Third Grade Strategies – *Multiplication and Division
Strategies the students will be using will vary depending on the size of the number. The focus is on grouping
numbers and not counting by ones.
Understanding Multiplication and Division:
This will include skip counting, looking for patterns, using
arrays, and drawing pictures. Example: 6 x 13 = 78 or 78 ÷ 6 = 13
Students may use the 100 chart to record the skip count
and look for patterns.
6 +6 +6 +6 +6 +6 +6 +6 +6 +6 +6 +6 +6 = 78
78 - 6- 6- 6- 6- 6- 6- 6- 6- 6- 6- 6- 6- 6 = 0
remaining
Drawing pictures:
3 x 4 = 12
Array model for skip counting
:
4 x 5 or 5 x 4
OR 20 ÷ 5 or 20 ÷ 4
“Four rows of 5 or five columns of 4.”
5
4
*Third grade students focus on becoming proficient in the basic multiplication/division combinations so they
can apply these strategies to more complex problems in 4
th
and 5
th
grade. They also focus on developing a
conceptual understanding of multiplication and division.
Strategies for fluency – some students may not need strategies depending on the number combination
and others may use a different one than is suggested below
(once student is proficient in these number
combinations move on to the next group):
Proficiency – student can say product (answer) quickly without much pause.
•
First focus on 0, 1, 2, and 10’s
0’s – answer always 0
1’s – answer always the number you multiplied by
2’s – always double
10’s – add a zero to the end
•
Building on from the 0, 1, 2, and 10’s practice 3, 4, 5, and 9’s
3’s – start with 2 groups then add one
3 x 9 = (9 + 9) + 9
= 18 + 9
= 27
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 89 99 100
4’s – double, double
4 x 2 = (2 + 2) + (2 + 2)
= 4 + 4
= 8
5’s – multiply by 10 and take half
5 x 2 = ½ of (10 x 2)
= ½ of 20
= 10
9’s – multiply by 10 and then take away one group
9 x 2 = (10 x 2) – 2
= 20 – 2
= 18
•
Build on the previous strategies by practicing 6, 7, and 8’s
6’s – look for groups of 3 or double the group of 3
6 x 7 = (7 + 7 + 7) + (7 + 7 + 7) OR (3 x 7) + (3 x 7)
= 21 + 21
= 42
7’s – break apart 7 into groups of 5 and 2
7 x 8 = (8 + 8 + 8 + 8 + 8) + 8 + 8 OR (8 x 5) + (8 x 2)
= 40 + 16
= 56
8’s – break into groups of 4 and 4
8 x 7 = (7 + 7 + 7 + 7) + (7 + 7 + 7 + 7) OR (4 x 7) + (4 x 7)
= 28 + 28
= 56
Shaded numbers are those the student should be proficient with by the end of third grade.
X
1
2 3
4 5
6
7
8
9
10 11
12
1
2
3
4
5
6
7
8
9
10
11
12
Third Grade Computation Expectations:
Fluent with facts shaded on multiplication chart; at least two strategies for
multiplying and dividing multi-digit numbers.
1
2
3
4
5
6
7
8
9
10
11
12
2
4
6
8 10 12 14 16 18
20
22
24
3
6
9 12 15 18 21 24 27
30
33
36
4
8 12 16 20 24 28 32 36
40
44
48
5 10 15 20 25 30 35 40 45
50
55
60
6 12 18 24 30 36 42 48 54
60
66
72
7 14 21 28 35 42 49 56 63
70
77
84
8 16 24 32 40 48 56 64 72
80
88
96
9 18 27 36 45 54 63 72 81
90
99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132
12 24 36 48 60 72 84 96 108 120 132 144
