Using “An Illustrated Theory of Numbers” with kids

I got a great book in the mail yesterday:

My plan is to spend the next 5 to 6 weeks using this book with the boys. They’ve both worked really hard this year going through Art of Problem Solving’s Geometry and Precalculus books and I want to end the year on a fun (and amazing!) note.

Today we took a quick look at Chapter 0. Here’s are a few initial thoughts from the boys:

For the project, I had each of the boys pick two problems from the end of Chapter 0 to talk through.

The first problem that my older son picked was about regular polygons. This led to a really nice discussion about which regular polygons can fold up into the Platonic solids

The first problem my younger son picked was about Hasse Diagrams – here we had a nice discussion about factoring:

My older son’s second problem asked to prove this statement -> If x divides x^2 + 1 then $altex x$ must be +1 or -1.

Finally, my younger son’s second problem asked how to represent this arithmetic identity as a “spiral”: 100 = 10 + 2*9 + 2*8 + . . . . + 2*2 + 2*1.

Honestly, I can’t wait to do more from this book. The end of the book gets into a few ideas that are probably a little too deep for kids, but there’s easily 4 weeks of material that we can enjoy as the school year comes to an end!

One thought on “Using “An Illustrated Theory of Numbers” with kids

  1. Dear Mike,

    I found this post through my weekly Googling, and I’m delighted that you and the kids are enjoying the book so far. I’ve gone through some of the material with students around the ages of 10-18, and the material on fractions and Ford circles (Chapter 3) and topographs (Chapter 9) worked particularly well. The topographs take a bit of practice, but they’re fascinating to draw and experiment with. Feel free to reach out anytime if you have questions, find mistakes, etc.. My email is weissman AT Also, I’ve set up a book webpage at, which contains some programming tutorials, the book’s errata, and maybe some other goodies later this summer.

    Marty Weissman

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