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'Bracelets' printed from http://nrich.maths.org/
Why do this problem?
is good for engaging pupils in number patterns, symmetry, factors, multiples, algebra and shape work, and allows them to be creative. It should also encourage pupils to persevere for a longer period of time than perhaps is usual.
This is best introduced by physically looking at bracelets made of beads and asking the pupils to talk about what they notice.
Beware that when children are counting or communicating generally about what they've done there is a tendency to count the number on each side of a shape inaccurately. In this example:
... there is the confusion of counting $4$ on each side and then multiplying by $6$, instead of counting the "new ones" each time and saying that there are $3$ new ones on each side.
Having dotty square and triangular paper available may help the children. Just let them enjoy this and see what opportunities arise!
Tell me about the shapes you've made.
How many beads would you need for the next size up/down?
Simply asking the question "I wonder what would happen if we ...?" will encourage learners to take the activity in new directions.
Any practical resources will help the majority of pupils, although some may like to construct them on a computer while others may prefer to draw their bracelets. I found old fashioned curtain rings to be really good but I guess that coins would also be useful!