I wanted to do a follow up to the 2nd project this morning to address one point that I sort of skipped over in that project. Unfortunately we got so caught up on what is the main point of the video that we didn’t get to it! Sort of good news / bad news, with the good news being that talking about graphs of distance and velocity with kids is amazingly fun.

Here’s the 2nd video in Sanderson’s series – the Derivative Paradox:

I got started this morning with a quick review of how to go from the graph of distance to the graph of velocity. The boys seemed to remember quite a bit from our last project, which was really nice:

Next I drew a graph that was similar to the one that gave the boys some trouble in our last project. I was hoping for this part to also be a review, but it gave them some trouble again. Part of the trouble was that I was a little careless in the presentation, unfortunately, but this was still the start of a very good conversation.

Drawing graphs of functions and derivatives was tricky for students that I was teaching in college. I’m happy to have these conversations with my kids, though, because I do think the ideas are accessible to them.

So, after stumbling through the conversation in the last video, I tried to take a different approach here. Almost starting over, actually.

One really interesting thing for me watching my older son talk about the pictures was that his intuition said that the velocity must be near 0 at time 0, but the graph was saying something different than that. He was really struggling to reconcile the two ideas.

Putting some numbers to the velocities helped straighten out that problem. By the end both kids had sort of an aha moment and realized that what we were talking about with these graphs

I can’t say enough good things about this new calculus series from Grant Sanderson. Not all of it is going to be accessible to kids, which is totally fine – he’s not pitching this series at kids. Some of it is, though, and his approach showed me how to make some of the ideas accessible. There’s probably at least 10 more projects to do that involve sharing his series with kids. I can’t wait!