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

This is the complete table:

Input	Output
6	2
7	3
8	4

Idea summary

Function 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.

Algorithms

To explore what an algorithm is, we'll use an example of getting dressed, then see how we can use an algorithm to sort some coins into order by value.

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Examples

Example 2

Write 327 in expanded form by following these steps:

First, write down the hundreds part.

Worked Solution

Create a strategy

Write the number in a place value table.

Apply the idea

Here is the 327 in a place value table:

Hundreds	Tens	Units
3	2	7

We have 3 hundreds which equals 300.

Next, write down the tens part.

Worked Solution

Apply the idea

Hundreds	Tens	Units
3	2	7

We have 2 tens which equals 20.

Now, write down the units (ones) part.

Worked Solution

Apply the idea

Hundreds	Tens	Units
3	2	7

We have 7 units which equals 7.

Now, write the number in expanded form by adding these three numbers together.

⬚+⬚+⬚

Worked Solution

Create a strategy

Write the numbers found from parts (a) to (c) in each box.

Apply the idea

300+20+7

Idea summary

An algorithm is a set of steps that tells us what we need to do, and when. It can be used in lots of ways, but we have seen how to use it to sort numbers into different orders.

12.01 Partitioning and Ordering

Ideas

Are you ready?

Examples

Example 1

Algorithms

Examples

Example 2

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