# Lesson 12

Edge Lengths and Volumes

### Lesson Narrative

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., $$\sqrt{8}$$. In the warm-up, 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 warm-up, 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.

### Learning Goals

Teacher Facing

• Comprehend the term “cube root of $a$” (in spoken language) and the notation $\sqrt{a}$ (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.

### 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 $\sqrt{5}$.

### 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 $$\sqrt{n}$$.

For example, the cube root of 64, written as $$\sqrt{64}$$, is 4 because $$4^3$$ is 64. $$\sqrt{64}$$ is also the edge length of a cube that has a volume of 64.