Problem Solving Workshop for Teachers

Today we had a great time solving math problems after school with teachers from various schools in our region.

Many thanks to Dr. Peter Taylor from Queen’s University, and his students for bringing us some great problems to explore.

The first problem was about 2 concentric circles that had a special property. The segment AB which is a cord to the outer circle, and tangent to the inner circle has length 10. We needed to find the area of the outer ring.

We had lots of ideas, and approaches. Some used trig, others substitution and pythagorean theorem. Some made assumptions at the beginning, others didn’t. It was very neat to see the various strategies all get us to the same answer in different ways.

The next problem was about mirrors. 2 mirrors are placed with a 50 degree angle between them. If you sit so your eyes are 1 m from where the mirrors meet you can see 6 images. The goal is to determine how far from each of your images you are.

We set up the mirrors, got to measuring, and then had a lot of fun mapping out light rays.

We needed our knowledge of reflection from science, and triangles from math. We didn’t get to the answer for this problem, but we have lots to consider and think about. Sometimes we think that math needs to happen in 75 minutes, but for some problems they need more time. Time to make connections with other math/science, time to think of different approaches, time to do the calculations, or time to make a good plan, or a generalization of patterns that you see. We need to give ourself the time to be playful with the math, and enjoy the collaboration and the journey to the solution.

Often teachers are caught up in the busy seasons of marking and setting exams, and we lose the spark of excitement that comes from working together and doing the math. Today was a lovely refreshing evening of collaboration which I hope we can do again in the fall.

Many thanks to all who came, and to Dr. Taylor for bringing us some great problems to try.