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875 KB|46 pages

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6th Grade – Ratios and Proportional Relationships includes ten activities that help students develop mastery of the mathematical practices within the content area of ratios and proportional relationships. For educators for whom the Common Core Standards are important, each activity is referenced to the sixth grade ratio and proportional relationships standards. The description of each standard follows:

6.RP.A.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.A.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."

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

6.RP.A.1 is addressed in Activities 1

6.RP.A.2 is addressed in Activities 2, 10

6.RP.A.3.a. is addressed in Activities 6, 10

6.RP.A.3.b. is addressed in Activities 7, 8, 9, 10

6.RP.A.3.c. is addressed in Activities 3, 5, 10

6.RP.A.3.d. is addressed in Activities 4

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The Make It Real Learning Middle Grades Math Series is a collection of 20 workbooks that address the mathematical content standards of Grades 5, 6, 7, and 8. Each workbook contains ten standards-aligned activities that develop mathematical thinking. Interesting real world contexts are integrated into many of the activities.

Fifth Grade Mathematics Workbooks

• 5th Grade Operations and Algebraic Thinking

• 5th Grade Numbers and Operations in Base 10

• 5th Grade Numbers and Operations – Fractions

• 5th Grade Measurement and Data

• 5th Grade Geometry

Sixth Grade Mathematics Workbooks

• 6th Grade Ratios and Proportional Relationships

• 6th Grade The Number System

• 6th Grade Expressions and Equations

• 6th Grade Geometry

• 6th Grade Statistics and Probability

Seventh Grade Mathematics Workbooks

• 7th Grade Ratios and Proportional Relationships

• 7th Grade The Number System

• 7th Grade Expressions and Equations

• 7th Grade Geometry

• 7th Grade Statistics and Probability

Eighth Grade Mathematics Workbooks

• 8th Grade The Number System

• 8th Grade Expressions and Equations

• 8th Grade Functions

• 8th Grade Geometry

• 8th Grade Statistics and Probability

6.RP.A.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.A.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."

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

6.RP.A.1 is addressed in Activities 1

6.RP.A.2 is addressed in Activities 2, 10

6.RP.A.3.a. is addressed in Activities 6, 10

6.RP.A.3.b. is addressed in Activities 7, 8, 9, 10

6.RP.A.3.c. is addressed in Activities 3, 5, 10

6.RP.A.3.d. is addressed in Activities 4

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The Make It Real Learning Middle Grades Math Series is a collection of 20 workbooks that address the mathematical content standards of Grades 5, 6, 7, and 8. Each workbook contains ten standards-aligned activities that develop mathematical thinking. Interesting real world contexts are integrated into many of the activities.

Fifth Grade Mathematics Workbooks

• 5th Grade Operations and Algebraic Thinking

• 5th Grade Numbers and Operations in Base 10

• 5th Grade Numbers and Operations – Fractions

• 5th Grade Measurement and Data

• 5th Grade Geometry

Sixth Grade Mathematics Workbooks

• 6th Grade Ratios and Proportional Relationships

• 6th Grade The Number System

• 6th Grade Expressions and Equations

• 6th Grade Geometry

• 6th Grade Statistics and Probability

Seventh Grade Mathematics Workbooks

• 7th Grade Ratios and Proportional Relationships

• 7th Grade The Number System

• 7th Grade Expressions and Equations

• 7th Grade Geometry

• 7th Grade Statistics and Probability

Eighth Grade Mathematics Workbooks

• 8th Grade The Number System

• 8th Grade Expressions and Equations

• 8th Grade Functions

• 8th Grade Geometry

• 8th Grade Statistics and Probability

Total Pages

46 pages

Answer Key

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