Lesson 4

Use Layers to Determine Volume

Lesson Purpose

The purpose of this lesson is for students to apply their understanding of the layered structure of rectangular prisms to find the volume of a prism when they cannot see all of the cubes.

Lesson Narrative

In previous lessons, students used the layered structure to determine the volume of rectangular prisms that were filled with cubes. The purpose of this lesson is to extend their understanding of the structure of rectangular prisms by conceptualizing a base layer in a rectangular prism and utilizing it to find the volume in a fully- or partially-filled prism. Students connect the layered structure to multiplication when they write and interpret expression that represent the volume of rectangular prisms (MP2, MP7). This is a conceptual way for students to make sense of the associative property of multiplication. Students do not, however, need to name or identify the property.

  • Action and Expression
  • MLR7

Activity 1: Layers in Rectangular Prisms

Learning Goals

Teacher Facing

  • Describe and represent the volume of a rectangular prism as the product of the number of cubes in one layer and the number of layers.
  • Write and interpret expressions and equations in the context of the volume of rectangular prisms.

Student Facing

  • Let's relate multiplication to how we use layers to find volume.

Required Materials

Materials to Gather

Required Preparation

Activity 1:

  • Have connecting cubes available for students who need them.

Activity 2:

  • Have connecting cubes available for students who need them.

CCSS Standards

Addressing

Building Towards

Lesson Timeline

Warm-up 10 min
Activity 1 20 min
Activity 2 15 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

In the upcoming section, students will connect multiplying the area of the base and the height to multiplying all three edge lengths when finding volume. Based on this lesson, what understandings do your students now have that will allow them to make that connection? 

Suggested Centers

  • Can You Build It? (3–5), Stage 3: Rectangular Prisms (Addressing)
  • Five in a Row: Multiplication (3–5), Stage 3: Two-digit Factors (Supporting)

Print Formatted Materials

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Additional Resources

Google Slides

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PowerPoint Slides

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