# Math and Numbers Art Lesson- Restaurant

Students will be able to...

Identify a whole and its fractions: 1/2, 1/4, 1/3, 2/3

Name and demonstrate eqivalent fractions such as: 2/4= 1/2, 3/3= 1 whole

Add money in dollars and cents

Extension: divide money

Create balance in a piece of artwork

Develop a theme in their writing by creating a menu and items for their own restaurant

#### 1 Intro

Teacher sets up dining tables with a place setting for each student. Menus will be premade by the teacher on either an IPad or hard copy. The menus will list fun items to order. Food items should be circular for fraction cutting later such as pies, pizzas, giant cookies, etc. Play music using a musical app such as Itunes to play restaurant music as students enter.

Students sit in groups of 2-4 at their dining tables. Students collaberate at their tables to order one food item from the menu to share.

#### 2 Development 1- Intro to Fractions

Teacher brings out 1 paper plate per table and students color/draw in their food on the paper plate. Introduce the terms sharing and fractions. Teacher demonstrates sitting with a group and cutting the food to share equally.

Demonstrate writing fractions and give examples

Students decide in teams how to cut their food order to give everyone an equal piece.

Students take turns coming up to a smart board to draw their food and demonstrate to the class how they split their food. Students practice using fractions to represent their portions.

#### 3 Development 2- Opening a Small Business

Present to students they will now be their own restaurant owners.

Prepare students to be chefs for their small business by playing YouTube video of making home made smelly play doh.

A kitchen area will be equipped with only certain measuring cups and spoons. When the recipe states 1/2 of a cup and some students only have 1/4 of a cup, students will have to problem solve the equivalent fraction for their recipe.

Students start to brainstorm a name for their restaurant and the kinds of foods they may want to serve. Use the app ithoughts to mind map.

Students move to "kitchen area" where they make their own smelly doh. Make one batch as a class together, discussing fractions as the students add to their recipes. Students will then make another two batches on their own.

#### 4 Development 3 Loking at Food in Fine Art

Prepare a gallery on the app ArtSite of food art images from historical and contemprary fine artists. Be sure to include past student work as well. Refer to the term balance in the artwork and show examples.

Students use the Artsite app to comment on the food gallery. Students should comment on what their favorite item is and why. Students list how the artists used balance. As an extension students may site other reasons how the artist made their food look appealing.

#### 5 Development 4 Food Preparation

Refer back to the term balance and discuss how it can be achieved on a food plate with food items. (Many small items on one side such as peas balanced with a large piece of meat on the other side)

Students will prepare least 2 foods with their home made play doh and create balance on the plate. Students go back and revise their menus. They will add details such as name of restaurant, prices, and pictures.

#### 6 Conclusion

Demonstrate making an order and totaling up a restaurant bill. An extension for higher skill level would be to add division if student were spitting the bill with a friend.

Play the YouTube video "Pop-Si-Co" (sounds like the popsicle song) or other food related song for getting up and dancing. This part can be anywhere in the project where students need to get up and move.

Students display their plates on one large table for a family style "feast." Students write down 2 or more items ( more than two items for higher skill level) what they would like to order. Students add up their total bills. Students can then use a polling app to see what the most popular items on the menus are.

#### 7 Assessment

*There is a new app debuting this month 8/15 called the National Art Education Toolbox. Webinar is 8/11/15 on using this app to site standards, assessments, class organization, and more.

Self or peer assessment possible questions to answer:

1. Consistency of the food (too soggy, too hard, or just right) 2. Comments on food gallery easy to understand and insightful 3. Plate display is balanced and visually appealing 4. Total on bill accurate

### Key Standards Supported

### Writing

**W.K.10**(Begins in grade 3)

**W.K.1**Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is...).

**W.K.2**Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic.

**W.K.3**Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened.

**W.K.4**(Begins in grade 3)

**W.K.5**With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed.

**W.K.6**With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including in collaboration with peers.

**W.K.7**Participate in shared research and writing projects (e.g., explore a number of books by a favorite author and express opinions about them).

**W.K.8**With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question.

**W.K.9**(Begins in grade 4)

**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.

**W.1.4**(Begins in grade 3)

**W.1.5**With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed.

**W.1.6**With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers.

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

**W.1.9**(Begins in grade 4)

**W.1.10**(Begins in grade 3)

**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.

**W.2.4**(Begins in grade 3)

**W.2.5**With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing.

**W.2.6**With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers.

**W.2.7**Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations).

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

**W.2.9**(Begins in grade 4)

**W.2.10**(Begins in grade 3)

**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.

**W.3.3**Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

**W.3.3a**Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally.

**W.3.3b**Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations.

**W.3.3c**Use temporal words and phrases to signal event order.

**W.3.3d**Provide a sense of closure.

**W.3.4**With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types are defined in standards 1–3 above.)

**W.3.5**With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

**W.3.6**With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others.

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

**W.3.8**Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories.

**W.3.9**(Begins in grade 4)

**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.4.1**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.

**W.4.3**Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

**W.4.3a**Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.

**W.4.3b**Use dialogue and description to develop experiences and events or show the responses of characters to situations.

**W.4.3c**Use a variety of transitional words and phrases to manage the sequence of events.

**W.4.3d**Use concrete words and phrases and sensory details to convey experiences and events precisely.

**W.4.3e**Provide a conclusion that follows from the narrated experiences or events.

**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.)

**W.4.5**With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing.

**W.4.6**With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting.

**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.

**W.4.9a**Apply grade 4 Reading standards to literature (e.g., “Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character’s thoughts, words, or actions].”).

**W.4.9b**Apply grade 4 Reading standards to informational texts (e.g., “Explain how an author uses reasons and evidence to support particular points in a text”).

**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.5.1**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.

**W.5.3**Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.

**W.5.3a**Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally.

**W.5.3b**Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations.

**W.5.3c**Use a variety of transitional words, phrases, and clauses to manage the sequence of events.

**W.5.3d**Use concrete words and phrases and sensory details to convey experiences and events precisely.

**W.5.3e**Provide a conclusion that follows from the narrated experiences or events.

**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.)

**W.5.5**With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

**W.5.6**With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of two pages in a single sitting.

**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]”).

**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.6.1**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.

**W.6.3**Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

**W.6.3a**Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

**W.6.3b**Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

**W.6.3c**Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.

**W.6.3d**Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events.

**W.6.3e**Provide a conclusion that follows from the narrated experiences or events.

**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.)

**W.6.5**With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

**W.6.6**Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting.

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

**W.6.8**Gather relevant information from multiple print and digital sources; assess the credibility of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and providing basic bibliographic information for sources.

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

**W.6.9a**Apply grade 6 Reading standards to literature (e.g., “Compare and contrast texts in different forms or genres [e.g., stories and poems; historical novels and fantasy stories] in terms of their approaches to similar themes and topics”).

**W.6.9b**Apply grade 6 Reading standards to literary nonfiction (e.g., “Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not”).

**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.7.1**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.

**W.7.3**Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

**W.7.3a**Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

**W.7.3b**Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

**W.7.3c**Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another.

**W.7.3d**Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events.

**W.7.3e**Provide a conclusion that follows from and reflects on the narrated experiences or events.

**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.)

**W.7.5**With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed.

**W.7.6**Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources.

**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.7.8**Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

**W.7.9**Draw evidence from literary or informational texts to support analysis, reflection, and research.

**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”).

**W.7.10****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.

**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.)

**W.8.5**With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed.

**W.8.6**Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others.

**W.8.7**Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

**W.8.8**Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

**W.8.9**Draw evidence from literary or informational texts to support analysis, reflection, and research.

**W.8.9a**Apply grade 8 Reading standards to literature (e.g., “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”).

**W.8.9b**Apply grade 8 Reading standards to literary nonfiction (e.g., “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”).

**W.8.10****W.9-10.1**Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

**W.9-10.1a**Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence.

**W.9-10.1b**Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns.

**W.9-10.1c**Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

**W.9-10.1d**Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

**W.9-10.1e**Provide a concluding statement or section that follows from and supports the argument presented.

**W.9-10.2**Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

**W.9-10.2a**Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.

**W.9-10.2b**Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic.

**W.9-10.2c**Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.

**W.9-10.2d**Use precise language and domain-specific vocabulary to manage the complexity of the topic.

**W.9-10.2e**Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

**W.9-10.2f**Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

**W.9-10.3**Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

**W.9-10.3a**Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.

**W.9-10.3b**Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

**W.9-10.3c**Use a variety of techniques to sequence events so that they build on one another to create a coherent whole.

**W.9-10.3d**Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

**W.9-10.3e**Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

**W.9-10.4****W.9-10.5**Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.

**W.9-10.6**Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically.

**W.9-10.7**Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.

**W.9-10.8**Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation.

**W.9-10.9**Draw evidence from literary or informational texts to support analysis, reflection, and research.

**W.9-10.9a**Apply grades 9–10 Reading standards to literature (e.g., “Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]”).

**W.9-10.9b**Apply grades 9–10 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning”).

**W.9-10.10**Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

**W.11-12.1**Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

**W.11-12.1a**Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence.

**W.11-12.1b**Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases.

**W.11-12.1c**Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

**W.11-12.1d**Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing.

**W.11-12.1e**Provide a concluding statement or section that follows from and supports the argument presented.

**W.11-12.2**Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content.

**W.11-12.2a**Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.

**W.11-12.2b**Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic.

**W.11-12.2c**Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.

**W.11-12.2d**Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic.

**W.11-12.2e****W.11-12.2f**Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic).

**W.11-12.3**Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details, and well-structured event sequences.

**W.11-12.3a**Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events.

**W.11-12.3b**Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters.

**W.11-12.3c**Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution).

**W.11-12.3d**Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

**W.11-12.3e**Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative.

**W.11-12.4****W.11-12.5**Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.

**W.11-12.6**Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.

**W.11-12.7**Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.

**W.11-12.8**Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.

**W.11-12.9**Draw evidence from literary or informational texts to support analysis, reflection, and research.

**W.11-12.9a**Apply grades 11–12 Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”).

**W.11-12.9b**Apply grades 11–12 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]”).

**W.11-12.10**Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes

### Measurement And Data

**K.MD.1**Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

**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.

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

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

**1.MD.2**Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

**1.MD.3**Tell and write time in hours and half-hours using analog and digital clocks.

**1.MD.4**Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

**2.MD.10**Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems4 using information presented in a bar graph.

**2.MD.9**Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

**2.MD.1**Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

**2.MD.2**Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

**2.MD.3**Estimate lengths using units of inches, feet, centimeters, and meters.

**2.MD.4**Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

**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.

**2.MD.6**Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

**2.MD.7**Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

**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.3**Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

**3.MD.4**Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

**3.MD.1**Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

**3.MD.2**Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve 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

**3.MD.5**Recognize area as an attribute of plane figures and understand concepts of area measurement.

**3.MD.5.a**A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

**3.MD.5.b**A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

**3.MD.6**Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

**3.MD.7**Relate area to the operations of multiplication and addition.

**3.MD.7.a**Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

**3.MD.7.b**Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

**3.MD.7.c**Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

**3.MD.7.d**Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

**3.MD.8**Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

**4.MD.1**Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

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

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

**4.MD.4**Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

**4.MD.5**Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

**4.MD.5.a**An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

**4.MD.5.b**An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

**4.MD.6**Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

**4.MD.7**Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

**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.

**5.MD.2**Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

**5.MD.3**Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

**5.MD.3.a**A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

**5.MD.3.b**A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

**5.MD.4**Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

**5.MD.5**Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

**5.MD.5.a**Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

**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.

**5.MD.5.c**Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

### Number And Operations—Fractions

**3.NF.1**Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

**3.NF.2**Understand a fraction as a number on the number line; represent fractions on a number line diagram.

**3.NF.2.a**Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

**3.NF.2.b**Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

**3.NF.3**Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

**3.NF.3.a**Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

**3.NF.3.b**Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

**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.

**4.NF.1**Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

**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.

**4.NF.3**Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a.

**4.NF.3.a**Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

**4.NF.3.b**Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

**4.NF.3.c**Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

**4.NF.3.d**Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

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

**4.NF.4.a**Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

**4.NF.4.b**Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

**4.NF.4.c**Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

**4.NF.5**Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

**4.NF.6**Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

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

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

**5.NF.2**Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions

**5.NF.3**Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

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

**5.NF.4.a**Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

**5.NF.4.b**Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

**5.NF.5**Interpret multiplication as scaling (resizing), by:

**5.NF.5.a**Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

**5.NF.5.b**Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

**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

**5.NF.7.a**Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

**5.NF.7.b**Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

**5.NF.7.c**Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

### Ratios And Proportional Relationships

**6.RP.1**Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

**6.RP.2**Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1

**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.

**6.RP.3.a**Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

**6.RP.3.b**Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

**6.RP.3.c**Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

**6.RP.3.d**Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

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

**7.RP.2**Recognize and represent proportional relationships between quantities.

**7.RP.2.a**Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

**7.RP.2.b**Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

**7.RP.2.c**Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

**7.RP.2.d**Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

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