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Measuring Volume by Counting Unit Cubes

written by: Donna Ventura • edited by: Michele McDonough • updated: 11/30/2013

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

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    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

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    Identifying Measurement of Rectangular Figures by Counting Unit Cubes

    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).

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    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?

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    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:

    1. 9 unit cubes, 9 cubic centimeters
    2. 27 unit cubes, 27 cubic centimeters
    3. 2 unit cubes, 2 cubic inches
    4. 16 unit cubes, 16 cubic inches
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    Individual or Group Work

    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:

    1. 13 unit cubes, 13 cubic inches
    2. 15 unit cubes, 15 cubic inches
    3. 25 unit cubes, 25 cubic centimeters
    4. 22 unit cubes, 22 cubic centimeters
    5. 8 cubic feet
    6. 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.

    Download a copy of this lesson plan.

Finding Volume Measurement With Unit Cubes

This collection of fifth grade lesson plans focuses on teaching the concept of the unit cube and how it can be used to develop volume measurement formulas. All lessons meet Common Core objectives.
  1. Finding Volume Measurement: Understanding the Unit Cube Concept
  2. Measuring Volume by Counting Unit Cubes
  3. Relating the Counting of Unit Cubes to Multiplication and Addition
  4. Finding Volume Measurement with Formulas
  5. Finding Volume Measurement of Solid Figures by Adding Component Parts

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