# Measuring Volume by Counting Unit Cubes

Students will investigate the concept of volume measurement by counting unit cubes, using cubic cm, cubic in, and cubic ft.

**Lesson Objective:** The lesson is aligned to the Common Core State Standards for Mathematics – 5MD.4 Geometric Measurement – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. At the end of this article, you'll find a link to a downloadable version of this lesson plan.

**Materials Required: **“unit cubes" using cubic cm, cubic in, cubic ft

## Identifying Measurement of Rectangular Figures by Counting Unit Cubes

Look at the cube on the above left. Each side of the cube measures 1 centimeter (cm). A cube with each side measuring 1 centimeter has a volume of one cubic centimeter. This unit cube can be used to measure volume in cubic centimeters.

To measure the volume of a rectangular figure, without gaps or overlaps pack the rectangular figure with the unit cubes.

Look at the rectangular figure to the above right. The rectangular figure is packed with 4 unit cubes. The volume of the rectangular figure is 4 cubic centimeters.

Look at the rectangular figures below. Count the number of unit cubes packed in the rectangular figure. The unit cubes measure volume in cubic centimeters (cm), cubic inches (in), and cubic feet (ft).

1. Look at Figure 1. The figure is packed with unit cubes with a volume of one cubic centimeter. How many unit cubes are packed in this rectangular? What is the volume in cubic centimeters?

2. Look at Figure 2. The figure is packed with unit cubes with a volume of one cubic centimeter. How many unit cubes are packed in this rectangular figure? What is the volume in cubic centimeters?

3. Look at Figure 3. The figure is packed with unit cubes with a volume of one cubic inch. How many unit cubes are packed in this rectangular figure? What is the volume in cubic inches?

4. Look at Figure 4. The figure is packed with unit cubes with a volume of one cubic inch. How many unit cubes are packed in this rectangular figure? What is the volume in cubic inches?

**Answers:**

- 9 unit cubes, 9 cubic centimeters
- 27 unit cubes, 27 cubic centimeters
- 2 unit cubes, 2 cubic inches
- 16 unit cubes, 16 cubic inches

## Individual or Group Work

Look at the figures above. Count the number of unit cubes packed in the rectangular figure.

1. Look at FIgure 5. The figure is packed with unit cubes with a volume of one cubic inch. How many unit cubes are packed in this figure? What is the volume in cubic inches?

2. Look at Figure 6. The figure is packed with unit cubes with a volume of one cubic inch. How many unit cubes are packed in this figure? What is the volume in cubic inches?

3. Look at Figure 7. The figure is packed with unit cubes with a volume of one cubic centimeter. How many unit cubes are packed in this figure? What is the volume in cubic centimeters?

4.Look at Figure 8. The figure is packed with unit cubes with a volume of one cubic centimeter. How many unit cubes are packed in this figure? What is the volume in cubic centimeters?

5. A rectangular box can hold 8 unit cubes without gaps or overlaps. Each unit cube has a volume of one cubic foot. What is the volume of the rectangular box in cubic feet?

6. A rectangular box is packed with unit cubes. Each unit cube has a volume of one cubic foot. Each layer of the rectangular box can hold 4 unit cubes without gaps or overlaps. There are 4 layers. What is the volume of the rectangular box in cubic feet?

**Answers:**

- 13 unit cubes, 13 cubic inches
- 15 unit cubes, 15 cubic inches
- 25 unit cubes, 25 cubic centimeters
- 22 unit cubes, 22 cubic centimeters
- 8 cubic feet
- 16 cubic feet

Students should be able to count the number of unit cubes used to fill rectangular figures to determine the volume of the figures in cubic centimeters, cubic inches, and cubic feet.