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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

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6-8 Grade 6 Unit 2

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K-5 Math •6-8 Math 9-12 Math

Course

•Grade 6 Grade 7 Grade 8

Unit

Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

K-5
6-8
9-12

Grade 6
Grade 7
Grade 8

Accelerated 6
Accelerated 7

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

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Unit 2

Student Learning Targets

Grade 6

Section AWhat Are Ratios?

Section BEquivalent Ratios

Section CRepresenting Equivalent Ratios

Section DSolving Ratio and Rate Problems

11

Representing Ratios with Tables

If I am looking at a table of values, I know where the rows are and where the columns are.
When I see a table representing a set of equivalent ratios, I can come up with numbers to make a new row.
When I see a table representing a set of equivalent ratios, I can explain what the numbers mean.

12

Navigating a Table of Equivalent Ratios

I can solve problems about situations happening at the same rate by using a table and finding a “1” row.
I can use a table of equivalent ratios to solve problems about unit price.

13

Tables and Double Number Line Diagrams

I can create a table that represents a set of equivalent ratios.
I can explain why sometimes a table is easier to use than a double number line to solve problems involving equivalent ratios.
I include column labels when I create a table, so that the meaning of the numbers is clear.

Section EPart-Part-Whole Ratios

Section FLet’s Put It to Work

Unit 2 Resources

Student Materials

14

Solving Equivalent Ratio Problems

I can decide what information I need to know to be able to solve problems about situations happening at the same rate.
I can explain my reasoning using diagrams that I choose.

1

Introducing Ratios and Ratio Language

I can write or say a sentence that describes a ratio.
I know how to say words and numbers in the correct order to accurately describe the ratio.

2

Representing Ratios with Diagrams

I can draw a diagram that represents a ratio and explain what the diagram means.
I include labels when I draw a diagram that represents a ratio, so that the meaning of the diagram is clear.

3

Recipes

I can explain what it means for two ratios to be equivalent using a recipe as an example.
I can use a diagram to represent a recipe and to represent a double batch and a triple batch of the recipe.
I know what it means to double or triple a recipe.

4

Color Mixtures

I can explain the meaning of equivalent ratios using a color mixture as an example.
I can use a diagram to represent a single batch, a double batch, and a triple batch of a color mixture.
I know what it means to double or triple a color mixture.

5

Defining Equivalent Ratios

If I have a ratio, I can create a new ratio that is equivalent to it.
If I have two ratios, I can decide whether they are equivalent to each other.

6

Introducing Double Number Line Diagrams

I can label a double number line diagram to represent batches of a recipe or color mixture.
When I have a double number line that represents a situation, I can explain what it means.

7

Creating Double Number Line Diagrams

I can create a double number line diagram and correctly place and label tick marks to represent equivalent ratios.
I can explain what the word "per" means.

8

How Much for One?

I can choose and create diagrams to help me reason about prices.
I can explain what the phrase “at this rate” means, using prices as an example.
If I know the price of multiple things, I can find the price per thing.

9

Constant Speed

I can choose and create diagrams to help me reason about constant speed.
If I know that an object is moving at a constant speed, and I know two of these things: the distance it travels, the amount of time it takes, and its speed, I can find the other thing.

10

Comparing Situations by Examining Ratios

I can decide whether or not two situations are happening at the same rate.
I can explain what it means when two situations happen at the same rate.
I know some examples of situations where things can happen at the same rate.

15

Part-Part-Whole Ratios

I can create tape diagrams to help me reason about problems that involve both a ratio and a total amount.
I can solve problems when I know a ratio and a total amount.

16

Solving More Ratio Problems

I can choose and create diagrams to help think through my solution.
I can solve all kinds of problems about equivalent ratios.
I can use diagrams to help someone else understand why my solution makes sense.

17

A Fermi Problem

I can apply what I have learned about ratios and rates to solve a more complicated problem.
I can decide what information I need to know to be able to solve a real-world problem about ratios and rates.