Exploring Hasse diagrams with kids thanks to Martin Weissman’s An Illustrated Theory of Numbers

I’ve just started the book An Illustrated Theory of Numbers by Martin Weissman with my son:

I've been debating a couple of different math paths to go down with my younger son. I offered up a few ideas to him tonight and he said that he was interested in studying Martin Weissman's An Illustrated Theory of Numbers. Excited to see how it goes! https://t.co/e8lcuXgSzL pic.twitter.com/52xhjneZyw

— Mike Lawler (@mikeandallie) May 20, 2020

We are going slowly and are just a few pages in, but I wanted to so a project with Hasse diagrams today because he told me last week that seeing those diagrams in the beginning of the book is what made him want to study the book a bit more.

We started today by looking at the book and exploring a bit about factoring integers:

After that introduction I had the boys read the section on the book on Hasse diagrams (roughly 1 page long) to be sure they understood how they worked. Here’s what they had to say and then a bit of practice:

It turned out that the final exercise in the last video – writing the Hasse diagram for 36 – proved to be a little tricky for my younger son. Because the last video was running long we broke things into two parts. Here we finish the diagram for 36:

We finished up by looking at one of the Hasse diagram exercises in the book. Here the boys wrote the diagrams for 7, 15, 18, and 105.

This project was a nice light touch one. It gave the boys an opportunity to review a bit of arithmetic and introductory number theory. It was also fun to explore this interesting connection between number theory and geometry.