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The Partial Products Method

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The Partial Products

Method

Differentiate By

Giving Students a Choice

- This slideshow is set up to demonstrate the partial product method.
- A detailed solution is offered for the traditional algorithm as well as the partial product method.
- You can focus on the partial products method, give students a choice, or have them solve each problem both ways.

Differentiate By

Giving Students a Choice

- When students learn multiple ways to solve arithmetic problems, they can choose the way that works best for them.
- This can lead to kids feeling more successful, and in many cases it helps them to understand the math better.

The Partial Products

Method

- The benefits to exposing students to this method include:
- It helps provide an understanding of what is happening when they use the traditional algorithm.
- It provides the a chance to reinforce the pattern of multiplying by powers of ten.
- It reinforces the definition of expanded form.

37

x 46

= 30 + 7

= 40 + 6

Write the expanded form of each of number.

37

x 46

= 30 + 7

30 x 40

= 40 + 6

7 x 40

30 x 6

Multiply both parts of the multiplicand (first or top number) by both parts of the multiplier (second or bottom number.)

7 x 6

37

x 46

= 30 + 7

1200

30 x 40

= 40 + 6

280

7 x 40

30 x 6

180

7 x 6

42

+

1702

Find the product.

84

x 92

= 80 + 4

= 90 + 2

Write the expanded form of each of number.

84

x 92

= 80 + 4

80 x 90

= 90 + 2

4 x 90

80 x 2

Multiply both parts of the multiplicand (first or top number) by both parts of the multiplier (second or bottom number.)

4 x 2

84

x 92

= 80 + 4

7200

80 x 90

= 90 + 2

360

4 x 90

80 x 2

160

4 x 2

8

+

7728

Another way to

check your solution

Find the product.

39

x 52

= 30 + 9

= 50 + 2

Write the expanded form of each of number.

39

x 52

= 30 + 9

30 x 50

= 50 + 2

9 x 50

30 x 2

Multiply both parts of the multiplicand (first or top number) by both parts of the multiplier (second or bottom number.)

9 x 2

39

x 52

= 30 + 9

1500

30 x 50

= 50 + 2

450

9 x 50

30 x 2

60

9 x 2

18

+

2028

Another way to

check your solution

Find the product.

23

x 27

= 20 + 3

= 20 + 7

Write the expanded form of each of number.

23

x 27

= 20 + 3

20 x 20

= 20 + 7

3 x 20

20 x 7

3 x 7

23

x 27

= 20 + 3

400

20 x 20

= 20 + 7

60

3 x 20

20 x 7

140

3 x 7

21

+

621

Another way to

check your solution

Find the product.

87

x 97

= 80 + 7

= 90 + 7

Write the expanded form of each of number.

87

x 97

= 80 + 7

80 x 90

= 90 + 7

7 x 90

80 x 7

7 x 7

87

x 97

= 80 + 7

7200

80 x 90

= 90 + 7

630

7 x 90

80 x 7

56

7 x 7

49

+

8439

Another way to

check your solution

Find the product.

63

x 54

= 60 + 3

= 50 + 4

Write the expanded form of each of number.

63

x 54

= 60 + 3

60 x 50

= 50 + 4

3 x 50

60 x 4

3 x 4

63

x 54

= 60 + 3

3000

60 x 50

= 50 + 4

150

3 x 50

60 x 4

240

3 x 4

12

+

3402

Another way to

check your solution

Find the product.

79

x 37

= 70 + 9

= 30 + 7

Write the expanded form of each of number.

79

x 37

= 70 + 9

70 x 30

= 30 + 7

9 x 30

70 x 7

9 x 7

79

x 37

= 70 + 9

2100

70 x 30

= 30 + 7

270

9 x 30

70 x 7

490

9 x 7

63

+

2923

Another way to

check your solution

Find the product.

94

x 77

= 90 + 4

= 70 + 7

Write the expanded form of each of number.

94

x 77

= 90 + 4

90 x 70

= 70 + 7

4 x 70

90 x 7

4 x 7

94

x 77

= 90 + 4

6300

90 x 70

= 70 + 7

280

4 x 70

90 x 7

630

4 x 7

28

+

7238

Another way to

check your solution