We had a fun summer talking through the first couple of chapters of Art of Problem Solvings “Introduction to Counting and Probability” book. It was the first time that I’d tried to do something with both kids at the same time. Having them work together seemed to go pretty well, but with the school year starting up now I’m going back to teaching them individually.

My older son wants to learn geometry this year, so we’ll be following Art of Problem Solving’s “Geometry” book. I’m really excited to go through this book – especially introductory proofs and constructions. Up until now, he’s mainly encountered only a little bit of basic geometry – areas of triangles, rectangles, and circles for example – so he’s a little biased to thinking that geometry is just a bunch of formulas. Hopefully that perception will change over the next year. For our first little discussion today, we talked through a common proof of the Pythagorean Theorem.

I gave my younger son a choice of continuing with pre-algebra, continuing with the counting book, or studying basic number theory. He picked number theory, so that’s what we’ll do for a couple of months at lesat. Art of Problem Solving’s “Introduction to Number Theory” book is fantastic, though the second half of the book is probably going to be a little much. I’m excited to use the ideas in the first half of the book to build up his number sense. For our first little talk today, we talked about the number of zeros at the end of 10!. It is an interesting problem for a kid because you can find the number of zeros without actually finding out what the number is. As you’ll see in the video, he thought that this fact was amazing:

As an aside, I let the kids pick the name for the new video series each year. This year “SuperMath” will be Geometry, and “AwesomeMath” will start with basic Number Theory. I can’t believe that “EpicMath” didn’t even come up! Looking forward to a fun year with both kids.