Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. 85% or more time spent in instruction in each grade Kindergarten, 1, and 2 align exclusively to the major work of the grade. For grade 7, more than 65% of instructional time is spent on the major focus standards.Supporting Content - informaiont that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your

classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

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Mathematical Practices(MP)

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning

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Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

Purpose of the Mathematics Curriculum Maps

The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students.

How to Use the Mathematics Curriculum Maps

Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards the supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentWeekly and daily objectives/learning targets should be included in your plans. These can be found under the column titled content. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

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Topics Addressed in QuarterAdd and Subtract Rational NumbersMultiply & Divide Rational NumbersRational Number Real-world Problems

Proportional RelationshipsRatios and Percent ProblemsSolve Multi-step Real-world Problems

Overview In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers. During this quarter students will experience various activities that create a conceptual understanding of integer operations and build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers (7.NS.1 & 2). They will perform operations with rational numbers (7.NS.A.3), incorporating them into algebraic expressions and equations. They will also represent and evaluate expressions in multiple forms, demonstrating how quantities are related (7.EE.A.3). Near the middle of the quarter students will continue to develop their understanding of ratio concepts and ratio reasoning, from grade 6, to solve mathematical and real-life problems.

Grade Level Standard Type of Rigor Foundational Standards Sample Assessment Items7.NS.1 Procedural/Fluency, Conceptual

Understanding & Application5.NF.1, 6.NS.5 TNCore Assessment Task: Video Games

7.NS.1 & 7.NS.2Achieve the Core Mini Assessment: Operations on Rational Numbers

7.NS.2 Procedural/Fluency, Conceptual Understanding & Application

5.NF.3, 5.NF.4, 6.NS.1

7.NS.3 Procedural Fluency & Application 6.NS.3 TNCore Assessment Task: Winter Denmark 7.NS.1 & 7.NS.3TNCore Assessment Task: Weight of Candies 7.NS.1 & 7.NS.3

7.RP.1 Procedural/Fluency 6.RP.1, 6.RP.2, 6.RP.3 Achieve the Core Mini Assessment: Proportional Relationships

7RP.2 Conceptual Understanding 6.RP.1, 6.RP.2, 6.RP.3 TNCore Assessment Task: Car Wash Lunch Time Snacks

7.RP.3 Application 6.RP.1, 6.RP.2, 6.RP.3 TNCore Assessment Task: Broken Light Bulb

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Fluency NCTM Position

Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

The fluency standards for 7th grade listed below should be incorporated throughout your instruction over the course of the school year. Click Engage NY Fluency Support to access exercises that can be used as a supplement in conjunction with building conceptual understanding.

7.NS.1 Apply and extend previous understandings of addition and subtraction 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.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by

reasoning about the quantities.

References: https://www.engageny.org/ http://www.corestandards.org/ http://www.nctm.org/ http://achievethecore.org/

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESAdd and Subtract Rational Numbers

(Allow 2 weeks for instruction, review and assessment)Domain: The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

7.NS.A 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.A.1a Describe situations in which opposite quantities combine to make 0.7.NS.A.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.7.NS.A.1d. Apply properties of operations as strategies to add and subtract rational numbers.

Enduring Understandings: Rational numbers use the same properties

as whole numbers. Rational numbers can be used to represent

and solve real‐life problems. Rational numbers can be represented with

visuals (including distance models), language, and real-life contexts.

Essential Questions: How are rational numbers used and applied

in real-life and mathematical situations? What is the relationship between properties

of operations and types of numbers?

Objectives: Students will represent addition and

subtraction on a horizontal or vertical number line.

Students will use words, visuals, and symbols to describe situations in which opposite quantities combine to make 0.

Students will represent addition of quantities with symbols, visuals, and words by showing positive or negative direction from one quantity to the other.

Students will show that a number and its opposite have a sum of 0 using visuals, symbols, words, and real-world contexts.

Students will use the term “additive inverse” to describe 2 numbers whose sum is zero.

Students will use commutative, distributive, associative, identity, and inverse properties to add and subtract rational numbers.

Students will use the term “absolute value” to describe the distance from zero on number line diagram and with symbols.

Glencoe

Impact Math Unit A pp. 2-3Impact Math Unit A Inv. 3-4 pp. 10-18(These are found on connected.mcgraw-hill.com. Click ‘Associated Course Content’ on home page then ‘Teacher Resources’)Math Connects2- 2A Add Integers (Pg. 86 – 87)2- 2B Add Integers (Pg. 88 – 92)2- 2C Subtract Integers (Pg. 93 – 94)2- 2D Subtract Integers (Pg. 95 – 98)

Holt2-1 Integers (pp.72-75)2-2 Adding Integers (pp. 80-83)2-3 Subtracting Integers (pp. 86-89)

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lessons:Engage NY: Lesson 4 Efficiently Adding Integers and Other Rational NumbersEngage NY: Lesson 7 Addition and Subtraction of Rational NumbersEngage NY: Lesson 8 Applying the Properties of Operations to Add and Subtract Rational NumbersConnected Math: Accentuate the Negative 7.NS.1a-d Investigations 1, 2 & 4Accentuate the Negative Support resources

Accentuate the Negative Additional ResourcesConnected Math Teacher's Guide: Accentuate the Negative

Vocabulary:Rational number, integers, additive inverse

Writing in Math:Compare and contrast a vertical number line and a horizontal number line.

Graphic Organizer:Complete a concept Map of adding the additive inverse.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESAdditional Information:Students add and subtract rational numbers. Visual representations may be helpful as students begin this work; they become less necessary as students become more fluent with these operations. The expectation of the standard is to build on student understanding of number lines developed in 6th grade.

Students should explore problems using various models to represent integers (e.g. number lines, algebra tiles, two-sided color counters).

Example(s):Use a number line to add -5 + 7.Solution:Students find -5 on the number line and move 7 in a positive direction (to the right). The stopping point of 2 is the sum of this expression. Students also add negative fractions and decimals and interpret solutions in given contexts.

Use a number line to illustrate:• p – q eg. 7 – 4• p + (-q) eg. 7 + (– 4)• Is this equation true p – q = p + (-q)?

Students explore the above relationship when p is negative and q is positive and when both p and q are negative. Is this relationship always true?

Math Shell: Using Positive and Negative Numbers in Context

Tasks:Illustrative Math: 7.NS.1TNCore Assessment Task: High and Low Elevations (NS.A.1) TNCore Assessment Task: Video Game Ratings (NS.A.1&2) Math Shell: Taxi Cabs

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Resources:Math Station Activities: Refer to p. 45Additive Inverse LessonNCTM: Deep Sea Duel Activity

Correlated iReady Lesson(s): Addition and Subtraction of Positive

and Negative Integers Understanding Adding and

Subtracting Positive and Negative Numbers

Addition and Subtraction of Rational Numbers

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESOperations with Rational Numbers

(Allow 1 week for instruction, review and assessment)Domain: The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

7.NS.A.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

7.NS.A.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers.7.NS.A.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Enduring Understanding(s): Rational numbers can be used to represent

and solve real‐life problems.

Essential Questions: How does division of fractions relate to

multiplication of fractions? How is division of fractions used in the real

world? How is division used to convert rational

numbers to decimals?

Objectives: Students will multiply and divide rational

numbers. Students will use the distributive property to

multiply positive and negative rational numbers using symbols, visuals, words, and real-life contexts.

Students will identify and apply properties used when multiplying and dividing rational numbers.

Students will convert a rational number to a decimal using long division.

Additional Information:Just as the relationship between addition and subtraction helps students understand subtraction of rational numbers, so the relationship between multiplication and division helps them understand division. To calculate -8÷4, students recall that (-2) x 4 = -8, and so -8 ÷ 4 = -2. By the same reasoning -8 ÷5= -85 because -8/5 x 5 = -8. This means it makes sense to write -8 ÷5 as−8/ 5. Until this point students have not seen fractions where the numerator or denominator could be a negative integer. But working with the corresponding

Glencoe2- 3B Multiply and Divide Integers (Pg.102 – 103)2- 3C Multiply Integers (Pg. 104 – 108)2- 3D Divide Integers (Pg. 109 – 113)

Holt2-4 Multiplying and Dividing IntegersHands on Lab: Model Integers Multiplications and Division2-10 Equivalent Fractions and Decimals

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lessons:Engage NY: Lesson 11 Multiply Signed NumbersEngage NY: Lesson 12 Division of IntegersEngage NY: Lesson 13 Converting Between Fractions and Decimals Using Equivalent FractionsEngage NY: Lesson 14 Converting Rational Numbers to Decimals Using Long DivisionConnected Math Lessons: 7.NS.2a-d Investigation 3Math Shell: Using Positive and Negative Numbers in ContextUtah Education Network Lesson: Operations with Fractions and Decimals

Tasks:Illustrative Math Tasks: 7.NS.2TNCore Assessment Task: Video Game Ratings (NS.A.1&2) TNCore Task: Video Game Ratings (NS.A.1&2)

Vocabulary: rational numbers, terminate

Middle School Mathematics Vocabulary Word Wall Cards

Writing in Math:Have students explain solutions of real-world problems. The included tasks and additional lessons provide opportunities for written explanations.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESmultiplication equations allows students to make sense of such fractions. In general, they see that –(p/q) = (–p)/q = p/(–q) for any integers p and q with q ≠ 0.

Students should be able to express fractions as decimals and identify which fractions will terminate.

TNCore Task: Leader of the PackTNCore Task: Extending the Number System

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Resources:Math Station Activities: Refer to p. 53Integers, Rational & Irrational NumbersNCTM: Deep Sea Duel ActivityInteger Chips

Correlated iReady Lesson(s): Multiplication and Division of Positive

and Negative Numbers Multiplication and Division of

Rational Numbers Expressing Fractions as Decimals

Domain: The Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.

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

Enduring Understandings: Rational numbers allow us to solve problems

that are not possible to solve with just whole numbers or integers.

Essential Questions: How are rational numbers used and applied

in real-life and mathematical situations?

Objectives: Students will solve problems using the four

operations with rational numbers.

Additional Information: Students use order of operations from 6th

grade to write and solve problems with all rational numbers.

Students will apply concepts and procedures for representing, interpreting, and solving

Use only the Problem Solving Exercises from the following sections

Glencoe3-2A Add and Subtract Like Fractions (Pg. 139 – 143)3-2C Add and Subtract Unlike Fractions (Pg. 146-151)3-2D Add and Subtract Mixed Numbers (Pg. 152 – 156)3-3B Multiply Fractions (Pg. 160 – 165)3-3C Problem Investigation (Pg. 166-167)3-3D Divide Fractions (Pg. 168 – 173)

Holt3-7 Adding and Subtracting Fraction (pg. 176-179)3-8 Adding and Subtracting Mixed Numbers (Pg. 180-183)

Writing in Math:Ask students to respond to either of the following prompts.

Your desk partner was absent from class today. They will need you to summarize the rules for him so he can do his math homework tonight. Write a summary with examples so he can successfully complete his homework tonight.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESreal-world and mathematical problems involving operations with rational numbers.

Example(s): 2/3 of the students at our school have cell phones. 1/4 of those students have Smart phones. What fraction of the students with phones have Smart Phones?

Sarah has $135 left in her checking account after writing checks for $25, $32.50 and $18.40. What was her balance before she wrote the checks?

3-9 Multiplying Fractions and Mixed Numbers (Pg. 186-189)3-10 Dividing Fractions and Mixed Numbers (Pg. 190-193)3-11 Solving Equations Containing Fractions (Pg. 194-197)

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lessons:Engage NY: Lesson Comparing Tape Diagram Solutions to Algebraic SolutionsEngage NY: Lesson 18 Writing, Evaluating, and Finding Equivalent Expressions with Rational NumbersEngage NY: Lesson 19 Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers

Tasks:Illustrative Math: Sharing Prize MoneyTNCore Instructional Tasks: Extending the Number System and The Leader of the PackTNCore Assessment Task: eReader Sales (7.NS.A.3)TNCore: Weight of Candles (NS.A.1&3) TNCore: Winter Denmark (NS.A.1&3) TNCore Task Arc: Adding/Subtracting Positive and Negative Rational Numbers7.NS.1 & 3

Additional Resources:NCTM Lesson: Problems for the Classroom 7.NS.A.3

Correlated iReady Lesson(s): Problem Solving with Rational

Numbers

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Ratio and Proportional Relationships(Allow 4 weeks for instruction, review and assessment)

Domain: Ratios and ProportionalRelationshipsCluster: 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.

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths from a scale drawing.

7.RP.2 Recognize and represent proportional relationships between quantities. 7.RP.2a 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.2b Identify the constant of proportionality (unit rate) in tables, graphs and equations, diagrams and verbal descriptions of proportional relationship. 7.RP.2c 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.2d 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.

Enduring Understanding(s):Ratios and proportional relationships are used to express how quantities are related and how quantities change in relation to each other.

Essential Question(s): What is a proportion? Why are multiplicative relationships

proportional? What is the difference between a unit rate

and a ratio? How are equivalent ratios, values in a table,

and ordered pairs connected? What characteristics define the graphs of all

proportional relationships? How can you apply ratios and proportional

reasoning to real-world situations? How can scale factor be applied to scale

drawings?

Objective(s): Students will calculate unit rates. Students will identify proportional and non-

proportional relationships. Students will use proportions to solve

problems. Students will solve problems involving scale

drawings. Students will compare and contrast

proportional and non-proportional linear functions.

Additional Information:The use of cross products is not the intent of the 7.RP.2 standards.Ratio is a unit or batch, for example, there are 3 cups of apple juice for every 2 cups of grape

Glencoe5-1A Unit Rates (p. 265)5-1B Rates (pgs. 266-271)Additional Lesson 1 (pg. 759-764)5-1C Proportional & Non-proportional Relationships (pgs. 272-275)Additional Lesson 2 (pg. 765-770)5-1E Extend Wildlife Sampling (pgs. 281)5-2A Problem-Solving Investigation (pgs. 282-283)5-2B Scale Drawings (pg. 284-290)Additional Lesson 10 (p.279 only)7-3B Proportional and Non-proportional Relationships (pg. 404)7-3C Direct Variation (pgs. 405-410)

Holt

4-2 Rates (pgs. 218-221)4-3 Identifying and Writing Proportions (pgs. 222-225)4-10 Scale Drawings and Scale Models (pgs. 256-259)5-8 Direct Variation (pgs. 313-317)

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lessons:Engage NY: Ratios and Rates Involving Fractions (RP.A.1,3,EE.4a) (lesson, p. 101)Math Shell Concept Development Lesson: Classifying Proportion and Non-Proportion SituationsCMP Comparing and Scaling Investigations 1-

Vocabulary: rate, unit rate, constant of proportionality, constant rate, proportional, non-proportional, equivalent ratios, proportion, cross products, scale drawing, scale model, scale, scale factor, percent equation, percent of change, percent proportion, simple interest, percent of increase, percent of decrease

Understanding the Vocabulary: Use the following explanations to help students learn the preview words.When a car moves at a constant rate of speed, the relationship between distance and time a proportional relationship because the ratio of distance to time remains constant.In a proportional relationship, the rate of change is constant and is called the constant of proportionality.

Graphic Organizer:Use a bubble map to help students review vocabulary associated with ratios. In each bubble have an example and students should write one or more review words associated with it.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESjuice in the mixture. This way uses a composed unit: 3 cups apple juice and 2 cups grape juice. Any mixture that is made from some number of the composed unit is in the ratio 3 to 2. In the table, each of the mixtures of apple juice and grape juice are combined in a ratio of 3 to 2:

The table below gives the price for different numbers of books. Do the numbers in the table represent a proportional relationship?

Number of Books Price1 33 94 127 18

Solution:Students can examine the numbers to determine that the price is the number of books multiplied by 3, except for 7 books. The row with seven books for $18 is not proportional to the other amounts in the table; therefore, the table does not represent a proportional relationship.

4Comparing and Scaling Teacher Guide

Task(s):TNCore Plant Species Task(RP.A.1-3)TNCore Assessment Tasks: Car Wash, Deshawn's Run, Digging a Ditch, Lemonade Stand, Orange Juice for Sale, Snack Mix, Amusement Park, Babysitting Fees or Basketball Scores(Choose from this list)Illustrative Math: 7.RP.1Illustratvie Math: 7.RP.2

Additional Resources:Math Station Activities pp. 1, 21, 28 & 37Solving Ratio Word Problems (Modeling Ratios)

Correlated iReady Lesson(s): Concept of Rate Ratios Involving Complex Fractions Recognizing Proportional

Relationships Equations for Proportional

Relationships

Three panel flip chartBefore beginning the chapter, have the students create a three panel flip chart to help them organize what they will learn. Label each flap with one of the lesson titles. As they study each lesson, write important ideas like the vocabulary, properties, and formulas under the appropriate flap.Three-panel flip chart examples

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Example(s):• A student is making trail mix. Create a graph to determine if the quantities of nuts and fruit are proportional for each serving size listed in the table. If the quantities are proportional, what is the constant of proportionality or unit rate that defines the relationship? Explain how you determined the constant of proportionality and how it relates to both the table and graph.

The relationship is proportional. For each of the other serving sizes there are 2 cups of fruit for every 1 cup of nuts (2:1). The constant of proportionality is shown in the first column of the table and by the slope of the line on the graph.

Percent and Proportional Relationships(Allow 2 weeks for instruction, review and assessment)

7.RP.A.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.

Enduring Understanding(s): Understanding mathematical relationships

allows us to make predictions, calculate and model unknown quantities.

Proportional relationships express how quantities change in relationship to each other.

Essential Question(s):

Focus On the Problem Solving and H.O.T. Exercises from the following sections

Glencoe6-2C The Percent Equation (p. 337 – 341)6-3B Percent of Change (pgs. 346-350)6-3C Sales Tax & Tips (p.351 – 354)6-3D Discount (p.355-358)6-3E Simple Interest (p.359-362)

Vocabulary: percent, percent of change, percent of increase, percent of decrease, percent equation, percent proportion, principal, simple interest, sales tax, tip, gratuity, commissions, discount

Writing in Math:Compare ratios and percent. How are they alike? How are they different?

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Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES How can you apply ratios and proportional

reasoning to real-world situations?

Objective(s): Students will create and model algebraic

representations and apply their understanding of percent to interpret and solve multi-step problems related to markups or markdowns, simple interest, sales tax, commissions, fees, and percent error.

Students will understand that percent compares relationships that are not based on the same reference whole by standardizing the comparison to a reference whole of 100.

Additional Information:In 6th grade, students used ratio tables and unit rates to solve problems. Students expand their understanding of proportional reasoning to solve problems

Example(s):Students write and solve 1-step equations as a part of their work with percent; for example, the question “ If Kevin paid a total of 13.50, including 8% sales tax, what was the price of the item he purchased?” can be represented by the equation 1.08x =13.50

After eating at a restaurant, Mr. Jackson’s bill before tax is $52.50 The sales tax rate is 8%. Mr. Jackson decides to leave a 20% tip for the waiter based on the pre-tax amount. How much is the tip Mr. Jackson leaves for the waiter? How much will the total bill be, including tax and tip? Express your solution as a multiple of the bill.Solution:

Holt6-5 Solving Percent Problems (p.351-354)6-6 Percent of Change (p.358-361)6-7 Simple Interest (p.362-365)

Choose from the following resources and use them to ensure that the intended outcome and level of rigor of the standards are met.

Additional Lessons:Engage NY ModulesMath Shell Lesson: Comparing Strategies for Proportion ProblemsLearnzillion Lesson

Task(s):Illustrative Math Tasks: 7.RP.3TNCore Task Arc 7.RP.1-3 TNCore Task: Plant Species 7.RP.1-3

Additional Resources:Math Station Activities pp. 1 & 14CPalms Lesson Ideas

Correlated iReady Lesson(s): Problem Solving with Proportional

Relationships

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Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESThe amount paid = 0.20 x $52.50 + 0.08 x $52.50 = 0.28 x $52.50 or $14.70 for the tip and tax. The total bill would be $67.20.

Example using the within ratios format:Three candies cost a total of $2.40. At that same price, how much would 10 candies cost?

The within ratios proportion is: $2.40

3candies

= x

10candies. To determine the factor of

change (unit cost) for one candy, divide $2.40 by 3.

The factor of change is 1

0.8 (or $0.80 for one

candy), meaning that as the number of candies increases by one, the total cost increases by $0.80. So, 10 candies ($0.80 x 10) would cost $8.00.

Example:Gas prices are projected to increase 124% by April 2015. A gallon of gas currently costs $4.17. What is the projected cost of a gallon of gas for April 2015?

A student might say: “The original cost of a gallon of gas is $4.17. An increase of 100% means that the cost will double. I will also need to add another 24% to figure out the final projected cost of a gallon of gas. Since 25% of $4.17 is about $1.04, the projected cost of a gallon of gas should be around $9.40.”$4.17 + 4.17 + (0.24 • 4.17) = 2.24 x 4.17

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100% 100% 24%$4.17 $4.17 ?

Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

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Curriculum and Instruction – Office of Mathematics Quarter 1 Grade 7

RESOURCE TOOLBOXNWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.Textbook Resourceswww.myhrw.comwww.connected.mcgraw-hill.com

TN Core/CCSSTNReady Math StandardsAchieve the Corehttp://www.edutoolbox.org

VideosKhan AcademyConcept Maps

Calculator ActivitiesTexas Instruments Education www.casioeducation.com

Interactive ManipulativesNational Library of Virtual ManipulativesIlluminationsGlencoe Virtual ManipulativesMath Manipulatives

Additional Siteshttp://www.learnzillion.comhttp://www.betterlessons.comhttp://www.insidemathematics.org

Otherhttp://community.ksde.org/LinkClick.aspx?fileticket=N2Pv3jNYF48%3d&tabid=5646&mid=13290

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