My older son is working through Stewart’s Calculus book this year (edition 3). Right now he is working on one of the introductory derivative sections. Today I picked to problems from that section and asked him to work through them live.
Here’s the first problem -> a problem about finding a line perpendicular to a parabola:
Here’s the second problem -> a problem about a piecewise defined function. I was using this problem to introduce the concept of “differentiable”. Although we had not discussed that definition ahead of this problem, he was able to reason through what it meant.
I think this is a really nice example of a kid working through a challenging problem.