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12.02 Function Machines


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You may have already seen some patterns, try this one.


Example 1

Write the next number in the pattern:


Worked Solution
Create a strategy

Find how much the numbers are increasing by each time and add that to the last value to complete the pattern.

Apply the idea

To work out how much the numbers are increasing by each time, you can count up or find the difference between the numbers.

\displaystyle 4-2\displaystyle =\displaystyle 2Subtract two numbers

Add 2 to each number to complete the pattern.

\displaystyle 12+2\displaystyle =\displaystyle 14Add 2 to 12

The complete pattern is 2,\,4,\,6,\,8,\,10,\,12,\,14.

Idea summary

Just like when you're counting, patterns can continue forever. You can always add or subtract the same amount to continue a pattern.

Number machines

Let's look at how number machines can be used to continue patterns when you have the rule.

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Example 2

Look at the following number machine:

A number machine that subtracts 4. Ask your teacher for more information.

Complete this table of inputs and outputs:

Worked Solution
Create a strategy

Subtract 4 from each input to get the output.

Apply the idea
\displaystyle 6-4\displaystyle =\displaystyle 2Subtract 4 from 6
\displaystyle 7-4\displaystyle =\displaystyle 3Subtract 4 from 7
\displaystyle 8-4\displaystyle =\displaystyle 4Subtract 4 from 8

This is the complete table:

Idea summary
  • Number machines show the relationship between the input (starting number) and output (answer).

  • If you are given the output, you can find the input by reversing the rule.

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