1 of 18

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2 of 18

I can find the area of a rectangle by decomposing the side length.

Common Core Standards: Grade 3

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

3.OA.C.7.c

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

3 of 18

5 x 9 = (5 x ) + (5 x )

5 x 9 = +

5 x 9 = square centimeters

Find the area of this rectangle by decomposing it into smaller rectangles.

3 cm 6 cm

5 cm

4 of 18

5 x 9 = (5 x ) + (5 x )

5 x 9 = +

5 x 9 = square centimeters

3

6

15

45

30

Find the area of this rectangle by decomposing it into smaller rectangles.

3 cm 6 cm

5 cm

5 of 18

D

B

(9 x 10) + (9 x 6)

(9 x 10) + (9 x 16)

(9 x 8) + (9 x 8)

(9 x 9) + (16 x 9)

A

C

Which equations are examples of correctly decomposing to find the area of this rectangle?

Extra Xs or checkmarks

16 m

9 m

6 of 18

D

B

(9 x 10)+ (9 x 6)

(9 x 10)+ (9 x 16)

(9 x 8)+ (9 x 8)

(9 x 9)+ (16 x 9)

A

✔

C

✔

Which equations are examples of correctly decomposing to find the area of this rectangle?

X

Extra Xs or checkmarks

✔X

16 m

9 m

7 of 18

9 x 7 = (9 x ) + (9 x )

9 x 7 = +

9 x 7 = square meters

Find the area of this rectangle by decomposing it into smaller rectangles.

4 m 3 m

9 m

8 of 18

9 x 7 = (9 x ) + (9 x )

9 x 7 = +

9 x 7 = square meters

4

3

36

63

27

Find the area of this rectangle by decomposing it into smaller rectangles.

4 m 3 m

9 m

9 of 18

D

B

(5 x 14)+ (5 x 5)

(5 x 10)+ (5 x 14)

(5 x 10)+ (5 x 4)

(5 x 7)+ (5 x 7)

A

C

Which equations are examples of correctly decomposing to find the area of this rectangle?

Extra Xs or checkmarks

14 m

5 m

10 of 18

D

B

(5 x 14)+ (5 x 5)

(5 x 10)+ (5 x 14)

(5 x 10)+ (5 x 4)

(5 x 7)+ (5 x 7)

A

X

C

✔

Which equations are examples of correctly decomposing to find the area of this rectangle?

X

✔

Extra Xs or checkmarks

✔X

14 m

5 m

11 of 18

7 x 17 = (7 x ) + (7 x )

+

square meters

Find the area of this rectangle by decomposing it into smaller rectangles.

10 m 7 m

7 m

12 of 18

7 x 17 = (7 x ) + (7 x )

+

square meters

10

7

70

119

49

Find the area of this rectangle by decomposing it into smaller rectangles.

10 m 7 m

7 m

13 of 18

Did Student 1 solve the problem correctly?

If not, where did they go wrong?

3 cm 6 cm

7 cm

Student 1

A = 7 + 9

A = 16 square centimeters

14 of 18

Did Student 1 solve the problem correctly?

If not, where did they go wrong?

3 cm 6 cm

7 cm

Student 1

A = 7 + 9

A = 16 square centimeters

Here is the mistake! They added the sides!

This problem was NOT solved correctly.

15 of 18

Did Student 2 solve the problem correctly?

If not, where did they go wrong?

3 cm 6 cm

7 cm

Student 2

A = (7 x 3) + (7 x 6)

A= 21 + 42

A = 63 square centimeters

16 of 18

Did Student 2 solve the problem correctly?

If not, where did they go wrong?

3 cm 6 cm

7 cm

Student 2

A = (7 x 3) + (7 x 6)

A= 21 + 42

A = 63 square centimeters

Did Student 1 solve the problem correctly?

If not, where did they go wrong?

This problem was solved correctly!

17 of 18

D

B

(2 x 4) + (2 x 4)

(2 x 5) + (2 x 9)

(2 x 9) + (2 x 4)

(2 x 5) + (2 x 4)

A

C

Which equations are examples of correctly decomposing to find the area of this rectangle?

18 of 18

D

B

(2 x 4) + (2 x 4)

(2 x 5) + (2 x 9)

(2 x 9) + (2 x 4)

(2 x 5) + (2 x 4)

A

C

Which equations are examples of correctly decomposing to find the area of this rectangle?

✔