# Sharing Grant Sanderson’s “derivative paradox” video with kids is really fun

Grant Sanderson’s new video series on calculus is incredible. We’ve done one project with the introductory video:

Sharing Grant Sanderson’s Calculus ideas video with kids

Today we looked at the second video in the series. This one introduces the idea of derivatives. The videos are not aimed at kids – not eve close. But watching it with them to explain (or just skip) some of the difficult parts was really fun.

The video below shows what they took away from the video when we talked about it roughly 2 hours after they watched it. I was pleasantly surprised by how much they remembered. They remembered the discussion about the moving car, they remembered the paradox of “instantaneous velocity”, and they remembered the rise over run idea of the derivative. Some of the main ideas stuck with them and those ideas definitely made them think!

Next we talked about the car and the graph of distance versus time. This discussion was really fun. The idea is not something that they’ve seen before but this short little discussion allowed us to explore the ideas in several different ways. It was a wonderful accidental moment when my younger son drew the graph heading back down to the x-axis – Sanderson does not touch on this idea in his movie!

I missed the chance to explore my younger son’s idea about the graph representing the velocity instead of distance – we’ll come back to that tomorrow.

Next we worked through one of the derivative calculations that Sanderson used to end his video. I picked the graph of $y = x^2$ just to keep the algebra on the easy side (he does $y = x^3$ in the video.

We didn’t have as much excitement here, but they were able to follow along pretty well. Most importantly, they were able to understand that “dx” was a variable rather than, say, “d” times “x” or something like that:

I’m not intending to teach my kids calculus right now. However, working through Grant Sanderson’s derivative video with them was really fun – and we have one more idea from this project still to study! I think I will go through some more of Sanderson’s videos with them – it is so great that he’s made something that makes some of the main ideas in calculus accessible to kids.