Unit 8

Edge Lengths and Volumes/ Cube Roots

Pythagorean Theorem & Irrational Numbers

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Lesson 12/13

8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form 𝘹² = 𝘱 and 𝘹³ = 𝘱, where 𝘱 is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

Expressions and Equations

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Warm Up

Unit 8 ● Lesson 12

1 min individual - 1 min team share - 3 mins class share

Page 182

a = 3

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b = 2

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c ≈ 3.2

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d ≈ 2.1

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e ≈ 2.8

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f ≈ 1.9

The order is f, b, d, e, a, c

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Warm Up

Unit 8 ● Lesson 12

1 min individual - 1 min team share - 3 mins class share

Page 182

∛7

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Glossary

Unit 8 ● Lesson 12

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

• Let’s explore the relationship between volume and edge lengths of cubes.

Unit 8 ● Lesson 12

We will be able to find a decimal approximation for cube roots so that we can plot cube roots on the number line.

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Learning

Goal

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Where were we? Where are we? Where are we going?

Unit 8 ● Lesson 12

Agenda Review

You are successful today when...,

• You know what a cube root is.
• You can approximate cube roots.
• You understand the meaning of expressions like ∛5.
• When you have a cube root, you can reason about which two whole numbers it is between.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

12.2 Activity: Name That Edge Length!

You can approximate cube roots.

10 mins total

3 min individual - 2 minutes group - 3 mins class share

pg 183

∛27 = 3

3

(∛5)³ = 5

5in³

∛16

16in³

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

13.2 Activity: Cube Root Values

You can approximate cube roots.

10 mins total

2 min individual - 2 minutes group - 4 mins class share

pg 188

No Calculators

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

13.3 Activity: Solutions on a Number Line

You can approximate cube roots.

10 mins total

2 min individual - 2 minutes group - 4 mins class share

pg 189

No Calculators

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Are you ready for more? Try this!

You can approximate cube roots.

3 mins total

2 min group - 1 mins class share

pg 189

You CANNOT take a square root of a negative number.

You CAN take a cube root of a negative number.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Cube Roots

You can approximate cube roots.

Find the two whole numbers they lie between, and determine the approximate location between them.

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Different Types of Roots

You can approximate cube roots.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 8 ● Lesson 12

• I know what a cube root is.
• I can approximate cube roots.
• I understand the meaning of expressions like ∛5.
• When I have a cube root, I can reason about which two whole numbers it is between.

Learning

Targets

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 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 are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 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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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 consent of Illustrative Mathematics.

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