This is the first of two lessons in which students learn about cube roots. In the first lesson, students learn the notation and meaning of cube roots, e.g., \(\sqrt[3]8\). In the warmup, they order solutions to equations of the form \(a^2=9\) and \(b^3=8\). They already know about square roots, so in the discussion of the warmup, they learn about the parallel definition of cube roots. In the following classroom activity, students use cube roots to find the edge length of a cube with given volume. A card sort activity helps them make connections between cube roots as values, as solutions to equations, and as points on the number line.
In the next lesson, students will find out that it is possible to find cube roots of negative numbers.
Lesson overview
 12.1 Warmup: Ordering Squares and Cubes (10 minutes)

12.2 Activity: Name That Edge Length! (10 minutes)
 Includes "Are you Ready for More?" extension problem
 12.3 Activity: Card Sort: Rooted in the Number Line (15 minutes)
 Lesson Synthesis
 12.4 Cooldown: Roots of 36 (5 minutes)
Learning goals:
 Comprehend the term “cube root of \(a\)” (in spoken language) and the notation \(\sqrt[3]{a}\) (in written language) to mean the side length of a cube whose volume is \(a\) cubic units.
 Coordinate representations of a cube root, including cube root notation, decimal representation, the side length of a cube of given volume, and a point on the number line.
Learning goals (student facing):
 Let’s explore the relationship between volume and edge lengths of cubes.
Learning targets (student facing):
 I can approximate cube roots.
 I know what a cube root is.
 I understand the meaning of expressions like \(\sqrt[3]5\).
Required materials:
 preprinted slips, cut from copies of the blackline master (See Additional Materials section of this lesson)
Required preparation:
 Copies of the blackline master for this lesson.
 Prepare 1 copy for every 3 students, and cut them up ahead of time.
Glossary:
 cube root  The cube root of a number \(n\) is the number whose cube is \(n\). It is also the edge length of a cube with a volume of \(n\). We write the cube root of \(n\) as \(\sqrt[3]{n}\). For example, the cube root of 64, written as \(\sqrt[3]{64}\), is 4 because \(4^3\) is 64. \(\sqrt[3]{64}\) is also the edge length of a cube that has a volume of 64.
 Access the complete Grade 8 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 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/mathcurriculum/.
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).
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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