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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).

IM 6-8 Math v.360, an IM v.360 curriculum, is a derivative of IM 6-8 Math.

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Adaptations and additions to create IM 6–8 Math v.360 Accelerated are ©2025 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY-NC 4.0).

Adaptations to add additional English language learner supports are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The second set of English assessments (marked as set “B”) are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) .

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6-8 Accelerated 6 Unit 2

Gradeband

K-5 Math •6-8 Math 9-12 Math

Course

•Accelerated 6 Accelerated 7

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

Accelerated 6
Accelerated 7

Grade 6
Grade 7
Grade 8

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

Accelerated 6

Section AWhat Are Ratios?

Section BRepresenting Equivalent Ratios

4

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.

5

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.

6

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.

7

Constant Speed

Section CPart-Part-Whole Ratios

Section DUnits of Measurement and Unit Conversion

14

Anchoring Units of Measurement

I can name common objects that are about as long as 1 inch, foot, yard, mile, millimeter, centimeter, meter, or kilometer.
I can name common objects that weigh about 1 ounce, pound, ton, gram, or kilogram, or that hold about 1 cup, quart, gallon, milliliter, or liter.
When I read or hear a unit of measurement, I know whether it is used to measure length, weight, or volume.

15

Measuring with Different-Size Units

When I know a measurement in one unit, I can decide whether it takes more or less of a different unit to measure the same quantity.

16

Converting Units

I can convert measurements from one unit to another, using double number lines, tables, or by thinking about “how much for 1.”
I know that when we measure things in two different units, the pairs of measurements are equivalent ratios.

Section ERates

Section FPercentages

Section GLet's Put It to Work

Unit 2 Resources

Student Materials

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.

8

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.

9

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.

10

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.

11

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.

17

Comparing Speeds and Prices

I understand that if two ratios have the same rate per 1, they are equivalent ratios.
When measurements are expressed in different units, I can decide who is traveling faster or which item is the better deal by comparing “how much for 1” of the same unit.

18

Interpreting Rates

I can choose which unit rate to use based on how I plan to solve the problem.
When I have a ratio, I can calculate its two unit rates and explain what each of them means in the situation.

19

Equivalent Ratios Have the Same Unit Rates

I can give an example of two equivalent ratios and show that they have the same unit rates.
I can multiply or divide by the unit rate to calculate missing values in a table of equivalent ratios.

20

Solving Rate Problems

I can see that thinking about “how much for 1” is useful for solving different types of problems.

1

Representing Ratios with Diagrams

I can draw a diagram that represents a ratio and explain what the diagram means.
I know how to say words and numbers in the correct order to accurately describe the ratio.

2

Mixtures

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.

3

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.

12

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.

13

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.

27

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.

28

Painting a Room

I can apply what I have learned about unit rates and percentages to predict how long it will take and how much it will cost to paint all the walls in a room.

21

What Are Percentages?

I can use double number line diagrams to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”

22

Representing Percentages in Different Ways

I can use tape diagrams and tables to solve different problems like “What is 40% of 60?” or “60 is 40% of what number?”

23

Benchmark Percentages

When I read or hear that something is 10%, 25%, 50%, or 75% of an amount, I know what fraction of that amount they are referring to.

24

Solving Percentage Problems

I can choose and create diagrams to help me solve problems about percentages.

25

Finding This Percent of That

I can solve different problems like “What is 40% of 60?” by dividing and multiplying.

26

Finding the Percentage

I can solve different problems like “60 is what percentage of 40?” by dividing and multiplying.