# Chocolate Fractions

'Use your knowledge of fractions to win the most chocolate!'

This is a lovely practical activity since it is a game. In the game, the aim is to win as much chocolate as possible. It is really simple to understand. Do you enjoy eating chocolate? In order to eat as much as possible you will need to consider the best place to sit to ensure that you have the most.

Here is an example of the kind of presentation that students can produce with this activity

## Part 1

### Resources

You will need 3 tables and 6 bars of chocolate set up as below.

### Description

• The optimum number of students to run this activity is 10 per game. It is easy to set it up so that there are two or three games happening at the same time.
• Students enter the scene one by one and go and sit at the table that will give them the most chocolate. The game finishes when all students are sat down.
• The game can get quite animated as students vie for the best positions.
• Students could be instructed to go and sit at the table that will give them the most chocolate at that moment of the game (the student makes the decision of course). Alternatively, you might want to let the game run more naturally and let the students think strategically about where later students will sit. It doesn’t matter which way around you do it since they will analyse the game afterwards.
• Teachers could help students consider how much chocolate they will get if they go to each table. For example, ‘there are three bars of chocolate and a fourth person is about to sit at the table, how much would they get each?’
• Player number 4 is an interesting one to take a little time to consider since it doesn’t matter (at this stage of the game) where they sit, they will always get one bar of chocolate. This is provided the students make optimum choices up to that point!
• Once the tenth person has sat down students should be asked how much chocolate they have each.
• A nice twist is to ask if anyone wants to change places at this stage.
• Usually I don’t allow students to eat the chocolate until they have completed part 2 of the activity!

## Part 2

### Description

• Here students should be encouraged to analyse the game.
• I tell them that I want to know which table each student should sit at to get the most chocolate at that part of the game. For example, they will have to decide which is more chocolate: 3/5 or 2/3.
• Students could use counters to represent the people sitting at the tables.
• The students can record their findings in the table below Chocolate Fractions.

## Part 3

### Description

• The final part of the activity is about good mathematical communication and I usually set this as a homework.
• Essentially, part 2 is not a very good way for the reader to follow the game.
• Students are asked to produce an animated solution of the problem. Students often like to use PowerPoint to create an animation, although there are lots of other tools that they could use. A short video could explain the solution nicely.
• I ask for two things: 1) a correct solution and 2) a creative and interesting animation.
• A video showing some of my students’ solutions is given below.

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