The Distributive Property and Area Models

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Presentation transcript:

The Distributive Property and Area Models

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

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

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

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

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

Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 20 ft + 4 ft

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 + 4 ft

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 + 4 ft

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 + 4 ft

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 + 4 ft

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 + 4 ft

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 + 4 ft

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

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

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

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

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

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

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

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

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

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

40 + 80 = 120 square yards 40 80 8 yds 5 yds 10 yds

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

Practice Time

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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