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Multiplication Strategies

Repeated Addition

As students begin learning multiplication, they see the connection between multiplication and repeated addition. 
3 x 4 = 4 + 4 + 4
6 x 5 = 5 + 5 + 5 + 5 + 5 + 5
 

Zero Property (x0)

The product of any number and 0 is 0. 
4 x 0 = 0       0 x 65 = 0

Times Ten (x 10)

Focus on the base ten aspect of our number system. Discuss moving a place.
 6 x 10 = 60       45 x 10 = 450
 

Doubles (x 2)

To multiply by 2, double the other number or think of the addition doubles.
2 x 5 = 5 + 5 = 10                   14 x 2 = 14 + 14 = 28
 

Double-Double-Double (x8)

To multiply by 8, double the other number, double the result and double it again.
8 = 2 x 2 x 2
8 x 6 = ((6x2) x2) x 2 = (12x2)x2= 24 x2= 48
8 x 43 = ((43x2) x2) x 2 = (86 x 2) x 2= 172 x 2 = 344
 

Double Plus a Set (x 3)

To multiply by 3, double the other number than add one more set of that number.

3 = 2 + 1
3 x 6 = (2 x 6) + 6
3 x 15 = (2 x 15) + 15
 

Visualizing Arrays

The array provides a visual model for multiplication. The numbers being multiplied correspond to the dimensions of the rectangle and the product of those numbers correspond to the area of the rectangle. 

Identity Property (x1)

The product of any number and 1 is that number.
5 x 1 = 5         1 x 43 = 43

Half Ten (x 5)

To multiply by 5, multiply by 10 and then divide the result in half. 5 = 10 ÷ 2
5 x 3= (10 x 3) ÷ 2 = 30 ÷ 2 = 15 
5 x 18 = (10 x 18) ÷2 = 180 ÷ 2 = 90
 

Double-Double (x 4)

To multiply by 4, double the other number and then double the result. 4 = 2 + 2
4 x 6 = 2 x (2 x 6) = 2 x 12 = 24
4 x 24 = 2 x(2x24) = 2 x 48= 96
 

Ten Minus a Set (x 9)

To multiply by 9, multiply the number first by ten and then subtract a set of that number.

9 = 10 - 1
9 x 6 = (10 x 6) – 6= 60 – 6 = 54
9 x 45 = (10 x 45) – 45 = 450 – 45 = 405
 

Half Ten Plus a Set (x 6)

To multiply by 6, carry out the steps for multiplying by 5 and then add a set. 

6= 5 + 1
6 x 7 = ((10 x 7) ÷ 2) + 7 = 42
6 x 42 = ((10 x 42) ÷2) + 42= (420÷2) + 42= 210 + 42 = 252
 

Fact Fluency Games: Multiplication