the distributive property and area models
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The Distributive Property and Area Models. Find the area of the rectangle. Area = length x width. 6 ft. 24 ft. Find the area of the rectangle. Area = length x width. 6 ft. 24 ft. Find the area of the rectangle. Area = length x width. 6 ft. 20 ft+ 4 ft. - PowerPoint PPT PresentationTRANSCRIPT
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The Distributive Propertyand
Area Models
![Page 2: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/2.jpg)
Find the area of the rectangle.Area = length x width
6 ft
24 ft
![Page 3: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/3.jpg)
Find the area of the rectangle.Area = length x width
6 ft
24 ft
![Page 4: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/4.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
![Page 5: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/5.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
![Page 6: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/6.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
6 ft
![Page 7: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/7.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
6 ft
Find the area of each rectangle.
![Page 8: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/8.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
6 ft
Find the area of each rectangle.
6 x 20 = 120 sq ft
![Page 9: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/9.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
6 ft
Find the area of each rectangle.
6 x 20 = 120 sq ft 6 x 4 = 24
sq ft
![Page 10: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/10.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
6 ft
Find the area of each rectangle.
120 sq ft 24 sq ft
![Page 11: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/11.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
6 ft
Now put the two rectangles back together.
120 sq ft 24 sq ft
![Page 12: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/12.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
Now put the two rectangles back together.
120 sq ft 24 sq ft
![Page 13: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/13.jpg)
Find the area of the rectangle.Area = length x width
6 ft
20 ft + 4 ft
Now put the two rectangles back together.
120 sq ft 24 sq ft
![Page 14: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/14.jpg)
Find the area of the rectangle.Area = length x width
6 ft
24 ft
Now put the two rectangles back together.
120 sq ft + 24 sq ft
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Find the area of the rectangle.Area = length x width
6 ft
24 ft
Now put the two rectangles back together.
144 sq ft
![Page 16: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/16.jpg)
A swimming pool has a shallow end and a deep end. Find the surface
area of the pool.
shallow waterdeepwater8
yds
5 yds 10 yds
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shallow waterdeepwater8
yds
5 yds 10 yds
8 yds
Break the pool into a deep end and a shallow end.
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shallow waterdeepwater8
yds
5 yds 10 yds
8 yds
Find the area of the deep end.
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shallow water8 x 5 = 40
8 yds
5 yds 10 yds
8 yds
Find the area of the deep end.
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shallow water8 x 5 = 40
8 yds
5 yds 10 yds
8 yds
Find the area of the shallow end.
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8 x 10 = 808 x 5 = 40
8 yds
5 yds 10 yds
8 yds
Find the area of the shallow end.
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8 x 10 = 808 x 5 = 40
8 yds
5 yds 10 yds
8 yds
Now sum the two areas together.
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80 408 yds
5 yds 10 yds
Now sum the two areas together.
+
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80 408 yds
5 yds 10 yds
40 + 80 = 120 square yards
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Write an expression that shows how to find the area of the rectangle and
uses the distributive property.
9 yds
5 yds 20 yds
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Write an expression that shows how to find the area of the rectangle and
uses the distributive property.
9 yds
5 yds 20 yds
9(5 + 20)
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Find the areas for each individual rectangle.
9 yds
5 yds 20 yds
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Find the areas for each individual rectangle.
9 yds
5 yds 20 yds
(9 x 5)
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Find the areas for each individual rectangle.
9 yds
5 yds 20 yds
(9 x 5) (9 x 20)
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Sum the two areas.
9 yds
5 yds 20 yds
(9 x 5) (9 x 20)+
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(9 x 5) + (9 x 20) = area
9 yds
5 yds 20 yds
(9 x 5) (9 x 20)
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(40) + (180) = area
9 yds
5 yds 20 yds
(40) (180)
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(40) + (180) = area
9 yds
5 yds 20 yds
212 yds2
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Write an expression that shows how to find the area of the rectangle and
uses the distributive property.
3
x 6
![Page 35: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/35.jpg)
Write an expression that shows how to find the area of the rectangle and
uses the distributive property.
3
x 6The length can be represented by x + 6.
![Page 36: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/36.jpg)
Write an expression that shows how to find the area of the rectangle and uses the distributive
property.
3
x 6Therefore, the area can be expressed as
3(x + 6)or
3x + 18
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The expression 10x + 15 can represent the area of the figure below.
10x 15
Find the expression that represents the length and the width.
This problem was taken from the 6th Grade Mathematics Unpacked Content Document
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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
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The GCF is 5.
10x 15
Then use the distributive property to find the length(2x + 3)
This problem was taken from the 6th Grade Mathematics Unpacked Content Document
5 2x 3
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The factors (dimensions) of this figure would be 5(2x + 3)
This problem was taken from the 6th Grade Mathematics Unpacked Content Document
5
2x 3
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Practice Time
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Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
![Page 43: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/43.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4(3 + 9)
![Page 44: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/44.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
![Page 45: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/45.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
![Page 46: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/46.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 yds
![Page 47: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/47.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 yds
4 x 3
![Page 48: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/48.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 yds
4 x 3 4 x 9
![Page 49: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/49.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 yds
4 x 3 4 x 9
![Page 50: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/50.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 x 3 4 x 9
![Page 51: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/51.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 x 3 4 x 9
![Page 52: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/52.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
4 yds
3 yds 9 yds
4 x 3 + 4 x 9
![Page 53: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/53.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
![Page 54: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/54.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6(4 + 8)
![Page 55: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/55.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
![Page 56: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/56.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
![Page 57: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/57.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 yds
![Page 58: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/58.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 yds
6 x 4
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Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 yds
6 x 4 6 x 8
![Page 60: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/60.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 yds
6 x 4 6 x 8
![Page 61: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/61.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 x 4 6 x 8
![Page 62: The Distributive Property and Area Models](https://reader036.vdocuments.us/reader036/viewer/2022062310/568167d4550346895ddd2893/html5/thumbnails/62.jpg)
Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 x 4 6 x 8
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7) Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
6 yds
4 yds 8 yds
6 x 4 + 6 x 8
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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
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Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
5 yds
x yds 10 yds
5(x + 10)
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Write an expression that shows how to find the area of the rectangle and uses the
distributive property.
5 yds
x yds 10 yds
5x 5 ∙ 10
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Write an expression that shows how to find the area of the rectangle and uses the distributive property.
5 yds
x yds 10 yds
5x + 5 ∙ 10
or
5x + 50
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Which expression is equivalent to 3(x + 7)?
3x + 7
x + 21
x + 10
3x + 21
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Which expression is equivalent to 3(x + 7)?
3x + 21 Correct!
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Which expression is equivalent to 4(x + 5)?
4x + 5
4x + 20
x + 9
9x
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Which expression is equivalent to 4(x + 5)?
4x + 20 Correct!
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Which expression is equivalent to 8(x + 2)?
8x + 16
8x + 2
10x
8x + 10
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Which expression is equivalent to 8(x + 2)?
8x + 16 Correct!
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Which expression is equivalent to 2(x + 3)?
2x + 3
2x + 5
2x + 6
2x + 2
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Which expression is equivalent to 2(x + 3)?
2x + 6 Correct!