Spatial Sense: Visualization and Geometric Models Build three-dimensional objects with cubes, and sketch the two-dimensional representations of each side; i.e., projection sets. 9/19/ v.1.0

68 Mathematics Grade 6 1, Patterns, Functions and Algebra: Use Patterns, Relations and Functions Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. 2 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Use words and symbols to describe numerical and geometric patterns, rules and functions. 3 Patterns, Functions and Algebra: Use Algebraic Representations Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(l + w) or 2l + 2w. 6,C,7: Algebraic Expressions 4 Patterns, Functions and Algebra: Use Algebraic Representations Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs. 6,C,10: Linear Equations 5 Patterns, Functions and Algebra: Produce and interpret graphs Use Algebraic Representations that represent the relationship between two variables. 6 Patterns, Functions and Algebra: Use Algebraic Representations Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations. 6,C,7: Algebraic Expressions 6,C,35: Algebraic Solution Sentences 7 Patterns, Functions and Algebra: Analyze Change Identify and describe situations with constant or varying rates of change, and compare them. 8 Patterns, Functions and Algebra: Analyze Change Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change. 9/19/ v.1.0

69 Mathematics Grade 6 1 Data Analysis and Probability: Data Read, construct and interpret 6,C,24: Interpreting Graphs Collection line graphs, circle graphs and 6,C,36: Graphs, Charts, & Data Management histograms. 6,C,48: Interpreting Data 2 Data Analysis and Probability: Data Collection Select, create and use graphical representations that are appropriate for the type of data collected. 3 Data Analysis and Probability: Data Collection Compare representations of the same data in different types of graphs, such as a bar graph and circle graph. 4 Data Analysis and Probability: Statistical Methods Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). 6,C,25: Determining Mean 5 Data Analysis and Probability: Statistical Methods Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers. 6 Data Analysis and Probability: Make logical inferences from 6,C,51: Logic Problems Statistical Methods statistical data. 7 Data Analysis and Probability: Probability Design an experiment to test a theoretical probability and explain how the results may vary. 1 Number, Number Sense and Demonstrate an 7,C,5: Scientific Notation Operations: Number and Number Systems understanding of place value using powers of 10 and write large numbers in scientific notation. 7,C,37: & Expanded Number Forms 2 Number, Number Sense and Explain the meaning of 7,C,4: Exponential Notation Operations: Number and Number exponents that are negative 7,C,5: Scientific Notation Systems or 0. 7,C,36: Number Systems & Functions 9/19/ v.1.0

70 Mathematics Grade 7 3 Number, Number Sense and Operations: Number and Number Systems Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non-terminating and non-repeating decimals. 7,C,4: Exponential Notation 7,C,55: Square Roots 4 Number, Number Sense and Operations: Meaning of Operations Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. 7,C,11: Algebraic Expressions 5 Number, Number Sense and Operations: Meaning of Operations Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can result in a lesser value. 6 Number, Number Sense and Operations: Computation and Estimation Simplify numerical expressions involving integers and use integers to solve reallife problems. 7,C,4: Exponential Notation 7,C,11: Algebraic Expressions 7 Number, Number Sense and Operations: Computation and Estimation Solve problems using the appropriate form of a rational number (fraction, decimal or percent). 7,C,3: Fractions, Decimals, & Percents: Conversions & Problem Solving 7,C,41: Problem Solving 7,C,51: Determining Discounts 8 Number, Number Sense and Operations: Computation and Estimation Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use. 7,C,41: Problem Solving 7,C,51: Determining Discounts 9 Number, Number Sense and Represent and solve problem 7,C,4: Exponential Notation Operations: Computation and Estimation situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares). 7,C,5: Scientific Notation 7,C,36: Number Systems & Functions 7,C,55: Square Roots 9/19/ v.1.0

71 Mathematics Grade 7 1 Measurement: Measurement Units Select appropriate units for measuring derived measurements; e.g., miles per hour, revolutions per minute. 2 Measurement: Measurement Units Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters. 7,C,15: Metric & Customary Measurement 7,C,29: Measurement 3 Measurement: Use Measurement Estimate a measurement to a 7,C,15: Metric & Customary Measurement Techniques and Tools greater degree of precision than the tool provides. 4 Measurement: Use Measurement Techniques and Tools Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system. 5 Measurement: Use Measurement Techniques and Tools Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems. 7,C,15: Metric & Customary Measurement 7,C,29: Measurement 6 Measurement: Use Measurement Techniques and Tools Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. 7,C,16: Area & Volume 7,C,26: Geometry: Basic Concepts 7 Measurement: Use Measurement Techniques and Tools Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors. 7,C,16: Area & Volume 7,C,26: Geometry: Basic Concepts 9/19/ v.1.0

72 Mathematics Grade 7 8 Measurement: Use Measurement Techniques and Tools Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas. 9 Measurement: Use Measurement Techniques and Tools Describe what happens to the surface area and volume of a three- dimensional object when the measurements of the object are changed; e.g., length of sides are doubled. 1 Geometry and Spatial Sense: Characteristics and Properties Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. 7,C,13: Similar, Congruent, & Symmetrical Figures 7,C,14: Geometry & Figure Construction 7,C,27: Similar, Congruent, & Symmetrical Figures II 2.a.. Geometry and Spatial Sense: Characteristics and Properties Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example: Determine when one set of figures is a subset of another; e.g., all squares are rectangles. 2.b.. Geometry and Spatial Sense: Characteristics and Properties Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example: Determine when one set of figures is a subset of another; e.g., all squares are rectangles. 9/19/ v.1.0

73 Mathematics Grade 7 3.a.. Geometry and Spatial Sense: Characteristics and Properties Use and demonstrate understanding of the properties of triangles. For example: Use Pythagorean Theorem to solve problems involving right triangles. 3.b.. Geometry and Spatial Sense: Characteristics and Properties Use and demonstrate understanding of the properties of triangles. For example: Use triangle angle sum relationships to solve problems. 4 Geometry and Spatial Sense: Characteristics and Properties Determine necessary conditions for congruence of triangles. 7,C,13: Similar, Congruent, & Symmetrical Figures 7,C,14: Geometry & Figure Construction 7,C,27: Similar, Congruent, & Symmetrical Figures II 5 Geometry and Spatial Sense: Characteristics and Properties Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures. 7,C,13: Similar, Congruent, & Symmetrical Figures 7,C,14: Geometry & Figure Construction 7,C,27: Similar, Congruent, & Symmetrical Figures II 6 Geometry and Spatial Sense: Spatial Relationships Determine and use scale factors for similar figures to solve problems using proportional reasoning. 7 Geometry and Spatial Sense: Transformations and Symmetry Identify the line and rotation symmetries of twodimensional figures to solve problems. 7,C,13: Similar, Congruent, & Symmetrical Figures 7,C,27: Similar, Congruent, & Symmetrical Figures II 8 Geometry and Spatial Sense: Transformations and Symmetry Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper). 9 Geometry and Spatial Sense: Draw representations of Visualization and Geometric three-dimensional geometric Models objects from different views. 9/19/ v.1.0

74 Mathematics Grade 7 1 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. 2 Patterns, Functions and Algebra: Generalize patterns by 7,C,7: Patterning Use Patterns, Relations and describing in words how to Functions find the next term. 3 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Recognize and explain when numerical patterns are linear or nonlinear progressions; e. g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, is nonlinear. 7,C,7: Patterning 4 Patterns, Functions and Algebra: Use Algebraic Representations Create visual representations of equation-solving processes that model the use of inverse operations. 7,C,9: Simple Equations 7,C,36: Number Systems & Functions 5 Patterns, Functions and Algebra: Represent linear equations by 7,C,10: Ordered Pairs Use Algebraic Representations plotting points in the coordinate plane. 6 Patterns, Functions and Algebra: Represent inequalities on a Use Algebraic Representations number line or a coordinate plane. 7 Patterns, Functions and Algebra: Use Algebraic Representations Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified; e.g., 4m = m + m + m + m or a a x = 5a Patterns, Functions and Algebra: Use formulas in problemsolving Use Algebraic Representations situations. 9 Patterns, Functions and Algebra: Use Algebraic Representations Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula. 7,C,9: Simple Equations 7,C,11: Algebraic Expressions 7,C,31: Equations & Inequalities 9/19/ v.1.0

75 Mathematics Grade 7 10 Patterns, Functions and Algebra: Analyze Change Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another. 11 Patterns, Functions and Algebra: Analyze Change Use graphing calculators or computers to analyze change; e.g., distance-time relationships. 1 Data Analysis and Probability: Data Collection Read, create and interpret box-and-whisker plots, stemand-leaf plots, and other types of graphs, when appropriate. 7,C,32: Graphs, Charts, & Data Management 7,C,42: Interpreting Data 2 Data Analysis and Probability: Data Collection Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph. 7,C,32: Graphs, Charts, & Data Management 7,C,42: Interpreting Data 3 Data Analysis and Probability: Statistical Methods Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures. 7,C,19: Mean, Median, & Mode 7,C,32: Graphs, Charts, & Data Management 7,C,42: Interpreting Data 4 Data Analysis and Probability: Statistical Methods Construct opposing arguments based on analysis of the same data, using different graphical representations. 7,C,32: Graphs, Charts, & Data Management 7,C,42: Interpreting Data 5 Data Analysis and Probability: Statistical Methods Compare data from two or more samples to determine how sample selection can influence results. 9/19/ v.1.0

76 Mathematics Grade 7 6 Data Analysis and Probability: Statistical Methods Identify misuses of statistical data in articles, advertisements, and other media. 7 Data Analysis and Probability: Probability Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models. 8 Data Analysis and Probability: Probability Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences. 2 Number, Number Sense and Operations: Number and Number Systems Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. 3 Number, Number Sense and Operations: Meaning of Operations Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. 8,C,6: Algebraic Expressions 4 Number, Number Sense and Operations: Meaning of Operations Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. 9/19/ v.1.0

77 Mathematics Grade 8 5 Number, Number Sense and Determine when an estimate 8,C,32: Estimation I Operations: Computation and Estimation is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. 8,C,41: Determining Reasonable Solutions 8,C,54: Estimation II 6 Number, Number Sense and Estimate, compute and solve 8,C,9: Ratio & Proportion Operations: Computation and Estimation problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. 8,C,32: Estimation I 8,C,33: Proportions 8,C,34: Problem Solving: Percents & Percentages 8,C,41: Determining Reasonable Solutions 8,C,54: Estimation II 7 Number, Number Sense and Operations: Computation and Estimation Find the square root of perfect squares, and approximate root of non-perfect squares as consecutive integers between the root lies; e.g., (positive square root of 130) is between 11 and 12. 8,C,59: Square Roots 8 Number, Number Sense and Add, subtract, multiply, divide 8,C,1: Using Scientific Notation Operations: Computation and and compare numbers written 8,C,3: Compare & Order Rational Numbers Estimation in scientific notation. 1 Measurement: Measurement Units Compare and order the relative size of common U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram. 8,C,18: Metric & Customary Measurement 8,C,19: Metric Conversions 8,C,20: Customary Conversions 8,C,23: Measurement Precision 2 Measurement: Measurement Units Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius. 8,C,9: Ratio & Proportion 8,C,18: Metric & Customary Measurement 3 Measurement: Use Measurement Use appropriate levels of 8,C,23: Measurement Precision Techniques and Tools precision when calculating with measurements. 9/19/ v.1.0

78 Mathematics Grade 8 4.a.. Measurement: Use Measurement Techniques and Tools Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: 4.b.. Measurement: Use Measurement Techniques and Tools Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: 5 Measurement: Use Measurement Determine surface area for Techniques and Tools pyramids by analyzing their parts. 6 Measurement: Use Measurement Techniques and Tools Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. 8,C,32: Estimation I 8,C,41: Determining Reasonable Solutions 8,C,54: Estimation II 7 Measurement: Use Measurement Techniques and Tools Apply proportional reasoning to solve problems involving indirect measurements or rates. 8 Measurement: Use Measurement Techniques and Tools Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. 9 Measurement: Use Measurement Techniques and Tools Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) 8,C,21: Perimeter & Circumference 8,C,22: Area & Volume 9/19/ v.1.0

79 Mathematics Grade 8 10 Measurement: Use Measurement Techniques and Tools Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. 8,C,22: Area & Volume 1 Geometry and Spatial Sense: Characteristics and Properties Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects. 2 Geometry and Spatial Sense: Characteristics and Properties Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. 8,C,14: Geometry: 2D & 3D Figures 8,C,17: Geometry & Figure Construction 3 Geometry and Spatial Sense: Characteristics and Properties Use proportions in several forms to solve problems involving similar figures (partto-part, part-to-whole, corresponding sides between figures). 8,C,9: Ratio & Proportion 8,C,16: Similar, Congruent, & Symmetrical Figures 8,C,33: Proportions 4 Geometry and Spatial Sense: Spatial Relationships Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. 5 Geometry and Spatial Sense: Transformations and Symmetry Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. 8,C,56: Translations 6 Geometry and Spatial Sense: Draw nets for a variety of Visualization and Geometric prisms, pyramids, cylinders Models and cones. 9/19/ v.1.0

80 Mathematics Grade 8 1 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. 2 Patterns, Functions and Algebra: Generalize patterns and 8,C,7: Patterning Use Patterns, Relations and sequences by describing how Functions to find the nth term. 3 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Identify functions as linear or nonlinear based on information given in a table, graph or equation. 4 Patterns, Functions and Algebra: Extend the uses of variables Use Algebraic Representations to include covariants where y depends on x. 4 Patterns, Functions and Algebra: Extend the uses of variables Use Algebraic Representations to include covariants where y depends on x. 5 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. 6 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems. 7 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. 9/19/ v.1.0

81 Mathematics Grade 8 8 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. 9 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Solve linear equations and inequalities graphically, symbolically and using technology. 10 Patterns, Functions and Algebra: Solve 2 by 2 systems of linear Use Patterns, Relations and equations graphically and by Functions simple substitution. 11 Patterns, Functions and Algebra: Use Patterns, Relations and Functions Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. 12 Patterns, Functions and Algebra: Solve simple quadratic Use Patterns, Relations and equations graphically; e.g., y Functions = x² Patterns, Functions and Algebra: Compute and interpret slope, Analyze Change midpoint and distance given a set of ordered pairs. 14 Patterns, Functions and Algebra: Analyze Change Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation. 15 Patterns, Functions and Algebra: Analyze Change Describe and compare how changes in an equation affects the related graphs; e. g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. 9/19/ v.1.0

82 Mathematics Grade 8 16 Patterns, Functions and Algebra: Analyze Change Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. 1 Data Analysis and Probability: Data Use, create and interpret 8,C,27: Frequency Distributions Collection scatterplots and other types of 8,C,40: Interpreting Graphs graphs as appropriate. 2 Data Analysis and Probability: Data Collection Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. 8,C,27: Frequency Distributions 8,C,40: Interpreting Graphs 3 Data Analysis and Probability: Data Collection Differentiate between discrete and continuous data and appropriate ways to represent each. 8,C,27: Frequency Distributions 8,C,40: Interpreting Graphs 4 Data Analysis and Probability: Statistical Methods Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). 5 Data Analysis and Probability: Statistical Methods Explain the mean's sensitivity to extremes and its use in comparison with the median and mode. 8,C,26: Mean, Median, & Mode 6 Data Analysis and Probability: Statistical Methods Make conjectures about possible relationship in a scatterplot and approximate line of best fit. 8,C,40: Interpreting Graphs 9/19/ v.1.0

83 Mathematics Grade 8 7 Data Analysis and Probability: Statistical Methods Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample. 8 Data Analysis and Probability: Statistical Methods Describe how the relative size of a sample compared to the target population affects the validity of predictions. 9 Data Analysis and Probability: Statistical Methods Construct convincing arguments based on analysis of data and interpretation of graphs. 8,C,27: Frequency Distributions 8,C,40: Interpreting Graphs 10 Data Analysis and Probability: Probability Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important. 8,C,24: Using Counting Arrangements 8,C,25: Probability 8,C,38: Problem Solving: Predicting Outcomes 11 Data Analysis and Probability: Probability Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. 8,C,37: Probability & Statistics 8,C,38: Problem Solving: Predicting Outcomes 9/19/ v.1.0

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