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Multiplication looks at equally sized groups.  Doubling  means multiplying equally sized groups by 2. Let's try this problem to remember how.


Example 1

Find the value of 9\times2.

Worked Solution
Create a strategy

Remember 9 \times 2 is the same as 2 \times 9. This can be thought of as 2 groups of 9.

The picture below shows 2 groups of 9 stars.

The image shows 2 circles with 9 stars  inside each circle.
Apply the idea

In the above image there are 18 stars altogether.

\displaystyle 9\times2\displaystyle =\displaystyle 18
Idea summary

Multiplying by two is the same as doubling and can be thought of as the total of two equally sized groups.

Multiply numbers by 8

4 groups is twice (two times) as many as 2 groups. 8 groups is twice (two times) as many as 4 groups. Let's look at how to multiply numbers by 8 using a Double, Double, Double strategy.

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Example 2

Find the value of 8 \times 5.

Worked Solution
Create a strategy

This can be thought of as 8 groups of 5 squares, as represented in the image below.

The image shows eight rows of five squares.
Apply the idea

There are 40 squares in the above image.8 \times 5 = 40

Reflect and check

Or we can use the double, double, double strategy on 5 to get:

\displaystyle 5 \times 2\displaystyle =\displaystyle 10Double 5
\displaystyle 10 \times 2\displaystyle =\displaystyle 20Double the answer
\displaystyle 20 \times 2\displaystyle =\displaystyle 40Double the answer again

Which means: 8 \times 5 = 40

Idea summary

You can use the Double, Double, Double strategy to multiply a number by 8. To do this, double the number, double the answer, then double the answer again.



uses mental and informal written strategies for multiplication and division

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