Finding Area using a Model of the Distributive Property: Math Lesson for Grade 3

written by: Donna Ventura • edited by: Carly Stockwell • updated: 10/14/2013

Students will investigate the concept of areas of rectangular figures by using area models to represent the distributive property. They will also use models to find the area of a rectangle with side lengths a and b + c is the same as the sum of a x b and a x c.

• slide 1 of 6

Lesson Objective: The lesson is aligned to the Common Core State Standards for Mathematics – 3.MD.7c Geometric Measurement – Use area models to represent the distributive property.

Materials Required: graph paper, calculator

• slide 2 of 6

Lesson Procedure:

Finding Area of Rectangular Figures using Distributive Property

Look at Rectangle 1 shown on the grid. Rectangle 1 has Side a and Side (b + c). Side length of each square on all grids measure one unit.

• slide 3 of 6

1. What is the length of Side a?

2. What is the length of Side (b + c)?

3. What is the area of Rectangle 1 with Side a and Side (b + c)?

4. Complete the chart.

• slide 4 of 6

Now look at Rectangle 2 and Rectangle 3 shown on the grid.

5. Rectangle 2 has Side a and Side b. Identify the lengths of the two sides of Rectangle 2.

6. Rectangle 3 has Side a and Side c. Identify the lengths of the two sides of Rectangle 3.

7. Find the areas of Rectangle 2 and Rectangle 3.

8. Complete the chart.

9. What is the area of Rectangle 1?

10. What is the sum of the areas of Rectangle 2 and Rectangle 3?

11. Compare the area of Rectangle 1 with sides a and (b + c) and the sum of the areas of Rectangle 2 and Rectangle 3.

12. Write a statement about the comparison.

• slide 5 of 6

1. 5 units

2. 7 units

3. 35 square units

4. Complete the chart.

5. 5 units and 3 units

6. 5 units and 4 units

7. 15 square units and 20 square units

8. Complete the chart.

9. 35 square units

10. 15 + 20 = 35 square units

11. The area of Rectangle 1 with sides 5 and (3 + 4) is 35. The sum of the areas of Rectangle 2, 15 square units, and Rectangle 3, 20 square units, is 35 square units.

12. The area of Rectangle 1 is equal to the sum of the areas of Rectangle 2 and Rectangle 3.

• slide 6 of 6