A. Unit Cubes and Volume

In this section, students learn to call the amount of space an object takes up volume. Volume is measured in unit cubes. For example, this prism has a volume of 120 unit cubes.

A rectangular prism made of unit cubes. The prism is 6 unit cubes wide, 5 unit cubes high, and 4 unit cubes deep.

To find the volume of any prism, students can count the number of unit cubes in one layer and multiply that number by the number of layers. In this example, students might describe this prism as having 5 layers of 24 unit cubes.
They can find the number of cubes by multiplying 5 and 24. So \(5\times24=120\).

B. Expressions for Finding Volume

In this section, students find the volume of a rectangular prism by multiplying the side lengths or by multiplying the area of the base by the height.

A rectangular prism labeled with a height of 6 units, width of 3 units, and depth of 5 units.

For example, they can multiply the length by the width by the height, or \(3\times5\times6\), or they can find the bottom area by multiplying \(3\times5\) to get 15 and then multiplying 15 by 6. The volume of this rectangular prism is 90 cubic units.

C. Volume of Solid Figures

In this section, students learn that some figures are made from two rectangular prisms. They break apart these figures and find the volume of each prism. Then they add the volumes of the two prisms to find the total volume of the figure.

A solid made of unit cubes. It is 5 unit cubes high. The base is an L-shape that is 6 unit cubes wide overall. The left 4 unit cubes of width are 4 unit cubes deep, and the right 2 unit cubes of width are 2 unit cubes deep.

Depending on how they break it apart, students can find the volume in different ways. They could multiply in these ways to find the volume of the figure:

\((3\times3\times5)+(5\times2\times5)\)

\((3\times5\times5)+(2\times2\times5)\)

Grade 5 Unit 1 | Finding Volume | Family Support