Lesson 9 Relate Area to Multiplication

    • Let’s explore the area of rectangles with one side length that is a unit fraction.

Warm-up Which One Doesn’t Belong: Area

Which one doesn’t belong?

  1. Rectangle. Width: 6. Height: 1. 
  2. Rectangle divided into same-sized squares. Width: 1. Height: 6. 
  3. Area diagram. Triangle. Base: 4. Height: 3. 
  4. Area diagram. Length, 12. Width, 1 half. 

Activity 1 Find the Area

Find the area of the shaded region. Explain or show your reasoning.

  1. Area diagram. Length, 6 units. Width, 1 unit.
  2. Area diagram. Length, 6. Width, 1 half. 
  3. Area diagram. Length, 6. Width, 1 third. 
  4. Area diagram. Length, 6. Width, 1 fourth.

Activity 2 Draw Rectangles

  1. Represent each rectangle on grid paper:

    • unit by 1 unit

    • unit by 2 units

    • unit by 3 units

    • unit by 4 units

  2. Find the area of each rectangle that you drew.

  3. What information do you need to find the area of the shaded region?

    Area diagram.

  4. What might the area of the shaded region be? Explain or show your reasoning.

Practice Problem

Problem 1

Area diagram. Length, 4. Width, 3. 
Area diagram. Length, 4. Width, 1 third. 

  1. How are the diagrams the same? How are they different?

  2. How is finding the area of the shaded region the same? How is it different?