This sequence explores the important mathematical idea that fractions represent division. Students are invited to solve problems involving fair shares. Through the tasks, students will recognise that the denominator represents how many shares and the numerator represents the number being shared. The second task also explores the idea that any fraction can be represented as the sum of unit fractions.

This sequence is for students who:

- recognise fractions as representing part of a whole
- have generalised definitions for numerator and denominator
- recognise division as a method for sharing objects fairly
- have developed strategies for division

### Lesson 1: Where Will You Stand?

This task explores fractions as division through a whole class problem. Three tables of lamingtons are at the front of the room: the first table has one lamington, the second has two and the third has three. Ten students are asked, one at a time, to stand at the table where they will receive the largest share of lamington, knowing that they will need to share with the other students standing at that table. At the end, students calculate how much lamington each person receives.

### Lesson 2: Sharing Lamingtons

Students are presented with the story of four different groups of children sharing different numbers of lamingtons. They are asked to determine if the children in any group received a greater share of lamington than in other groups. Students use unit fractions to compare quantities.

### Lesson 3: Fairer Shares

Students review the findings from the previous lesson. They determine a fairer way to share the lamingtons across all four groups.

Last updated April 20 2020.