# The Puzzling Sweet Shop

## Problem

Rosie went into the sweet shop with 10p to spend.

There were cola bottles for 2p, mini eggs for 3p, marshmallow twists for 5p and lollipops for 7p.

2p | 3p | 5p | 7p |

Image
Cola bottles |
Image
Mini eggs |
Image
Marshmallow twists |
Image
Lollipops |

What could she buy if she wanted to spend all her money?

Alice, James, Katie and Henry went into the shop too. They each had 20p to spend and they all spent all of their money.

Alice bought at least one of each kind of sweet. Which one did she have two of?

James spent his money on just one kind of sweet, but he does not like cola bottles. Which sweets did he buy?

Katie bought the same number of sweets as James but she had 3 different kinds. Which sweets did she buy?

Henry chose 8 sweets. What could he have bought?

(If you want to do this with cents instead go here

## Getting Started

Think of ways that $10$ and $20$ can be divided up.

## Student Solutions

These solutions are for a previous version of this task, where cola bottles were called chews and marshmallow twists were chocko bars instead.

Kaylee J sent us answers to the Puzzling Sweet Shop problem:

Rosie can buy:

one lollypop and one mini egg.

one chocko bar, one mini egg and one chew.

Are there any other combinations of sweets Rosie can buy? Let us know if you think there are.

Kaylee goes on to answer the rest of the questions:

Alice bought two mini eggs. I know this because this is the only combination of sweets which add up to 20p where she bought at least one set of every sweet.

James bought 4 chocko bars. I know this because it is the only sweet that has a price that can divide into 20p exactly when chews are not included.

Katie bought 2 chocko bars, one lollypop, and mini egg.

Henry bought one chocko bar, one mini egg, and 6 chews.

There may be some other sweets that Henry could buy too. Jessica suggests 4 chews and 4 mini eggs. I wonder if there are any other combinations?

During the 2020 Lockdown we had this solution come in from a pupil at St. Thomas' London

Thank you very much! This is a really good submission.

## Teachers' Resources

### Why do this problem?

This problem presents learners with a pleasant and familiar situation in which to explore aspects of the four operations. It also relies on finding all possibilities so can be used to focus on working systematically.

### Possible approach

It might be helpful just to have the image displayed, or for you to redraw a similar image, and for you to ask the questions orally rather than children having to read from the screen.

Begin with Rosie and suggest children work in pairs to find possible solutions. After a minute or so, you might like to take a couple of answers and then emphasise you'd like to know *all* the combinations that Rosie could have bought. In a mini-plenary invite learners to share different ways of going about finding them all and draw attention to those who have
developed a system, for example starting with the most expensive sweet (a lollipop) and seeing what could be bought with that; then looking at the next most expensive and finding the combinations which could go with it etc. At this stage, you may also want to highlight some good ways of recording that children have come up with.

Once you have explained about the other four children, you could jot a reminder of how they each spent their $20$p on the board and leave the class to explore possibilities this time. When you bring their ideas together, you may want to praise those who have developed systematic ways of working based on the earlier discussions and those who explain their reasoning clearly.

### Key questions

How do you know you have all the possibilities?

### Possible extension

Learners could investigate how other amounts of money perhaps between $10$p and $20$p, could be spent exactly.

### Possible support

It could be useful for children to have objects to represent the sweets, for example coloured counters.