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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.

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    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

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    Lesson Procedure:

    Rectangle 1 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.

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    Chart lesson 4 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.

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    Rectangles 2 and 3 

    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.

    2nd Chart Lesson 4 

    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.

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    Answers:

    1. 5 units

    2. 7 units

    3. 35 square units

    4. Complete the chart.Chart Answers 1 

    5. 5 units and 3 units

    6. 5 units and 4 units

    7. 15 square units and 20 square units

    8. Complete the chart.Chart Answers 2 

    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.

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    Download Lesson with Individual or Group Work

    To view the Individual or Group Work segment of this lesson, please download it here. Group work is at the end of the lesson.