I have been trying to structure my geometry classes this year with a problem to think about so that they can discover something. I believe that if they learn something without me, they take ownership of it and actually remember it. I gave them this triangle midsegment problem the other day in class:
As you can tell, it is nothing fancy. Maybe because I have been doing things like this all year long but my students dove in and tried to figure out a whole bunch of stuff. After they made their conjectures, I drew another one on the board and they had to figure out everything again and see if their conjectures worked. Some did and some didn’t…which lead to some great discussions. After 30 minutes, we were done discussing and everyone was convinced that this always worked. I threw a sketchpad up on the board and played around with it and they double checked it always worked (they love watching these things fly around on the screen).
I could have easily just told the students to accept this fact and do 10 practice problems on it but instead, I thought that this would be much more beneficial. I then proceeded to give them a few practice problems in different contexts involving midsegments…they rocked through all of them. Love it when kids tell you that this concept was easy when reality, they think it is “easy” because they worked hard to understand the idea behind and not just memorize that it is parallel and half the measure of the base. I need to remember to do more of this as it is so powerful!