This activity has been particularly created for the higher attaining pupils so these notes are shorter than usual for our activities. It was used in the preliminary rounds of the Young Mathematicans' Award 2012.
Why do this problem?
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?
Explore the differences between this challenge and when the bracelets are like a non-reversable necklace.