Lesson 4 Use Layers to Determine Volume

    • Let’s relate multiplication to how we use layers to find volume.

Warm-up Estimation Exploration: How Many Cubes?

Rectangular prism. 3 cubes by unknown number between 8 to 10 cubes. Height is 3 cubes.

About how many cubes were used to build this prism?

Record an estimate that is:

too low

about right

too high

Activity 1 Layers in Rectangular Prisms

Problem 1

Rectangular prism. Base shown with cubes: 2 cubes by 7 cubes. Height partially shown with 3 cubes. 

Complete the table. Be prepared to explain your reasoning.

Prism A
Rectangular prism. 2 cubes by 3 cubes by 4 cubes. 
Prism B
Rectangular prism. 3 cubes by 5 cubes by 2 cubes. 
Prism C
Rectangular prism partially filled. Base shown as 3 cubes by 2 cubes. Height shown as 5 cubes. 
Prism D
Rectangular prism, partially filled with cubes. Base shown as 4 cubes by 2 cubes. Height shown as three cubes. 

prism

number of cubes in one layer

number of layers

volume

A

B

C

D

Problem 2

Find the volume of each prism. Explain or show your reasoning.

  1. Prism E
    Rectangular prism. 4 cubes by 1 cubes by 2 cubes. 
  2. Prism F
    Partially filled Rectangular prism. 2 cubes wide. 7 cubes long. 6 cubes high.

Problem 3

How can you find the volume of any rectangular prism?

Activity 2 Finding Volume in Different Ways

Rectangular prism. 6 cubes by 4 cubes by 5 cubes. 

  1. Explain or show how the expression represents the volume of this rectangular prism.

  2. Explain or show how the expression represents the volume of this rectangular prism. 

  3. Find a different way to calculate the volume of this rectangular prism. Explain or show your thinking.

  4. Write an expression to represent the way you calculated the volume.

Practice Problem

Problem 1

Find the volume of each rectangular prism. Explain or show your reasoning.

  1. Prism. 3 by 1 by 4 cubes.
  2. Rectangular prism. Base, 2 cubes by 3 cubes. Height shown with 3 cubes.