Lesson 10 Represent Volume with Expressions

    • Let’s write expressions for the volume of figures.

Warm-up Notice and Wonder: Prism Pieces

What do you notice? What do you wonder?

Yellow rectangular prism with blue rectangular prism on top. 
Blue rectangular prism joined on the side with a yellow rectangular prism. 

Activity 1 Compare Expressions

Figure composed of two attached prisms.

  1. Write an expression to represent the volume of the figure in unit cubes.

  2. Compare expressions with your partner.

    • How are they the same?

    • How are they different?

  3. If they are the same, try to find another way to represent the volume.

Activity 2 Find the Volume in Different Ways

  1. Find the volume of the figure by decomposing the figure 2 different ways. Show your thinking. Organize it so it can be followed by others.

    6-sided rectangular prism. 
    6-sided rectangular prism. 

  2. For each way you decomposed the figure, write an expression that represents the volume.

  3. Mai used this expression to find the volume of the figure:

    .

    Use the diagram to interpret Mai’s expression. Show your thinking. Organize it so it can be followed by others.

    6-sided rectangular prism.

Practice Problem

Problem 1

Find the volume of the figure. Explain or show your reasoning.

Two rectangular prisms, one in front of the other.