Learn on PengiIllustrative Mathematics, Grade 5Chapter 1: Finding Volume

Lesson 2: Calculate Volume Using Layers

In this Grade 5 Illustrative Mathematics lesson, students learn to calculate the volume of rectangular prisms by counting unit cubes organized into horizontal or vertical layers. Using connecting cubes and prism images, they practice multiplying the number of layers by the number of cubes in each layer to find total volume, building toward standard 5.MD.C.5. The lesson connects multiplication of three factors to the layered structure of prisms as a systematic strategy for measuring volume.

Section 1

Identifying Layers in Prism Drawings

Property

To find the number of cubes in one layer from a 2D drawing, multiply the number of cubes along its length and width. The total number of layers is the height of the prism.

Cubes in one layer=(cubes in length)×(cubes in width) \text{Cubes in one layer} = (\text{cubes in length}) \times (\text{cubes in width})
Number of layers=cubes in height \text{Number of layers} = \text{cubes in height}

Examples

Section 2

Calculating Volume by Layers

Property

The volume of a rectangular prism can be found by multiplying the number of unit cubes in a single layer by the total number of layers.

V=(cubes in one layer)×(number of layers)V = (\text{cubes in one layer}) \times (\text{number of layers})

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Identifying Layers in Prism Drawings

Property

To find the number of cubes in one layer from a 2D drawing, multiply the number of cubes along its length and width. The total number of layers is the height of the prism.

Cubes in one layer=(cubes in length)×(cubes in width) \text{Cubes in one layer} = (\text{cubes in length}) \times (\text{cubes in width})
Number of layers=cubes in height \text{Number of layers} = \text{cubes in height}

Examples

Section 2

Calculating Volume by Layers

Property

The volume of a rectangular prism can be found by multiplying the number of unit cubes in a single layer by the total number of layers.

V=(cubes in one layer)×(number of layers)V = (\text{cubes in one layer}) \times (\text{number of layers})