Navigation

6-8 Accelerated 6 Unit 4 Lesson 9

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

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 •Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

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

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

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

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

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/ .

Adaptations and updates to IM 6-8 Math v.360 are ©2024 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution-Noncommercial 4.0 International License (CC BY-NC 4.0).

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) .

Spanish translation of the “B” assessments are ©2020 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 4, Lesson 9

The Distributive Property, Part 2

Accelerated 6

Practice

Problem 1

Here is a rectangle.

Area diagram. A rectangle partioned vertically into 3 smaller rectangles.

Explain why the area of the large rectangle is \(2a + 3a + 4a\).
Explain why the area of the large rectangle is \((2+3+4)a\).

to access Practice Problem Solutions.

Lesson 9 Resources

Student Materials

Problem 2

Is the area of the shaded rectangle \(6(2-m)\) or \(6(m-2)\)? Explain how you know.

Area diagram partitioned into two attached rectangles one with a shaded area.

to access Practice Problem Solutions.

Problem 3

Select all the expressions that represent the total area of the rectangle.

A rectangle partitioned by a vertical line segment into two smaller rectangles. the vertical side is labeled t and the top horizontal side lengths are labeled 5 and 4.

\(5t + 4t\)
\(t + 5 + 4\)
\(9t\)
\(4 \boldcdot 5 \boldcdot t\)
\(t(5+4)\)

to access Practice Problem Solutions.

Problem 4

ForLesson 8: The Distributive Property, Part 1

Use the distributive property to write an equivalent expression.

\(35\boldcdot 91-35\boldcdot 89\)
\(22\boldcdot 87+22\boldcdot 13\)
\(\frac{9}{11}\boldcdot \frac{7}{10}-\frac{9}{11}\boldcdot \frac{3}{10}\)

to access Practice Problem Solutions.

Problem 5

ForLesson 7: Equal and Equivalent

Select all the expressions that are equivalent to \(4b\).

\(b+b+b+b\)
\(b+4\)
\(2b+2b\)
\(b \boldcdot b \boldcdot b \boldcdot b\)
\(b \div \frac{1}{4}\)

to access Practice Problem Solutions.

Problem 6

ForLesson 4: Practice Solving Equations

Solve each equation. Show your reasoning.

\(111=14a\)

\(13.65 = b + 4.88\)

\(c+ \frac{1}{3} = 5\frac{1}{8}\)

\(\frac{2}{5} d = \frac{17}{4}\)

\(5.16 = 4e\)

to access Practice Problem Solutions.

Problem 7

ForLesson 5: Represent Situations with Equations

A robot did \(5\frac12\) laps around a track in 8 minutes. It took the robot \(x\) minutes to complete each lap at a constant speed. Select all the equations that represent this situation.

\(\left(5\frac{1}{2}\right)x = 8\)
\(5 \frac{1}{2} + x = 8\)
\(5 \frac{1}{2} - x = 8\)
\(5 \frac{1}{2} \div x = 8\)
\(x = 8 \div \left(5\frac{1}{2}\right)\)
\(x = \left(5\frac{1}{2}\right) \div 8\)

to access Practice Problem Solutions.