Topics
4. Multiplication and division
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Australia
Year 4

4.05 Patterns

Lesson
Practice
Lesson

Are you ready?

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.

Examples

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

So:6\times8=48

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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Examples

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.

Outcomes

AC9M4N09

follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

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