# Front Row

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- letter or word recognition
- phonics
- reading comprehension
- text analysis
- using supporting evidence

- algebra
- counting
- fractions
- geometry

- asking questions

- memorization
- part-whole relationships
- thinking critically

###### Pros

Interactive student assessments are tightly aligned with Common Core standards, and the teacher dashboard is very easy to use.###### Cons

The customizable, printable worksheets may not engage as much as more interactive, online resources.###### Bottom Line

From content-aligned assessments and printable worksheets to excellent progress analytics, this valuable resource targets Common Core mastery.Easy-to-use dashboard includes options for individual and whole-class reports.

Assessments and virtual manipulatives offer fun ways to practice math skills. Though the printable worksheets won't be as lively as a more dynamic tool, the ability to individualize them might help boost kids' interest.

Pre-assessment items are tightly aligned with the standards and increase in difficulty as students master skills. ELA activities are also closely aligned to Common Core.

The dashboard's FAQ section, demo videos, and blog give teachers useful guidance. Students get video feedback for incorrect answers. Virtual manipulatives, audio options, and a scratch pad support different learning needs.

While Front Row may be intended for practice and reinforcement, the site also provides some valuable teaching resources. For example, if you're working on a specific Common Core standard -- say, 4.NBT.4 -- a simple click from the dashboard gives access to a host of instructional materials, including video lessons from the likes of Khan Academy and LearnZillion. There are also printable worksheets and activities in a variety of subject areas which you can align to the specific standards your students find challenging.

At any point, you can have students complete a pre-assessment for any domain; be sure to allow them anywhere from 10 to 30 minutes to complete these. Afterward, check your dashboard to gauge their progress and assign more practice as needed. Using this information, you can group your students accordingly to encourage more social learning. Though kids have the option to use either the Web or the tablet app, they're likely to find the app more appealing; the touch interface may allow better manipulation of tools such as the virtual scratch pad.

Read More Read LessFront Row is a math and ELA practice website (and app) for grades K-8 that is aimed at addressing Common Core skills. From the dashboard, teachers can create rosters and add students. Teachers will also find a report card feature, printable worksheets, a weekly student practice feed, grade-level graphs of student progress, a variety of articles and assignments for ELA, and more. Upon clicking lists of K-8 standards, teachers can peruse a set of sample student questions and teacher resources as well. Front Row is offered to teachers for free. But, for an additional fee, a school edition offers even more comprehensive reports and lets teachers assign an unlimited number of targeted benchmark assessments for students. The school edition also includes a greater number of inquiry-based lessons.

In either version, students are prompted to complete a baseline assessment upon first logging in. They'll choose one of the program's 11 domains, targeting either foundational or more advanced skills, before answering at least 10 questions. Teachers can use the results to assign students additional practice as needed throughout the program. Students can access Front Row using a tablet or from a web browser (Front Row recommends Chrome). All information is stored in the cloud, so kids can use different devices interchangeably. Furthermore, individual logins make it easy for students to share devices, if necessary.

Read More Read LessUsing Front Row's interactive assessments, fact practice, and printable worksheets, students can become fluent in key skills to meet the Common Core standards in math. New activities also make it easy to progress through Common Core standards in reading, writing, and phonics/spelling. Throughout, students receive excellent video feedback for incorrect answers, and they'll have access to virtual manipulatives such as number lines, graphs, and shapes for many of the quiz items. These resources encourage kids to fully comprehend a skill before mastering it. Also, as students master skills, they'll progress to more challenging skills within the same domain. The printable worksheets are automatically personalized for each student's current learning level. Though these won't be as interactive as an on-screen exercise, the leveled work should help engage kids in a way that challenges them.

The pre-assessments provide a good diagnostic baseline for all work moving forward. The language on the domain selection page might be out of reach for some younger users; more advanced students may have to answer a lot of low-level questions before showing mastery. Nevertheless, once students complete this first step, they're given appropriate quizzes and worksheets to help them master more advanced skills. And, with the school edition, they can receive assignments for benchmark assessments, which can be used to measure progress over time, identify strengths and weaknesses, or zero in on standards practice before taking a high-stakes state assessment.

Read More Read Less## Key Standards Supported

## Language | |

L.1: Conventions of Standard English | |

L.1.1c | Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop). |

Vocabulary Acquisition and Use | |

L.1.4c | Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking). |

L.1.5 | With guidance and support from adults, demonstrate understanding of figurative language, word relationships and nuances in word meanings. |

L.2: Conventions of Standard English | |

L.2.1c | Use reflexive pronouns (e.g., myself, ourselves). |

L.2.2a | Capitalize holidays, product names, and geographic names. |

L.2.2e | Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. |

Vocabulary Acquisition and Use | |

L.2.4c | Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., addition, additional). |

L.3: Conventions of Standard English | |

L.3.1a | Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences. |

L.3.1c | Use abstract nouns (e.g., childhood). |

L.3.2e | Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). |

L.3.2f | Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words. |

L.3.2g | Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. |

Knowledge of Language | |

L.3.3a | Choose words and phrases for effect.* |

L.4: Conventions of Standard English | |

L.4.1 | Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. |

L.4.1g | Correctly use frequently confused words (e.g., to, too, two; there, their).* |

L.4.2 | Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. |

L.4.2d | Spell grade-appropriate words correctly, consulting references as needed. |

Knowledge of Language | |

L.4.3 | Use knowledge of language and its conventions when writing, speaking, reading, or listening. |

L.5: Conventions of Standard English | |

L.5.1 | Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. |

Knowledge of Language | |

L.5.3 | Use knowledge of language and its conventions when writing, speaking, reading, or listening. |

L.6: Conventions of Standard English | |

L.6.1 | Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. |

L.6.2 | Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. |

L.6.2.B | Spell correctly. |

L.7: Conventions of Standard English | |

L.7.1 | |

L.7.2 | Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. |

L.7.2b | Spell correctly. |

Knowledge of Language | |

L.7.3 | Use knowledge of language and its conventions when writing, speaking, reading, or listening. |

L.8: Conventions of Standard English | |

L.8.1 | |

L.8.2 | |

L.8.2c | Spell correctly. |

Knowledge of Language | |

L.8.3 | Use knowledge of language and its conventions when writing, speaking, reading, or listening. |

Reading Foundational Skills: RF.1 | |

RF.1.2 | Demonstrate understanding of spoken words, syllables, and sounds (phonemes). |

Phonics and Word recognition | |

RF.1.3 | Know and apply grade-level phonics and word analysis skills in decoding words. |

RF.1.3a | Know the spelling-sound correspondences for common consonant digraphs. |

RF.1.3b | Decode regularly spelled one-syllable words. |

RF.1.3c | Know final -e and common vowel team conventions for representing long vowel sounds. |

RF.1.3d | Use knowledge that every syllable must have a vowel sound to determine the number of syllables in a printed word. |

RF.1.3e | Decode two-syllable words following basic patterns by breaking the words into syllables. |

RF.1.3f | Read words with inflectional endings. |

RF.1.3g | Recognize and read grade-appropriate irregularly spelled words. |

Fluency | |

RF.1.4 | Read with sufficient accuracy and fluency to support comprehension. |

RF.1.4a | Read on-level text with purpose and understanding. |

RF.2: Phonics and Word recognition | |

RF.2.3 | Know and apply grade-level phonics and word analysis skills in decoding words. |

RF.2.3a | Distinguish long and short vowels when reading regularly spelled one-syllable words. |

RF.2.3b | Know spelling-sound correspondences for additional common vowel teams. |

RF.2.3c | Decode regularly spelled two-syllable words with long vowels. |

RF.2.3d | Decode words with common prefixes and suffixes. |

RF.2.3e | Identify words with inconsistent but common spelling-sound correspondences. |

Fluency | |

RF.2.4a | Read on-level text with purpose and understanding. |

RF.3: Phonics and Word recognition | |

RF.3.3 | Know and apply grade-level phonics and word analysis skills in decoding words. |

RF.3.3a | Identify and know the meaning of the most common prefixes and derivational suffixes. |

RF.3.3b | Decode words with common Latin suffixes. |

RF.3.3c | Decode multisyllable words. |

RF.3.3d | Read grade-appropriate irregularly spelled words. |

Fluency | |

RF.3.4 | Read with sufficient accuracy and fluency to support comprehension. |

RF.3.4a | Read on-level text with purpose and understanding. |

RF.4: Phonics and Word recognition | |

RF.4.3 | Know and apply grade-level phonics and word analysis skills in decoding words. |

RF.4.3a | Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. |

Fluency | |

RF.4.4 | Read with sufficient accuracy and fluency to support comprehension. |

RF.4.4a | Read on-level text with purpose and understanding. |

RF.5: Phonics and Word recognition | |

RF.5.3 | Know and apply grade-level phonics and word analysis skills in decoding words. |

RF.5.3a | Use combined knowledge of all letter-sound correspondences, syllabication patterns, and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic words in context and out of context. |

Fluency | |

RF.5.4 | Read with sufficient accuracy and fluency to support comprehension. |

RF.5.4a | Read on-level text with purpose and understanding. |

## Reading History/Social Studies | |

RH.6-8: Key Ideas and Details | |

RH.6-8.1 | Cite specific textual evidence to support analysis of primary and secondary sources. |

Craft and Structure | |

RH.6-8.4 | Determine the meaning of words and phrases as they are used in a text, including vocabulary specific to domains related to history/social studies. |

RH.6-8.6 | Identify aspects of a text that reveal an author’s point of view or purpose (e.g., loaded language, inclusion or avoidance of particular facts). |

Integration of Knowledge and Ideas | |

RH.6-8.7 | Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts. |

RH.6-8.8 | Distinguish among fact, opinion, and reasoned judgment in a text. |

Range of Reading and Level of Text Complexity | |

RH.6-8.10 | By the end of grade 8, read and comprehend history/social studies texts in the grades 6–8 text complexity band independently and proficiently. |

## Reading Informational Key Ideas and Details | |

RI.1: Key Ideas and Details | |

RI.1.1 | Ask and answer questions about key details in a text. |

RI.1.2 | Identify the main topic and retell key details of a text. |

RI.1.3 | Describe the connection between two individuals, events, ideas, or pieces of information in a text. |

Craft and Structure | |

RI.1.5 | Know and use various text features (e.g., headings, tables of contents, glossaries, electronic menus, icons) to locate key facts or information in a text. |

Integration of Knowledge and Ideas | |

RI.1.7 | Use the illustrations and details in a text to describe its key ideas. |

RI.1.8 | Identify the reasons an author gives to support points in a text. |

Range of Reading and Level of Text Complexity | |

RI.1.10 | With prompting and support, read informational texts appropriately complex for grade 1. |

RI.2: Key Ideas and Details | |

RI.2.1 | Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. |

RI.2.2 | Identify the main topic of a multiparagraph text as well as the focus of specific paragraphs within the text. |

RI.2.3 | Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text. |

Craft and Structure | |

RI.2.5 | Know and use various text features (e.g., captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently. |

RI.2.6 | Identify the main purpose of a text, including what the author wants to answer, explain, or describe. |

Integration of Knowledge and Ideas | |

RI.2.8 | Describe how reasons support specific points the author makes in a text. |

Range of Reading and Level of Text Complexity | |

RI.2.10 | By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RI.3: Key Ideas and Details | |

RI.3.1 | Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. |

RI.3.2 | Determine the main idea of a text; recount the key details and explain how they support the main idea. |

Integration of Knowledge and Ideas | |

RI.3.7 | Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur). |

RI.3.8 | Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence). |

RI.3.9 | Compare and contrast the most important points and key details presented in two texts on the same topic. |

Range of Reading and Level of Text Complexity | |

RI.3.10 | By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2–3 text complexity band independently and proficiently. |

RI.4: Key Ideas and Details | |

RI.4.1 | Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. |

RI.4.2 | Determine the main idea of a text and explain how it is supported by key details; summarize the text. |

RI.4.3 | Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text. |

Craft and Structure | |

RI.4.5 | Describe the overall structure (e.g., chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text. |

Integration of Knowledge and Ideas | |

RI.4.7 | Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears. |

RI.4.8 | Explain how an author uses reasons and evidence to support particular points in a text. |

Range of Reading and Level of Text Complexity | |

RI.4.10 | By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RI.5: Key Ideas and Details | |

RI.5.2 | Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text. |

Craft and Structure | |

RI.5.6 | Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent. |

Integration of Knowledge and Ideas | |

RI.5.8 | Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s). |

Range of Reading and Level of Text Complexity | |

RI.5.10 | By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently. |

RI.6: Key Ideas and Details | |

RI.6.1 | Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. |

RI.6.2 | Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments. |

Craft and Structure | |

RI.6.5 | Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas. |

RI.6.6 | Determine an author’s point of view or purpose in a text and explain how it is conveyed in the text. |

Integration of Knowledge and Ideas | |

RI.6.7 | Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. |

RI.6.8 | Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not. |

Range of Reading and Level of Text Complexity | |

RI.6.10 | By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RI.7: Key Ideas and Details | |

RI.7.2 | Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text. |

RI.7.3 | Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events). |

Craft and Structure | |

RI.7.5 | Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas. |

RI.7.6 | Determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others. |

Integration of Knowledge and Ideas | |

RI.7.8 | Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims. |

Range of Reading and Level of Text Complexity | |

RI.7.10 | By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RI.8: Key Ideas and Details | |

RI.8.1 | Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. |

RI.8.2 | Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text. |

RI.8.3 | Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories). |

Craft and Structure | |

RI.8.6 | Determine an author’s point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. |

Integration of Knowledge and Ideas | |

RI.8.7 | Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. |

RI.8.8 | Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced. |

Range of Reading and Level of Text Complexity | |

RI.8.10 | By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6–8 text complexity band independently and proficiently. |

## Reading Literature | |

RL.1: Key Ideas and Details | |

RL.1.1 | Ask and answer questions about key details in a text. |

Craft and Structure | |

RL.1.4 | Identify words and phrases in stories or poems that suggest feelings or appeal to the senses. |

RL.1.6 | Identify who is telling the story at various points in a text. |

Integration of Knowledge and Ideas | |

RL.1.7 | Use illustrations and details in a story to describe its characters, setting, or events. |

Range of Reading and Level of Text Complexity | |

RL.1.10 | With prompting and support, read prose and poetry of appropriate complexity for grade 1. |

RL.2: Key Ideas and Details | |

RL.2.1 | Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. |

RL.2.3 | Describe how characters in a story respond to major events and challenges. |

Integration of Knowledge and Ideas | |

RL.2.7 | Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot. |

Range of Reading and Level of Text Complexity | |

RL.2.10 | By the end of the year, read and comprehend literature, including stories and poetry, in the grades 2–3 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RL.3: Key Ideas and Details | |

RL.3.1 | Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. |

Craft and Structure | |

RL.3.6 | Distinguish their own point of view from that of the narrator or those of the characters. |

Range of Reading and Complexity of Text | |

RL.3.10 | By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 2–3 text complexity band independently and proficiently. |

RL.4: Key Ideas and Details | |

RL.4.1 | Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. |

RL.4.2 | Determine a theme of a story, drama, or poem from details in the text; summarize the text. |

Craft and Structure | |

RL.4.6 | Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations. |

Range of Reading and Complexity of Text | |

RL.4.10 | By the end of the year, read and comprehend literature, including stories, dramas, and poetry, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RL.5: Key Ideas and Details | |

RL.5.2 | Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text. |

Craft and Structure | |

RL.5.6 | Describe how a narrator’s or speaker’s point of view influences how events are described. |

Integration of Knowledge and Ideas: Range of Reading and Complexity of Text | |

RL.5.10 | By the end of the year, read and comprehend literature, including stories, dramas, and poetry, at the high end of the grades 4–5 text complexity band independently and proficiently. |

RL.6: Key Ideas and Details | |

RL.6.1 | Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. |

RL.6.2 | Determine a theme or central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments. |

Craft and Structure | |

RL.6.6 | Explain how an author develops the point of view of the narrator or speaker in a text. |

Range of Reading and Level of Text Complexity | |

RL.6.10 | By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RL.7: Key Ideas and Details | |

RL.7.2 | Determine a theme or central idea of a text and analyze its development over the course of the text; provide an objective summary of the text. |

Craft and Structure | |

RL.7.6 | Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. |

Integration of Knowledge and Ideas: Range of Reading and Level of Text Complexity | |

RL.7.10 | By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. |

RL.8: Key Ideas and Details | |

RL.8.1 | Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. |

RL.8.3 | Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision. |

Craft and Structure | |

RL.8.6 | nalyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. |

Integration of Knowledge and Ideas | |

RL.8.9 | Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. |

Range of Reading and Level of Text Complexity | |

RL.8.10 | By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6–8 text complexity band independently and proficiently. |

## Writing | |

W.1: Text Types and Purposes | |

W.1.1 | Write opinion pieces in which they introduce the topic or name the book they are writing about, state an opinion, supply a reason for the opinion, and provide some sense of closure. |

W.1.2 | Write informative/explanatory texts in which they name a topic, supply some facts about the topic, and provide some sense of closure. |

W.1.3 | Write narratives in which they recount two or more appropriately sequenced events, include some details regarding what happened, use temporal words to signal event order, and provide some sense of closure. |

Research to Build and Present Knowledge | |

W.1.7 | Participate in shared research and writing projects (e.g., explore a number of “how-to” books on a given topic and use them to write a sequence of instructions). |

W.2: Text Types and Purposes | |

W.2.1 | Write opinion pieces in which they introduce the topic or book they are writing about, state an opinion, supply reasons that support the opinion, use linking words (e.g., because, and, also) to connect opinion and reasons, and provide a concluding statement or section. |

W.2.2 | Write informative/explanatory texts in which they introduce a topic, use facts and definitions to develop points, and provide a concluding statement or section. |

W.2.3 | Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure. |

Research to Build and Present Knowledge | |

W.2.8 | Recall information from experiences or gather information from provided sources to answer a question. |

W.3: Text Types and Purposes | |

W.3.1 | Write opinion pieces on topics or texts, supporting a point of view with reasons. |

W.3.1a | Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons. |

W.3.1b | Provide reasons that support the opinion. |

W.3.1c | Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons. |

W.3.1d | Provide a concluding statement or section. |

W.3.2 | Write informative/explanatory texts to examine a topic and convey ideas and information clearly. |

W.3.2a | Introduce a topic and group related information together; include illustrations when useful to aiding comprehension. |

W.3.2b | Develop the topic with facts, definitions, and details. |

W.3.2c | Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information. |

W.3.2d | Provide a concluding statement or section. |

Research to Build and Present Knowledge | |

W.3.7 | Conduct short research projects that build knowledge about a topic. |

Range of Writing | |

W.3.10 | Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. |

W.4: Text Types and Purposes | |

W.4.1 | Write opinion pieces on topics or texts, supporting a point of view with reasons and information. |

W.4.1a | Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer’s purpose. |

W.4.1b | Provide reasons that are supported by facts and details. |

W.4.1c | Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition). |

W.4.1d | Provide a concluding statement or section related to the opinion presented. |

W.4.2 | Write informative/explanatory texts to examine a topic and convey ideas and information clearly. |

W.4.2a | Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. |

W.4.2b | Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. |

W.4.2c | Link ideas within categories of information using words and phrases (e.g., another, for example, also, because). |

W.4.2d | d.Use precise language and domain-specific vocabulary to inform about or explain the topic. |

W.4.2e | Provide a concluding statement or section related to the information or explanation presented. |

Production and Distribution of Writing | |

W.4.4 | Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) |

Research to Build and Present Knowledge | |

W.4.7 | Conduct short research projects that build knowledge through investigation of different aspects of a topic. |

W.4.8 | Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources. |

W.4.9 | Draw evidence from literary or informational texts to support analysis, reflection, and research. |

Range of Writing | |

W.4.10 | Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. |

W.5: Text Types and Purposes | |

W.5.1 | Write opinion pieces on topics or texts, supporting a point of view with reasons and information. |

W.5.1a | Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer’s purpose. |

W.5.1b | Provide logically ordered reasons that are supported by facts and details. |

W.5.1c | Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically). |

W.5.1d | Provide a concluding statement or section related to the opinion presented. |

W.5.2 | Write informative/explanatory texts to examine a topic and convey ideas and information clearly. |

W.5.2a | Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. |

W.5.2b | Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. |

W.5.2c | Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). |

W.5.2d | Use precise language and domain-specific vocabulary to inform about or explain the topic. |

W.5.2e | Provide a concluding statement or section related to the information or explanation presented. |

Production and Distribution of Writing | |

W.5.4 | Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) |

Research to Build and Present Knowledge | |

W.5.7 | Conduct short research projects that use several sources to build knowledge through investigation of different aspects of a topic. |

W.5.8 | Recall relevant information from experiences or gather relevant information from print and digital sources; summarize or paraphrase information in notes and finished work, and provide a list of sources. |

W.5.9 | Draw evidence from literary or informational texts to support analysis, reflection, and research. |

W.5.9a | Apply grade 5 Reading standards to literature (e.g., “Compare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]”). |

W.5.9b | Apply grade 5 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point[s]”). |

Range of Writing | |

W.5.10 | Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. |

W.6: Text Types and Purposes | |

W.6.1 | Write arguments to support claims with clear reasons and relevant evidence. |

W.6.1a | Introduce claim(s) and organize the reasons and evidence clearly. |

W.6.1b | Support claim(s) with clear reasons and relevant evidence, using credible sources and demonstrating an understanding of the topic or text. |

W.6.1c | Use words, phrases, and clauses to clarify the relationships among claim(s) and reasons. |

W.6.1d | Establish and maintain a formal style. |

W.6.1e | Provide a concluding statement or section that follows from the argument presented. |

W.6.2 | Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. |

W.6.2a | Introduce a topic; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. |

W.6.2b | Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. |

W.6.2c | Use appropriate transitions to clarify the relationships among ideas and concepts. |

W.6.2d | Use precise language and domain-specific vocabulary to inform about or explain the topic. |

W.6.2e | Establish and maintain a formal style. |

W.6.2f | Provide a concluding statement or section that follows from the information or explanation presented. |

Production and Distribution of Writing | |

W.6.4 | Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) |

Research to Build and Present Knowledge | |

W.6.7 | Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate. |

W.6.9 | Draw evidence from literary or informational texts to support analysis, reflection, and research. |

Range of Writing | |

W.6.10 | Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and |

W.7: Text Types and Purposes | |

W.7.1 | Write arguments to support claims with clear reasons and relevant evidence. |

W.7.1a | Introduce claim(s), acknowledge alternate or opposing claims, and organize the reasons and evidence logically. |

W.7.1b | Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. |

W.7.1c | Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), reasons, and evidence. |

W.7.1d | Establish and maintain a formal style. |

W.7.1e | Provide a concluding statement or section that follows from and supports the argument presented. |

W.7.2 | Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. |

W.7.2a | Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information, using strategies such as definition, classification, comparison/contrast, and cause/effect; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. |

W.7.2b | Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. |

W.7.2c | Use appropriate transitions to create cohesion and clarify the relationships among ideas and concepts. |

W.7.2d | Use precise language and domain-specific vocabulary to inform about or explain the topic. |

W.7.2e | Establish and maintain a formal style. |

W.7.2f | Provide a concluding statement or section that follows from and supports the information or explanation presented. |

Production and Distribution of Writing | |

W.7.4 | Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) |

Research to Build and Present Knowledge | |

W.7.7 | Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation. |

W.7.9a | Apply grade 7 Reading standards to literature (e.g., “Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history”). |

W.7.9b | Apply grade 7 Reading standards to literary nonfiction (e.g. “Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims”). |

Range of Writing | |

W.7.10 | |

W.8: Text Types and Purposes | |

W.8.1 | Write arguments to support claims with clear reasons and relevant evidence. |

W.8.1a | Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. |

W.8.1b | Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. |

W.8.1c | Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. |

W.8.1d | Establish and maintain a formal style. |

W.8.1e | Provide a concluding statement or section that follows from and supports the argument presented. |

W.8.2 | Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. |

W.8.2a | Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. |

W.8.2b | Develop the topic with relevant, well-chosen facts, definitions, concrete details, quotations, or other information and examples. |

W.8.2c | Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts. |

W.8.2d | Use precise language and domain-specific vocabulary to inform about or explain the topic. |

W.8.2e | Establish and maintain a formal style. |

W.8.2f | Provide a concluding statement or section that follows from and supports the information or explanation presented. |

W.8.3 | Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences. |

W.8.3a | Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. |

W.8.3b | Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters. |

W.8.3c | Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events. |

W.8.3d | Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. |

W.8.3e | Provide a conclusion that follows from and reflects on the narrated experiences or events. |

Production and Distribution of Writing | |

W.8.4 | Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) |

Range of Writing | |

W.8.10 | |

## Counting And Cardinality | |

K.CC: Compare Numbers. | |

K.CC.6 | Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1 |

K.CC.7 | Compare two numbers between 1 and 10 presented as written numerals. |

Count To Tell The Number Of Objects. | |

K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. |

K.CC.4.a | When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. |

K.CC.4.b | Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. |

K.CC.4.c | Understand that each successive number name refers to a quantity that is one larger. |

K.CC.5 | Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. |

Know Number Names And The Count Sequence. | |

K.CC.1 | Count to 100 by ones and by tens. |

K.CC.2 | Count forward beginning from a given number within the known sequence (instead of having to begin at 1). |

K.CC.3 | Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). |

## Expressions And Equations | |

6.EE: Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions. | |

6.EE.1 | Write and evaluate numerical expressions involving whole-number exponents. |

7.EE: Use Properties Of Operations To Generate Equivalent Expressions. | |

7.EE.1 | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. |

8.EE: Work With Radicals And Integer Exponents. | |

8.EE.1 | Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. |

## Geometry | |

1.G: Reason With Shapes And Their Attributes. | |

1.G.1 | Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. |

2.G: Reason With Shapes And Their Attributes. | |

2.G.1 | Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. |

3.G: Reason With Shapes And Their Attributes. | |

3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. |

4.G: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles. | |

4.G.2 | Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. |

5.G: Classify Two-Dimensional Figures Into Categories Based On Their Properties. | |

5.G.3 | Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. |

6.G: Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume. | |

6.G.1 | Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. |

6.G.2 | Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. |

7.G: Draw, Construct, And Describe Geometrical Figures And Describe The Relationships Between Them. | |

7.G.1 | Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. |

Solve Real-Life And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume. | |

7.G.6 | Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. |

8.G: Solve Real-World And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres. | |

8.G.9 | Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. |

Understand And Apply The Pythagorean Theorem. | |

8.G.6 | Explain a proof of the Pythagorean Theorem and its converse. |

8.G.7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. |

K.G: Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres). | |

K.G.1 | Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. |

K.G.2 | Correctly name shapes regardless of their orientations or overall size. |

K.G.3 | Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). |

## Measurement And Data | |

1.MD: Measure Lengths Indirectly And By Iterating Length Units. | |

1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. |

2.MD: Relate Addition And Subtraction To Length. | |

2.MD.5 | Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. |

Work With Time And Money. | |

2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? |

3.MD: Solve Problems Involving Measurement And Estimation Of Intervals Of Time, Liquid Volumes, And Masses Of Objects. | |

3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 |

4.MD: Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit. | |

4.MD.2 | Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. |

4.MD.3 | Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. |

5.MD: Convert Like Measurement Units Within A Given Measurement System. | |

5.MD.1 | Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. |

Geometric Measurement: Understand Concepts Of Volume And Relate Volume To Multiplication And To Addition. | |

5.MD.5.b | Apply the formulas V=l×w×handV=b×h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems. |

K.MD: Classify Objects And Count The Number Of Objects In Each Category. | |

K.MD.3 | Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3 |

Describe And Compare Measurable Attributes. | |

K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. |

## Number And Operations In Base Ten | |

1.NBT: Extend The Counting Sequence. | |

1.NBT.1 | Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. |

Understand Place Value. | |

1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: |

1.NBT.3 | Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. |

2.NBT: Understand Place Value. | |

2.NBT.1 | Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: |

2.NBT.3 | Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. |

2.NBT.4 | Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. |

Use Place Value Understanding And Properties Of Operations To Add And Subtract. | |

2.NBT.5 | Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. |

2.NBT.7 | Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. |

3.NBT: Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4 | |

3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. |

3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. |

3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. |

5.NBT: Perform Operations With Multi-Digit Whole Numbers And With Decimals To Hundredths. | |

5.NBT.5 | Fluently multiply multi-digit whole numbers using the standard algorithm. |

5.NBT.6 | Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |

5.NBT.7 | Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. |

Understand The Place Value System. | |

5.NBT.3 | Read, write, and compare decimals to thousandths. |

5.NBT.3.a | Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). |

5.NBT.3.b | Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. |

5.NBT.4 | Use place value understanding to round decimals to any place. |

K.NBT: Work With Numbers 11–19 To Gain Foundations For Place Value. | |

K.NBT.1 | Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. |

4.NBT: Generalize Place Value Understanding For Multi-Digit Whole Numbers. | |

4.NBT.2 | Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. |

4.NBT.3 | Use place value understanding to round multi-digit whole numbers to any place. |

Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic. | |

4.NBT.4 | Fluently add and subtract multi-digit whole numbers using the standard algorithm. |

4.NBT.5 | Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |

4.NBT.6 | Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |

## Number And Operations—Fractions | |

5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. | |

5.NF.4 | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. |

5.NF.6 | Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. |

5.NF.7 | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 |

Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. | |

5.NF.1 | Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) |

4.NF: Extend Understanding Of Fraction Equivalence And Ordering. | |

4.NF.2 | Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |

Understand Decimal Notation For Fractions, And Compare Decimal Fractions. | |

4.NF.7 | Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. |

3.NF: Develop Understanding Of Fractions As Numbers. | |

3.NF.3.c | Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. |

3.NF.3.d | Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |

## Operations And Algebraic Thinking | |

1.OA: Add And Subtract Within 20. | |

1.OA.6 | Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). |

2.OA: Add And Subtract Within 20. | |

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

3.OA: Multiply And Divide Within 100. | |

3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. |

4.OA: Use The Four Operations With Whole Numbers To Solve Problems. | |

4.OA.3 | Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. |

K.OA: Understand Addition As Putting Together And Adding To, And Under- Stand Subtraction As Taking Apart And Taking From. | |

K.OA.2 | Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. |

K.OA.5 | Fluently add and subtract within 5. |

## Ratios And Proportional Relationships | |

6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. | |

6.RP.3 | Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. |

7.RP: Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems. | |

7.RP.1 | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. |

7.RP.3 | Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. |

## The Number System | |

6.NS: Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions. | |

6.NS.1 | Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? |

Compute Fluently With Multi-Digit Numbers And Find Common Factors And Multiples. | |

6.NS.2 | Fluently divide multi-digit numbers using the standard algorithm. |

6.NS.3 | Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. |

6.NS.4 | Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). |

7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers. | |

7.NS.1 | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. |

7.NS.1.d | Apply properties of operations as strategies to add and subtract rational numbers. |

7.NS.2 | Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. |

7.NS.2.c | Apply properties of operations as strategies to multiply and divide rational numbers. |

7.NS.3 | Solve real-world and mathematical problems involving the four operations with rational numbers. |

8.NS: Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers. | |

8.NS.2 | Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. |