Lesson 10
Edge Lengths, Volumes, and Cube Roots
Lesson Narrative
In this lesson, students extend their thinking from square roots to cube roots. They learn the notation and meaning of cube roots, such as \(\sqrt[3]{8}\). In the warm-up, they order solutions to equations of the form \(a^2=9\) and \(b^3=8\). Next, 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 last activity, students continue to work with cube roots, moving away from the geometric interpretation in favor of the algebraic definition. They approximate cube roots and locate them on the number line. They see their first negative cube root, and locate it on the number line. The following lessons build on the work here as students further their study of decimal representations of rational and irrational numbers.
Learning Goals
Teacher Facing
- Approximate the value of a cube root to the nearest whole number and to the nearest tenth.
- Reason about cube roots.
- Recognize and use cube root notation to represent the edge length of a cube given its volume.
- Understand that given the volume of a cube, the length of its edge is called the cube root of the volume.
Student Facing
Required Materials
Required Preparation
Learning Targets
Student Facing
- I can approximate cube roots.
- I know what a cube root is.
- I understand the meaning of expressions like $\sqrt[3]{5}$.
Glossary Entries
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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.
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