The Partial Products

1
The Partial Products Method
2
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.

3
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.

4
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.

5
37 x 46
30 7
40 6
Write the expanded form of each of number.
6
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
7
37 x 46
30 7
1200
30 x 40
40 6
280
7 x 40
30 x 6
180
7 x 6
42

1702
8
Find the product.
9
84 x 92
80 4
90 2
Write the expanded form of each of number.
10
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
11
84 x 92
80 4
7200
80 x 90
90 2
360
4 x 90
80 x 2
160
4 x 2
8

7728
12
Another way to check your solution
13
Find the product.
14
39 x 52
30 9
50 2
Write the expanded form of each of number.
15
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
16
39 x 52
30 9
1500
30 x 50
50 2
450
9 x 50
30 x 2
60
9 x 2
18

2028
17
Another way to check your solution
18
Find the product.
19
23 x 27
20 3
20 7
Write the expanded form of each of number.
20
23 x 27
20 3
20 x 20
20 7
3 x 20
20 x 7
Multiply both parts of the multiplicand (first or
top number) by both parts of the multiplier
(second or bottom number.)
3 x 7
21
23 x 27
20 3
400
20 x 20
20 7
60
3 x 20
20 x 7
140
3 x 7
21

621
22
Another way to check your solution
23
Find the product.
24
87 x 97
80 7
90 7
Write the expanded form of each of number.
25
87 x 97
80 7
80 x 90
90 7
7 x 90
80 x 7
Multiply both parts of the multiplicand (first or
top number) by both parts of the multiplier
(second or bottom number.)
7 x 7
26
87 x 97
80 7
7200
80 x 90
90 7
630
7 x 90
80 x 7
56
7 x 7
49

8439
27
Another way to check your solution
28
Find the product.
29
63 x 54
60 3
50 4
Write the expanded form of each of number.
30
63 x 54
60 3
60 x 50
50 4
3 x 50
60 x 4
Multiply both parts of the multiplicand (first or
top number) by both parts of the multiplier
(second or bottom number.)
3 x 4
31
63 x 54
60 3
3000
60 x 50
50 4
150
3 x 50
60 x 4
240
3 x 4
12

3402
32
Another way to check your solution
33
Find the product.
34
79 x 37
70 9
30 7
Write the expanded form of each of number.
35
79 x 37
70 9
70 x 30
30 7
9 x 30
70 x 7
Multiply both parts of the multiplicand (first or
top number) by both parts of the multiplier
(second or bottom number.)
9 x 7
36
79 x 37
70 9
2100
70 x 30
30 7
270
9 x 30
70 x 7
490
9 x 7
63

2923
37
Another way to check your solution
38
Find the product.
39
94 x 77
90 4
70 7
Write the expanded form of each of number.
40
94 x 77
90 4
90 x 70
70 7
4 x 70
90 x 7
Multiply both parts of the multiplicand (first or
top number) by both parts of the multiplier
(second or bottom number.)
4 x 7
41
94 x 77
90 4
6300
90 x 70
70 7
280
4 x 70
90 x 7
630
4 x 7
28

7238
42
Another way to check your solution