Well, I think they key is I try and select topics that I find very fun, even they are a little off the beaten path. I know there's pressure to teach the curricu

Well, I think they key is I try and select topics that I find very fun, even they are a little off the beaten path. I know there's pressure to teach the curriculum, but honestly there are some cool things you can do with students if there's extra time that might get them hooked even if it's not in the curriculum, like: 1. Coloring maps (four color theorem) 2. Drawing curves and then looking for pathological ones (quadratic equations ...but more of an exploratory rather than methodological approach) 3. Infinite series (but just discuss some paradoxes people thought of centuries ago...) 4. Triangles on spheres ...if you don't make some of it extremely rigorous, there's a lot of basic facets of these things like the drawing aspect that can be quite fun. And TBH it makes sense to start there because mathematicians started out exploring these topics just with random calculations and doodles rather than rigorous proofs.