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6-8 Accelerated 6 Unit 5

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•Accelerated 6 Accelerated 7

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Curriculum

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.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is ©2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) . OUR's 6-8 Math Curriculum is available at https://openupresources.org/math-curriculum/ .

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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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Unit 5

Student Learning Targets

Accelerated 6

Section ARepresenting Proportional Relationships with Equations

Section BComparing Proportional and Nonproportional Relationships

4

Comparing Relationships with Tables

I can decide if a relationship represented by a table could be proportional and when it is definitely not proportional.

5

Comparing Relationships with Equations

I can decide if a relationship represented by an equation is proportional or not.

6

Solving Problems about Proportional Relationships

I can ask questions about a situation to determine whether two quantities are in a proportional relationship.
I can solve all kinds of problems involving proportional relationships.

Section CRepresenting Proportional Relationships with Graphs

Section DCircumference of a Circle

Section EArea of a Circle

Section FLet’s Put It to Work

Unit 5 Resources

Student Materials

1

Proportional Relationships and Equations

I can write an equation of the form to represent a proportional relationship shown in a table or described in a story.
I can write the constant of proportionality as an entry in a table.

2

Two Equations for Each Relationship

I can find two constants of proportionality for a proportional relationship.
I can write two equations representing a proportional relationship described by a table or story.

3

Writing Equations to Represent Relationships

I can find missing information in a proportional relationship using the constant of proportionality.
I can relate all parts of an equation like to the situation it represents.

7

Graphs of Proportional Relationships

I can find the constant of proportionality from a graph.
I know that the graph of a proportional relationship lies on a line through .

8

Using Graphs to Compare Relationships

I can compare two, related proportional relationships based on their graphs.
I know that the steeper graph of two proportional relationships has a larger constant of proportionality.

9

Two Graphs for Each Relationship

I can interpret a graph of a proportional relationship using the situation.
I can write an equation representing a proportional relationship from a graph.

17

Four Representations

I can make connections between the graphs, tables, and equations of a proportional relationship.
I can use units to help me understand information about proportional relationships.

18

Using Water Efficiently

I can answer a question by representing a situation using proportional relationships.

19

Distinguishing Circumference and Area

I can decide whether a situation about a circle has to do with area or circumference.
I can use formulas for circumference and area of a circle to solve problems.

20

Stained-Glass Windows

I can apply my understanding of area and circumference of circles to solve more complicated problems.

14

Estimating Areas

I can calculate the area of a complicated shape by breaking it into shapes whose area I know how to calculate.

15

Area of a Circle

I know the formula for area of a circle.
I know whether or not the relationship between the diameter and area of a circle is proportional and can explain how I know.

16

Applying Area of Circles

I can calculate the area of more complicated shapes that include fractions of circles.
I can write exact answers in terms of .

10

How Well Can You Measure?

I can examine quotients and use a graph to decide whether two associated quantities are in a proportional relationship.
I understand that it can be difficult to measure the quantities in a proportional relationship accurately.

11

Exploring Circles

I can describe the characteristics that make a shape a circle.
I can identify the diameter, center, radius, and circumference of a circle.

12

Exploring Circumference

I can describe the relationship between circumference and diameter of any circle.
I can explain what means.

13

Applying Circumference

I can choose an approximation for based on the situation or problem.
If I know the radius, diameter, or circumference of a circle, I can find the other two.