Sharing Grant Sanderson’s “derivatives through geometry” video with kids

We’ve done a few projects inspired by Grant Sanderson’s incredible new calculus series:

Sharing Grant Sanderson’s Calculus ideas video with kids

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

Sharing Grant Sanderson’s derivative paradox video with kids part 2

Today we returned to Sanderson’s series to look at his “derivatives through geometry video”:

We watched the video last night. To get started today I reminded the boys about the concepts in Sanderson’s video. The specific example we looked at was how the area of a square with side length’s X changes as the side length’s change:

Next we moved on to the first of two challenges in Sanderson’s video. In this video we tackle the function y = 1/x. How does this function change as the value of x changes?

The second challenge problem involved the function y = \sqrt{x}. The ideas here are slightly more complicated than in the prior video and my younger son wanted a more detailed explanation. I’m glad he did, though, because going though this example a little slower I think helped the general ideas sink in.

I didn’t want to have the project end with all of the algebra in the last video, so I decided to return to the two challenge functions and look at their graphs again. Did the answers we found for the derivatives match up with what we were seeing with the slope of the function in the pictures?

This new calculus series from Grant Sanderson is one of the best “math for the masses” projects that I’ve seen. He is not pitching the series at kids, but I think there are many ideas throughout the series that are accessible to kids. I have no intention of trying to teach my kids a full course in calculus, but I do think that they will find exploring a few ideas here and there to be really fun. After we finished today my younger son’s first comment was that he wanted to do more projects like this one – yay 🙂

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