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## 'The Games' Medals' printed from http://nrich.maths.org/

## The Games' Medals

Some children from the class are thinking about races because they are interested in the Olympics. Afzal, Bengy and Chrissy like the idea of getting medals. They know that there are Gold, Silver and Bronze medals.

Afzal says that if he won he'd get Gold and if Bengy then came second he'd get Silver and Chrissy would then get Bronze.

Chrissy says that's right but if she'd come first she would get the Gold and then when Bengy came second he'd get Silver again and Afzal would get Bronze.

Bengy has other ideas too.

If the children found all the different ways in which they could be first, second and third, how many would they find?

If we think of Gold first and then Silver and lastly Bronze then so far we have:

Afzal, Bengy, Chrissy

Chrissy, Bengy, Afzal

and whatever Bengy's ideas are.

Which ways can you find?

### Why do this problem?

This activity can be approached practically with young pupils, and it could be used as a starter for class/group discussions. Some children will acquire new mathematical concepts and vocabulary, whilst others will find it helps them to develop skills connected with solving numerical problems.

### Possible approach

After telling the story (or your own version appropriate to the children and the classroom context) model the activity with three pupils involved and use the session purely as a discussion in which the children do not necessarily need to do any recording.

### Key questions

What other ways of ordering can there be?

Do you have any other ideas?

Is that all the possible ways?

### Possible extension

Some might like to think about what if there is a "draw" for one of the medals.

Some might like to think up a fourth medal - what it could be made of - and four or five pupils being involved.