So, here's the plan for my 10th grade topology students.

Today, we'll abandon algebraic topology completely, and instead go into knot theory. I'll want to discuss what we mean by a knot (embedding of [tex]S^1[/tex] in [tex]S^3[/tex]), what we mean by a knot deformation (thus introducing isotopies while we're at it) and the Reidemeister moves. Also we'll discuss knot invariants - and their use analogous to topological invariants.

Later on, we'll continue with other invariants; definitely including the Jones polynomial, and possibly even covering Khovanov homology. One possible end report would be to explain a bunch of knot invariants and show using examples how these have different coarseness.

*Edited to add:* I got myself some damn smart students. They figured out
the Reidemeister moves on their own - as well as minimal crossing number
in a projection being highly relevant - with basically no prompting from
me. I'm impressed.