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# Make Those Bracelets

## Make Those Bracelets

The Challenge

#### Final Challenge

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### Possible approach

### Key questions

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Here are two pictures of children and parents in Africa making bracelets. They have lots of colourful beads to choose from.

Let's think about making a bracelet using two different colours of beads.

The smallest bracelet will have four beads and the largest will have ten beads.

The Challenge

Find some ways of arranging four beads and then five beads on the bracelets, each time using two colours. Be careful not to have any arrangements the same! These two will be counted the same, as they are both 3 of one colour and 2 of the other colour.

If two arrangements would make the same bracelet when they are turned around or flipped over, these count as the same arrangement as well.

Try to find all the ways. Can you convince others that you have found them all?

Try this next for six, seven, eight, nine and ten beads.

Try this next for six, seven, eight, nine and ten beads.

A new person joins your group and wants to make bracelets.

Can you write down some guidance for them so that they have a system to make sure they find all the different arrangements and avoid repeats?

This activity engages the pupils in both a spatial and numerical context. It challenges their ability to see symmetrical reflections. It also gives them the freedom to choose how they go about the task - visualising in their head, using pencil and paper, beads, cubes or other counters that they have requested, and/or making use of a spreadsheet. They
can learn a lot from adopting one method and then realising that an alternative method might be better.

You could introduce the task as presented as on the problem page.

You may find it appropriate to make use of this interactive help

useful as part of designing the bracelets.

Use open questions such as "tell me about this ..."

How did you decide on this approach to finding all the possibilities?

Possible extension

Explore the differences between this challenge and when the bracelets are like a non-reversable necklace.