On Monday, Sam, Sonny and Sylvia share some lollies they'd been given.

Sonny got half as many lollies as Sam, and Sylvia got a third as many lollies as Sam got.

They got the same number of lollies each day up to (and including) Friday.

If Sam got 18 lollies on Wednesday, how many lollies did Sonny get on Thursday?

How many lollies did Sylvia get that week?

In this problem students apply a range of strategies to solve fraction problems that involve one half and one third.

This is one of six problems: Lollies! (Level 1), More Lollies (Level 1), Sharing Lollies (Level 2), Lollies, Lollies, Lollies (Level 3) and Still More Lollies (Level 4), which become more algebraic in their focus at each level.

### The Problem

On Monday, Sam, Sonny and Sylvia share some lollies they'd been given. Sonny got half as many lollies as Sam, and Sylvia got a third as many lollies as Sam got.

They got the same number of lollies each day up to (and including) Friday. If Sam got 18 lollies on Wednesday, how many lollies did Sonny get on Thursday?

How many lollies did Sylvia get that week?

### Lesson Sequence

- Ask some quick warm-up questions to get the students thinking about halves and thirds.

*Show a piece of paper and ask the students to find a third of it. How do you know you have a third?*

Show the students 6 counters and ask the students to find a third of them? How do you know? How did you work it out? - Pose the problem to the class and have students suggest how they could approach the problem.
- Have the students work on the problem in pairs.
- As the students work ask questions that focus on their choice of problem solving strategy and their understanding of fractions.

*Can you tell me what you are doing?*

Why did you decide to solve the problem that way?

What is a third? What is a half?

How do you know when you have third? - Share solutions to the problem. Discuss the different approaches used by the students.

#### Other Contexts

This problem can be posed in a number of contexts: money, time, temperature or length

### Solution

Students will use a range of strategies including drawing and equipment.

Sonny gets half as many lollies as Sam. Sam gets 18 and half of 18 is 9. Sunny got 9 lollies.

Since Sam gets 18 lollies on any day and Sylvia gets a third of that, then Sylvia gets 6 lollies. Five lots of six is thirty.