Lesson 5 Side Lengths of Rectangular Prisms

    • Let’s describe the side lengths of a prism and find the volume.

Warm-up Notice and Wonder: Prism Print

What do you notice? What do you wonder?

Prism. 2 by 1 by 6 cubes.
Prism. 6 by 1 by 2 cubes.
Prism. 2 by 6 by 1 cubes.
Rectangle. 2 squares by 1 squares.
Rectangle. 6 squares by 1 square. 
Rectangle. 2 squares by 6 squares.

Activity 1 All About That Base

Here are 3 rectangular prisms.

1
Prism. 3 by 4 by 4 cubes. 
2
Prism. 3 by 6 by 4 cubes. 
3
Prism. 3 by 5 by 4 cubes.

These rectangles represent bases of the prisms.

A
Rectangle. 3 by 6 squares.
B
Rectangle. 3 by 4 squares.
C
Rectangle. 5 squares by 3 squares.

  1. Match each prism with a rectangle that represents its base. Note: Some prisms may match more than 1 rectangular base.

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

Activity 2 Growing Prism

Here is a base of a rectangular prism.

Rectangle. 10 squares by 4 squares.

Fill out the table for the volumes of rectangular prisms with this base and different heights.

height

multiplication expression to represent the volume

volume

Activity 3 What is the Question?

This is the base of a rectangular prism that has a height of 5 cubes.

Diagram. Rectangle partitioned into 3 rows of 4 of the same size squares.

These are answers to questions about the prism. Read each answer and determine what question it is answering about the prism.

  1. 3 is the answer. What is the question?

  2. 5 is the answer. What is the question?

  3. . The answer is 12. What is the question?

  4. . The answer is 60 cubes. What is the question?

  5. 3 by 4 by 5 is the answer. What is the question?

Practice Problem

Problem 1

Andre and Clare used different strategies to find the volume of this rectangular prism.

Prism. 8 by 6 by 4 units. 

  1. Andre says the volume of this rectangular prism is cubic units. Explain or show why Andre is correct.

  2. Clare says the volume of the rectangular prism is cubic units. Explain or show why Clare is also correct.