1. The Distributive Property and Area Models

2. Find the area of the rectangle. Area = length x width

3. Find the area of the rectangle. Area = length x width

4. Find the area of the rectangle. Area = length x width
20 ft ft

5. Find the area of the rectangle. Area = length x width
20 ft ft

6. Find the area of the rectangle. Area = length x width
20 ft ft

7. Find the area of the rectangle. Area = length x width
Find the area of each rectangle.
6 ft
6 ft
20 ft ft

8. Find the area of the rectangle. Area = length x width
Find the area of each rectangle.
6 ft
6 ft
6 x 20 = 120 sq ft
20 ft ft

9. Find the area of the rectangle. Area = length x width
Find the area of each rectangle.
6 ft
6 ft
6 x 20 = 120 sq ft
6 x 4 = 24
sq ft
20 ft ft

10. Find the area of the rectangle. Area = length x width
Find the area of each rectangle.
6 ft
6 ft
120 sq ft
24 sq ft
20 ft ft

11. Find the area of the rectangle. Area = length x width
Now put the two rectangles back together.
6 ft
6 ft
120 sq ft
24 sq ft
20 ft ft

12. Find the area of the rectangle. Area = length x width
Now put the two rectangles back together.
6 ft
120 sq ft
24 sq ft
20 ft ft

13. Find the area of the rectangle. Area = length x width
Now put the two rectangles back together.
6 ft
120 sq ft
24 sq ft
20 ft ft

14. Find the area of the rectangle. Area = length x width
Now put the two rectangles back together.
6 ft
120 sq ft
+ 24 sq ft
24 ft

15. Find the area of the rectangle. Area = length x width
Now put the two rectangles back together.
6 ft
144 sq ft
24 ft

16. A swimming pool has a shallow end and a deep end
A swimming pool has a shallow end and a deep end. Find the surface area of the pool.
deepwater
8 yds
shallow water
5 yds
10 yds

17. Break the pool into a deep end and a shallow end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds

18. Find the area of the deep end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds

19. Find the area of the deep end.
8 x 5 = 40
8 yds
8 yds
shallow water
10 yds
5 yds

20. Find the area of the shallow end.
8 x 5 = 40
8 yds
8 yds
shallow water
10 yds
5 yds

21. Find the area of the shallow end.
8 x 5 = 40
8 yds
8 yds
8 x 10 = 80
10 yds
5 yds

22. Now sum the two areas together.
8 x 5 = 40
8 yds
8 yds
8 x 10 = 80
10 yds
5 yds

23. Now sum the two areas together.40 80 +
8 yds
10 yds
5 yds

24. = 120 square yards 40 80
8 yds
5 yds
10 yds

25. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
9 yds
5 yds
20 yds

26. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
9 yds
9(5 + 20)
5 yds
20 yds

27. Find the areas for each individual rectangle.
9 yds
5 yds
20 yds

28. Find the areas for each individual rectangle.
9 yds
(9 x 5)
5 yds
20 yds

29. Find the areas for each individual rectangle.
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds

30. Sum the two areas.
9 yds +
(9 x 5)
(9 x 20)
5 yds
20 yds

31. (9 x 5) + (9 x 20) = area
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds

32. (40) + (180) = area
9 yds
(40)
(180)
5 yds
20 yds

33. (40) + (180) = area
212 yds2
9 yds
5 yds
20 yds

34. Write an expression that shows how to find the area of the rectangle and uses the distributive property. 3 x 6

35. Write an expression that shows how to find the area of the rectangle and uses the distributive property. 3 x 6
The length can be represented by x + 6.

36. 3 x 6 Therefore, the area can be expressed as 3(x + 6) or 3x + 18
Write an expression that shows how to find the area of the rectangle and uses the distributive property. 3 x 6
Therefore, the area can be expressed as
3(x + 6) or
3x + 18

37. The expression 10x + 15 can represent the area of the figure below.
Find the expression that represents the
length and the width.
This problem was taken from the 6th Grade Mathematics Unpacked Content Document

38. First, find the greatest common factor to represent the width.
10x 15
What is the greatest common factor?
This problem was taken from the 6th Grade Mathematics Unpacked Content Document

39. The GCF is 5. 5
10x 15 2x 3
Then use the distributive property to find the length
(2x + 3)
This problem was taken from the 6th Grade Mathematics Unpacked Content Document

40. The factors (dimensions) of this figure would be 5(2x + 3)
This problem was taken from the 6th Grade Mathematics Unpacked Content Document

41. Practice Time

42. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 yds
3 yds
9 yds

43. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4(3 + 9)
4 yds
3 yds
9 yds

44. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 yds
3 yds
9 yds

45. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 yds
3 yds
9 yds

46. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 yds
4 yds
3 yds
9 yds

47. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 yds
4 yds
4 x 3
3 yds
9 yds

48. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 yds
4 yds
4 x 3
4 x 9
3 yds
9 yds

49. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 x 3
4 x 9
4 yds
4 yds
3 yds
9 yds

50. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 x 3
4 x 9
4 yds
3 yds
9 yds

51. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 x 3
4 x 9
4 yds
3 yds
9 yds

52. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
4 x 3 +
4 x 9
4 yds
3 yds
9 yds

53. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 yds
4 yds
8 yds

54. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6(4 + 8)
6 yds
4 yds
8 yds

55. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 yds
4 yds
8 yds

56. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 yds
4 yds
8 yds

57. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 yds
6 yds
4 yds
8 yds

58. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 yds
6 yds
6 x 4
4 yds
8 yds

59. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 yds
6 yds
6 x 4
6 x 8
4 yds
8 yds

60. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 x 4
6 x 8
6 yds
6 yds
4 yds
8 yds

61. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 x 4
6 x 8
6 yds
4 yds
8 yds

62. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 x 4
6 x 8
6 yds
4 yds
8 yds

63. 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.
6 x 4 +
6 x 8
6 yds
4 yds
8 yds

64. 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property.
5 yds
x yds
10 yds

65. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
5(x + 10)
5 yds
x yds
10 yds

66. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
5 yds 5x
5 ∙ 10
x yds
10 yds

67. Write an expression that shows how to find the area of the rectangle and uses the distributive property.
5x + 5 ∙ 10 or
5x + 50
5 yds
x yds
10 yds

68. Which expression is equivalent to 3(x + 7)?

69. Which expression is equivalent to 3(x + 7)?
Correct!
3x + 21

70. Which expression is equivalent to 4(x + 5)?

71. Which expression is equivalent to 4(x + 5)?
Correct!

72. Which expression is equivalent to 8(x + 2)?

73. Which expression is equivalent to 8(x + 2)?
Correct!

74. Which expression is equivalent to 2(x + 3)?

75. Which expression is equivalent to 2(x + 3)?
Correct!