# Starting some fun new chapters in our books today

As luck would have it I started new chapters with both boys this morning.  In our number theory book we’ll be looking at different bases and in the geometry book we’ll be looking at right triangles.   Both are such fun topics and I’m super excited about spending the next few weeks exploring them.

I’ve touched on both of these topics previously with each kid.  Not really formally, but I’ve found doing calculations in different bases to be a great way to build number sense, for example.  We even did an old project about fractions and decimals in binary:

Fractions and Decimals in Binary

We also did a really fun project where we made a “binary adding machine” out of Duplo blocks.  This is a great activity for building up the idea of place value and is really one of my favorite math activities that we’ve ever done (the subtraction machine was especially fun!):

As for the geometry, we’ve touched on the Pythagorean theorem several times, even just by accident a few days ago in a snap cube project with my younger son:

It is exciting to be covering right triangles and the Pythagorean theorem more formally now, and so fun to be sitting with my son as he walks through one of the proofs of the theorem this morning.  It thought Art of Problem Solving made a nice choice in the proof they selected to use as an example.  Tlast chapter in the book was about similar triangles, and this proof helps you move forward with new right triangle material while reviewing the old similar triangle material at the same time:

Following our talk this morning we watched Numberphile’s excellent video with Barry Mazur explaining the “blob” Pythagorean theorem, because why not learn about the Pythagorean theorem from a Harvard math professor?:

Such fun topics!  Going to be a great couple of weeks leading up to Thanksgiving 🙂