Learn on PengiPengi Math (Grade 5)Chapter 8: Measurement — Volume & Unit Conversions

Lesson 4: Measure Volume with Unit Cubes, Layers, and Shape Comparisons

In this Grade 5 lesson from Pengi Math Chapter 8, students learn to find the volume of solid figures by counting unit cubes, including hidden cubes in drawings, and by using the formula length × width × number of layers. Students also compare solids built from the same number of unit cubes to understand why different shapes can have equal volume. The lesson directly addresses the common misconception that taller or wider shapes always have greater volume.

Section 1

Measuring Volume with Unit Cubes

Property

Volume is the measure of the amount of space inside a solid, three-dimensional figure. We measure volume by counting the number of unit cubes that are used to build the figure or fill the space.

Volume=Number of unit cubes \text{Volume} = \text{Number of unit cubes}

Section 2

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 3

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})

Section 4

Same Volume, Different Shapes

Property

If two solid objects are composed of the same number of identical unit cubes, their volumes are equal, regardless of their shape. If object A has NN cubes and object B has NN cubes, then VolumeA=VolumeBVolume_A = Volume_B.

Examples

Book overview

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Chapter 8: Measurement — Volume & Unit Conversions

  1. Lesson 1

    Lesson 1: Convert Measurement Units

  2. Lesson 2

    Lesson 2: Solve Measurement Word Problems with Conversions

  3. Lesson 3

    Lesson 3: Introduction to Volume and Cubic Units

  4. Lesson 4Current

    Lesson 4: Measure Volume with Unit Cubes, Layers, and Shape Comparisons

  5. Lesson 5

    Lesson 5: Volume Formulas and Equivalent Expressions

  6. Lesson 6

    Lesson 6: Volume of Composite Solids

  7. Lesson 7

    Lesson 7: Solve Multi-Step Word Problems Using Volume

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Measuring Volume with Unit Cubes

Property

Volume is the measure of the amount of space inside a solid, three-dimensional figure. We measure volume by counting the number of unit cubes that are used to build the figure or fill the space.

Volume=Number of unit cubes \text{Volume} = \text{Number of unit cubes}

Section 2

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 3

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})

Section 4

Same Volume, Different Shapes

Property

If two solid objects are composed of the same number of identical unit cubes, their volumes are equal, regardless of their shape. If object A has NN cubes and object B has NN cubes, then VolumeA=VolumeBVolume_A = Volume_B.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Measurement — Volume & Unit Conversions

  1. Lesson 1

    Lesson 1: Convert Measurement Units

  2. Lesson 2

    Lesson 2: Solve Measurement Word Problems with Conversions

  3. Lesson 3

    Lesson 3: Introduction to Volume and Cubic Units

  4. Lesson 4Current

    Lesson 4: Measure Volume with Unit Cubes, Layers, and Shape Comparisons

  5. Lesson 5

    Lesson 5: Volume Formulas and Equivalent Expressions

  6. Lesson 6

    Lesson 6: Volume of Composite Solids

  7. Lesson 7

    Lesson 7: Solve Multi-Step Word Problems Using Volume