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

Sonny was given twice as many lollies as Sam.

Sylvia was given three times as many lollies as Sam.

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

If Sylvia got a total of 18 lollies on Tuesday and Wednesday, how many lollies did Sonny get for the whole five days?

How many lollies would Sam need to get on Saturday if he wanted to have 39 lollies altogether?

In this problem students use logic, number operations and relational (algebraic) thinking as they seek a solution.

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 that they've been given. Sonny was given twice as many lollies as Sam. Sylvia was given three times as many lollies as Sam.

They are given the same number of lollies each day up to (and including) Friday. If Sylvia got a total of 18 lollies on Tuesday and Wednesday, how many lollies did Sonny get for the whole five days?

How many lollies would Sam need to get on Saturday if he wanted to have 39 lollies altogether?

### Teaching Sequence

- Pose first part of the problem to the class.
*On Monday, Sam, Sonny and Sylvia share some lollies that they've been given. Sonny was given twice as many lollies as Sam. Sylvia was given three times as many lollies as Sam.* - Ask some simple questions to get the students thinking about the problem.
*If Sam has ten lollies how many have Sonny and Sylvia got?*

If Sylvia has 30 lollies how many does Sonny and Sam have?

Ask the students to use number sentences to express their answers. Share and discuss. - Give the students time to think about the first part of the problem and to discuss it with their friends.
- Ask the students for their solutions to the first part.
- Pose the rest of the problem for the students to work on in pairs. Have the students use number sentences in their written record of the solution.
- As the students work ask questions that focus on their choice of number operation and their use of number sentences to record their answer.
*Why did you use multiplication?*

What number operation have you selected? Why?

Tell me what this number sentence tells us. - Share solutions to the problem discussing the different approaches used.

#### Extension

#### Other Contexts

sharing fruit, collectibles

### Solution

Sylvia got 18 in two days, so 9 lollies a day.

Sylvia gets three times as many lollies as Sam, so Sam gets 3 lollies a day.

Sonny gets 6 (= 2 x 3) lollies per day.

So over a five-day period Sonny gets 5 x 6 = 30 lollies.

Sam gets 3 lollies a day, so he gets 15 from Monday to Friday. 15 + 24 = 39. Sam needs 24 lollies on Saturday.