Disclaimer: quarter-baked
Roughly half of primary school students have some experience with the concept of braids and maybe with the practice of making them. At the same time braids are nice objects to study, because they form a noncommutative group with infinite order elements.
So, would it be possible to pose some interesting-but-approachable problems about braids[1] to primary school kids? Obvious ideas for me are:
- how can we describe a braid?
- do two braid descriptions describe the same braid? what does this even mean? this can naturally introduce a concept of "invariants" (in the sense of a function from a braid representation that is equal for all representations of the same braid) and the concept of transformations of descriptions (and then maybe completeness of that)
- is every braid a commutator of two braids? (sadly this doesn't seem very natural here),
- what generator sets are there? is it sufficient to flip adjacent strands only?
[1] morally similar to "how many isometries does a cube have?"