Applying Volume and Surface Area

5 min

Teacher Prep
Setup
Students in groups of 2. 1 minutes of quiet work time followed by partner and whole-class discussions.

Narrative

In this activity, students are given two contextual situations and determine if the situation requires surface area or volume to be calculated. This prepares students to solve problems involving surface area and volume in situations that will arise in upcoming activities.

Launch

Arrange students in groups of 2. Give students 1 minute of quiet work time, followed by time to discuss their reasoning with a partner. Follow with a whole-class discussion.

Student Task

For each situation, decide if it requires Noah to calculate surface area or volume. Explain your reasoning.

  1. Noah is planning to paint the bird house he built. He is unsure if he has enough paint.

  2. Noah is planning to use a box with a trapezoid base to hold modeling clay. He is unsure if the clay will all fit in the box.

Sample Response

  1. Surface area. The surface area is what Noah will calculate because he would need to calculate how much area he needs to cover on the surface of the bird house.
  2. Volume. The volume is what Noah will calculate because he needs to calculate how much space the box has inside of it to determine if it will hold all of his clay.
Activity Synthesis (Teacher Notes)

Select students to share their responses. Ask students to describe why the bird house situation calls for surface area and why the clay context calls for volume. To highlight the differences between the two uses of the box, ask:

  • “What are the differences in how Noah is using the boxes in these situations?”
  • “How can you determine if a situation is asking you to calculate surface area or volume?”

The goal is to ensure that students understand the differences between situations that require them to calculate surface area and those that require them to calculate volume.

Standards
Addressing
  • 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
  • 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

15 min

10 min