The purpose of this activity is to engage students in finding many ways to form one (whole) with fractional units. In doing so they will use simple equivalence and learn the recognise non-unit fractions as iteration of unit fractions.

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.

Here are three ways to make one (whole) with halves, thirds, quarters and sixths of a circle.

How might these ways to make one be recorded as equations or expressions?

What other ways to make one can you find just using halves, thirds, quarters and sixths?

Can you prove you have found all the possible ways?

### The procedural approach (show more)

- The student uses trial and error approaches to find other ways to make one.

### The conceptual approach (show more)

- The student uses a systematic strategy to find all the possible ways to make one and uses expressions or equations to record the ways.