Yesterday I saw an incredible new video from Grant Sanderson:
As is the case with all of his videos, this one totally blew me away. I also thought that it has some fantastic ideas to share with kids. So, this morning we tried it out!
I started by asking the boys about the area of a circle – how do you find the area?
We have studied the idea before. Here’s the previous idea (that we got from a Steven Strogatz tweet):
and here are the projects inspired by Strogatz’s tweet:
Fortunately, the boys were able to remember that idea and explain it pretty well:
After this short discussion I had the boys watch the new “Essence of Calculus” video. I actually left the room so that I wouldn’t interfere. The video below shows the ideas that they found interesting. One thing – luckily! – was the idea of making lots of slices and getting a better and better approximation to a shape. We were able to connect that idea to our prior way of finding the area of a circle, which was nice 🙂
Next we talked about the new (to them) way of finding the area of a circle that Sanderson explains in his video. What made me really happy here is that my younger son was able to understand and explain most of the ideas. It think that a 5th grader being able to grasp these ideas really shows the tremendous quality of Sanderson’s explanation in his video. I also think that it shows that many important ideas from advanced math are both accessible and interesting(!) to kids
Finally, I showed the boys some 3d prints that I made overnight.
These prints were pretty easy to make and I hoped that they would make some of the approximation ideas seem more real. In the middle of the video I remembered that I’d actually tried this idea before (ha!):
After remembering the old project, I ran and got the old shapes, too:
I’m really excited for the rest of this new calculus series. Some of the more advanced ideas might not be so great for kids, but I hope to share one or two more with the boys just to show them a few ideas that they’ve probably never seen before. Plus – I’ve got no doubt at all that this whole series is going to be amazing!