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4.05 Patterns


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We've seen how multiplying by 2 helps us  multiply by  4, and then by 8. Let's try this problem to help us remember.


Example 1

Find 6 \times 8.

Worked Solution
Create a strategy

To multiply 6 by 8 we can multiply 6 by 2 three times.

Apply the idea
\displaystyle 6\times 2\displaystyle =\displaystyle 12Double 6
\displaystyle 12\times 2\displaystyle =\displaystyle 24Double the answer
\displaystyle 24\times 2\displaystyle =\displaystyle 48Double the answer


Idea summary

We can use any of the following to work out multiplications:

  • repeated addition

  • arrays to show equal sized groups

  • patterns, such as doubling and skip-counting

  • multiplication tables

Patterns in multiplication

What if we could use things we already know to solve multiplication or division? We can. Let's see how.

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Example 2

If 2 \times 8 =16, what is 20 \times 8?

Worked Solution
Create a strategy

Since 20 is 10 times larger than 2, we can multiply 16 by 10.

Apply the idea
\displaystyle 20 \times 8\displaystyle =\displaystyle 10 \times 16Rewrite the multiplication
\displaystyle =\displaystyle 160Add a 0
Idea summary

For every multiplication problem we know, there's another one we also know. If we know our 3 times tables, including 3 \times 7 = 21, then we know that 7 \times 3 = 21.



uses mental and informal written strategies for multiplication and division


generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

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