# Patty Paper Geometry

Saw this interesting recommendation from Kate Nowak on Twitter last week:

The book (and some extra patty paper) arrived today and it looks like it has some great activities. I found one that seemed fairly easy to implement and gave it a shot with both kids. The project is a little lesson about the perpendicular bisectors in a triangle.

I tried it out first with my older son. We’ve just finished studying Art of Problem Solving’s Introduction to Geometry book which means that he’s seen a little bit about perpendicular bisectors before. He recognizes pretty quickly what he needs to do to make the project work, so we moved fairly quickly. Based on how this project went, I’m pretty excited about reviewing some more geometry concepts with him using this book.

My younger son has not had much geometry and I’m pretty sure has not heard the term “perpendicular bisector” before. I thought this project would still be interesting for him, though, because of the surprising result that the three perpendicular bisectors intersect in a single point. We went through the project a little slower than my older son’s pace, but he seemed to really enjoy it. He even wanted to try out a second triangle.

I was glad that he wanted to look at another triangle because that gave us a chance to try a triangle that wasn’t a right triangle. His interest and engagement in the overall project left me pretty excited to try teaching him some new geometry using the approach in the book.

So, I’m really happy with how this project went with both kids. Looks like this book gives you a great opportunity to review and to learn new geometry. Can’t wait to try out a few more of these explorations. Thanks to Kate Nowak for this awesome recommendation!

# Starting Art of Problem Solving’s Introduction to Counting and Probability

The math project I’m doing with the boys this summer is working through Art of Problem Solving’s Introduction to Counting and Probability

We also spent a little time in this book last summer, which was fun. What I like about this book is that the mathematical ideas do not require much beyond basic arithmetic which means that the boys can work together pretty well. The extra work that my older son has done in algebra and geometry doesn’t put him too far ahead of my older son in this particular topic.

I also think the ideas in counting and probability are great for helping kids begin to understand how to organize ideas when solving math problems. The first problem from today is a good example of how organizing a few ideas helps with problem solving. The problem is a Venn diagram puzzle. In the first part of this project we talk through a problem that gave my younger son a little trouble and hear his initial thoughts on the problem:

In this next part of the talk we dive into the solution. We’ve got a good picture on the board, but my younger son is struggling a little to see how to pull together the information from the problem. My older son has an important idea – the number of people in four overlapping regions must add up to 20. That idea allows them to see the solution to the problem.

In the last part of this project I show them an alternate solution. The idea here is to use the fact that the 20 people are separated into two different groups in two different ways: left vs right handed, and like jazz vs. don’t like jazz. Recognizing either of these subdivisions allows you to see a little more structure than was initially apparent in the problem.

So a nice start to our little summer project. My hope is that we’ll have a nice and stress free walk through the book this summer and the boys will learn a bit about counting and problem solving.