# 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.
• 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

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

### Required Preparation

Copies of the blackline master for this lesson. Prepare 1 copy for every 3 students, and cut them up ahead of time.

### 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

• 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.