# 12.01 Partitioning and Ordering

Lesson

## Ideas

Do you know how to use a function machine? It's like an algorithm with just one step.

### Examples

#### Example 1

Look at the following function machine:

Complete this table of inputs and outputs:

Worked Solution
Create a strategy

Subtract 4 from each input to get the output.

Apply the idea

This is the complete table:

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.

### Examples

#### Example 2

Write 327 in expanded form by following these steps:

a

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:

We have 3 hundreds which equals 300.

b

Next, write down the tens part.

Worked Solution
Apply the idea

We have 2 tens which equals 20.

c

Now, write down the units (ones) part.

Worked Solution
Apply the idea

We have 7 units which equals 7.

d

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.