Unit 8, Lesson 12
Edge Lengths, Volumes, and Cube Roots
Accelerated 7
Preparation
Lesson Narrative
In this lesson, students are formally introduced to cube roots and cube root notation where is the length of the edge of a cube whose volume is cubic units.
Students begin by ordering solutions to equations of the form and . Since they are already familiar with square roots and square root notation, this allows for a smooth transition to the parallel definition of cube roots. A Card Sort helps students make connections between square roots and cube roots as values, as solutions to equations, and as points on the number line.
Then students are encouraged to transition from the geometric characterization of cube roots as edge lengths to an algebraic characterization of cube roots as solutions to equations of the form that can be understood as values on a number line.
- Comprehend the term “cube root of $n$” (in spoken language) and the notation $\sqrt[3]{n}$ (in written language) to mean the edge length of a cube whose volume is $n$ cubic units.
- Coordinate representations of a cube root, including cube root notation, decimal representation, the edge length of a cube of given volume, and a point on the number line.
- Generalize a process for approximating the value of the cube root of a number, and justify (orally and in writing) that if $x^3=n$, then $x=\sqrt[3]{n}$.
Let's explore the relationship between volume and edge lengths of cubes.
Required Materials
Activity 2
Required Preparation
None