The first example we looked at were the “hexagonal” numbers. Here my son explains what those numbers are and gives a little introduction into the surprising geometric idea that helps understand these numbers:

My son had some difficulty seeing the argument from the pictures in the book, so we tried out a few examples (a few days before this project) using snap cubes. Here’s his explanation of the surprising geometry:

The next thing we looked at in the book were the “tetrahedral” numbers. The book game an amazing proof showing a formula for these tetrahedral numbers. Here he explains this clever proof:

This was a really fun project, and I’m also really happy that this book is teaching my son a bit about reading math books – sometimes even reading and understanding just a couple of pages can take time.