## Buckets of Thinking

There are three buckets: one red, one blue and one yellow. They each hold a maximum of $5$ litres.

Liquid is measured carefully in whole litres and poured into the buckets, a different number of litres in each one.

If the liquid in the red bucket was poured into the blue bucket, it would then contain the same amount of liquid as the yellow bucket.

Half the contents of the yellow bucket is the same as twice that in the red bucket.

How much liquid is there in each bucket?

This problem is also available in French:

Question de chaudières.

### Why do this problem?

This problem is a nice, simple activity which stimulates discussion and some real thinking. It can also be opened out in ways that will appeal to older or higher-attaining learners. It uses some basic arithmetic and encourages trial and improvement. It can also be used as an introduction to algebra because of the
unknowns in each bucket.

### Possible approach

You could start by showing the group the picture of the three buckets and asking for suggestions as to the maximum amount each might hold. Use this discussion to inform the class that each is $5$ litres. Then, reveal each clue in turn and invite pairs of children to talk about possible conclusions.

Give learners time to work in pairs on the problem, warning them that you will be focusing on how they worked out their solution. Learners could be asked to find some other arrangements of buckets along with two or three statements that would challenge someone else to work out the amount of water in each. They could keep to the rules that there is a different amount in each bucket, measurements
are in whole litres and $5$ litres is the maximum. (See

this sheet for further ideas.)

At the end of the lesson when various solutions and methods of reaching them have been discussed, it might be appropriate to model how the problem could be written algebraically.

### Key questions

What is the maximum amount of water that the bucket can hold?

What do you know about the amount of water in this bucket?

Can you think of a way of writing this down or doing a drawing to help?

### Possible extension

This sheet gives more detail about extending the task by encouraging children to make up their own problems, firstly by sticking to the same 'rules', then by varying the constraints.

### Extension for the exceptionally mathematically able

Go to

More and More buckets
### Possible support

Suggest working with counters representing each litre and pictures of the buckets.