Going through Joel David Hamkins’s Graph Theory for Kids

Denise Gaskins published the latest issue of Math Teachers at Play today. As usual it is a wonderful compilation of math activities and one, in particular, caught my eye. Here’s the latest issue:

Math Teachers at Play issue 85

And here’s the activity from Joel David Hamkins that caught my eye:

Graph Theory for Kids

After downloading and flipping through Joel’s activity this afternoon, I thought that it would be really fun to run through it with the boys tonight. I’ll present the videos without much comment since they really speak for themselves. The short summary is that I absolutely love this activity and think that many kids will love it, too. My kids were totally engaged for the full hour that it took to work through it.

The only warning I’d give is that in the part where the kids draw their own graphs – part D in our set of videos – make sure they are careful when counting. My kids drew some pretty complicated graphs and we had to slow down and count really carefully.

So, here’s our tour through Joel David Hamkins’s Graph Theory for Kids:

Part A: getting into the activity and explaining a few of the terms that we’ll be using


Part B: Going through a few more examples and introducing the definition of Euler Characteristic

Part C: There were lots of examples to do in the last section, so I had the boys work through all of them off camera and then had them each explain their work on one of them. This section also introduces the idea of a “connected” graph:

Part D: At the end of last section the kids were asked to draw their own graphs. My kids drew some complicated graphs and had a hard time counting the various pieces. Here we are just going through and counting carefully.

Part E: The next section of the activity introduces the idea of a “planar” graph

Part F: Now we move on to the end of the activity and look at some calculations for 3-Dimensional shapes

Part G: I thought it would be fun to end with a shape that didn’t have an Euler Characteristic of 2, so we built a torus out of our Zometool set. We also looked up the Euler characteristic of a few other shapes off camera and my son mentions a Klein bottle at the end.

So, a really fantastic activity. As I said, my kids were really engaged for over an hour and seemed to find all parts of the activity to be really interesting. There’s a ton of fun math here and lots of ways for kids to get creative. Also lots of great opportunities to hear kids talking about their own mathematical ideas.

Thanks to Denise Gaskins for sharing this one and to Joel David Hamkins for putting this awesome activity together.



5 Comments so far. Leave a comment below.
  1. Looks really great! I’m glad you enjoyed it.

    About the pagination, since you made a remark about it at the beginning: the pages were designed to be printed double-sided, and then folded to make a book. The first page is the cover, and the rest fit one after the other side it (not nested). Thus, the 3D page at the beginning was actually the inside of the back cover, and the pages make sense in that order.

  2. Ad,

    This looks fun. I printed out 3 copies for my kids to work through.

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