The beginnings of abstraction

I’ve been working on basic techniques of proof with the kids for the last couple of weeks and I’m hoping to incorporate that work in with what they are studying in their books.

My older son is working through Art of Problem Solving’s Introduction to Geometry. Today he picked a problem for our movie which leads pretty naturally to a discussion about proof and abstraction.

The problem is:

A regular polygon has the same number of diagonals as sides. What is the sum of the interior angles of this polygon?

Here is his solution to the problem:

After he finished I tried to get him to think about the problem more abstractly, and that led to a nice discussion. His approach to counting the number of diagonals was really interesting.

This was a fun way to start the 7th grade school year – can’t wait to see where the next 12 months take us 🙂