Navigation

6-8 Grade 8 Unit 8 Lesson 14

Gradeband

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

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

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

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 | 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 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

Language

Audience

family

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.

English
Español

teacher
student
family

Lesson 14

14.1 Warm-up 14.2 Activity 14.3 Activity Student Lesson Summary Glossary

Unit 8, Lesson 14

Edge Lengths and Volumes

Grade 8

14.1

Warm-up

Ordering Squares and Cubes

Let , , , , , and be positive numbers.

Given these equations, arrange , , , , , and from least to greatest. Explain your reasoning.

Are You Ready for More?

14.2

Activity

Name That Edge Length!

Fill in the missing values using the information provided:

A cube.

sides	volume	volume equation
	27 in³
in

Are You Ready for More?

14.3

Activity

Card Sort: Rooted in the Number Line

Your teacher will give you a set of cards. Each card has a number line with a plotted point, an equation, or a square or cube root value.

For each card with a letter and square or cube root value, match it with the location on a number line where the value exists, and the equation that the value makes true. Record your matches and be prepared to explain your reasoning.

Are You Ready for More?

Student Lesson Summary

For a square, its side length is the square root of its area. For example, this square has an area of 16 square units and a side length of 4 units.

Both of these equations are true:

A square with a side length of 4 units on a square grid.

For a cube, the edge length is the cube root of its volume. For example, this cube has a volume of 64 cubic units and an edge length of 4 units:

Both of these equations are true:

A solid cube composed of 64 unit cubes. Each edge length is 4 unit cubes.

is pronounced “the cube root of 64.” Here are some other values of cube roots:

because

because

because

Glossary

cube root

The cube root of a number is the number whose cube is . It is also the edge length of a cube with a volume of . The cube root of is written as .

The cube root of 64 is written as . Its value is 4 because is 64.

is also the edge length of a cube that has a volume of 64.