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

Lesson 1: Introduction to Volume and Measurement

In this Grade 5 Illustrative Mathematics lesson (Chapter 1: Finding Volume), students are introduced to volume as the measurable attribute describing the amount of space a solid object takes up. Using connecting cubes, students build and compare three-dimensional objects to discover that different shapes can have the same volume. This lesson lays the conceptual groundwork for standard 5.MD.C.3 before students move on to measuring volume in cubic units and calculating the volume of rectangular prisms.

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

Finding Volume by Counting Unit Cubes

Property

The volume (VV) of a solid is the total number of unit cubes it contains. To accurately count cubes in a 2D representation, count the cubes in each layer (or column) and add the totals. This method ensures all hidden cubes are included.

V=Sum of cubes in all layersV = \text{Sum of cubes in all layers}

Section 3

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 1: Finding Volume

  1. Lesson 1Current

    Lesson 1: Introduction to Volume and Measurement

  2. Lesson 2

    Lesson 2: Calculate Volume Using Layers

  3. Lesson 3

    Lesson 3: Side Lengths and Volume Expressions

  4. Lesson 4

    Lesson 4: Cubic Units of Measure

  5. Lesson 5

    Lesson 5: Composite Figures: Volume of Combined Prisms

  6. Lesson 6

    Lesson 6: Apply Volume Knowledge

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

Finding Volume by Counting Unit Cubes

Property

The volume (VV) of a solid is the total number of unit cubes it contains. To accurately count cubes in a 2D representation, count the cubes in each layer (or column) and add the totals. This method ensures all hidden cubes are included.

V=Sum of cubes in all layersV = \text{Sum of cubes in all layers}

Section 3

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 1: Finding Volume

  1. Lesson 1Current

    Lesson 1: Introduction to Volume and Measurement

  2. Lesson 2

    Lesson 2: Calculate Volume Using Layers

  3. Lesson 3

    Lesson 3: Side Lengths and Volume Expressions

  4. Lesson 4

    Lesson 4: Cubic Units of Measure

  5. Lesson 5

    Lesson 5: Composite Figures: Volume of Combined Prisms

  6. Lesson 6

    Lesson 6: Apply Volume Knowledge