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Decompose Rectangular Prisms

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Videos, examples, solutions, and lessons to help Grade 5 students learn how to compose and decompose right rectangular prisms using layers.

New York State Common Core Math Module 5, Grade 5, Lesson 3

Common Core Standards: 5.MD.3, 5.MD.4

Lesson 3 Concept Development

Lesson 3 Problem Set

1. Use the prisms to find the volume.
• Build the rectangular prism pictured below to the left with your cubes, if necessary.
• Decompose it into layers in three different ways, and show your thinking on the blank prisms.
• Complete the missing information in the table.

2. Josh and Jonah were finding the volume of the prism to the right. The boys agree that 4 layers can be added together to find the volume. Josh says that he can see on the end of the prism that each layer will have 16 cubes in it. Jonah says that each layer has 24 cubes in it. Who is right? Explain how you know using words, numbers, and/or pictures.

Lesson 3 Homework

This video shows how to find the volume of rectangular prisms using a method of decomposing in layers.

1. Use the prisms to find the volume.

  • The rectangular prisms pictured below were constructed with 1-cm cubes
  • Decompose each prism into layers in three different ways, and show your thinking on the blank prisms.
  • Complete each table

2. Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters. Chelsea wants to add eight layers and Stephen says they only need to add four layers.
Their teacher tells them they are both correct. Explain how this is possible. Lesson 3 Homework

4. Imagine the rectangular prism below is 4 meters long, 3 meters tall, and 2 meters wide. Draw horizontal lines to show how the prism could be decomposed into layers that are 1 meter in height.
It has _____ layers from left to right.
Each layer contains ______ cubic units.
The volume of this prism is __________.

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