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!