# Multiplication Strategies

## Multo 2 0

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