Middle school students love challenges. If you tell them that you’re not sure they can do something, they will do everything in their power to prove you wrong. That happened today in my geometry classes. We are going to be learning about points of concurrency in triangles this week so today with about 20 minutes left of class I held up some large triangles that I had cut out of old manilla folders and told them that I had a challenge for them. I told them that they needed to find the exact point on the triangle in which I could balance the triangle on the tip of a pencil. I told them that they could probably do it by simply holding the triangle and making constant adjustments, but I challenged them to find a method for finding the point on ANY triangle using any tools they wanted.
What followed was a fantastic exploration where students used rulers, compasses, and protractors to try and find the point where the triangle would balance on a pencil. They constructed angle bisectors, perpendicular bisectors, and drew midsegments among other things. I heard a ton of excitement throughout the room, and a bunch of “AWWW’s” when their triangles fell. We ended class on a cliffhanger, and promised I would show them how to find the point on Thursday. It was great.