I went through the project below with my older son on Sunday night. The question we were talking through is here:
This is problem 20 from the 2011 AMC 10 A. My son really struggled with this problem, and I also struggled finding ways to help him.
It was one of those times where I think the overall struggle was productive, but I was left feeling that I could have done a lot better. After the project I saw that the Week 3 MTBoS blogging challenge was about good questioning. Since I wasn’t satisfied with how this one went, I thought I’d use it as an example of where I’d like to improve.
In the first part of the project we discussed the problem and why it was giving him trouble. I was actually pretty happy with how this part went – we identified an initial misconception and then made some good progress toward drawing a good picture.
Having walked oh so close toward perpendicular bisectors in the first part of our talk, I thought that the next part would go pretty smoothly. We got off track, though, and struggled to get back on track. I really did nothing productive to help him here. Part of my problem is that I was overly focused on the two equilateral triangles in the picture and he was having a hard time seeing those triangles.
In the next part my struggles continued. My son was focused on one of the 30-60-90 triangles and I was hoping beyond hope that he’d see the equilateral triangles. I really should have found a good question about the 30-60-90 triangles he was seeing.
So, at the end of the last video my son had made some great progress and had reduced the problem down to finding the area of a pentagon. In the last part of the project he finishes that calculation.
So, a challenging problem for sure and a nice opportunity for me to look back and wonder what I could have done differently. It is funny that from my perspective during this conversation my son was stuck because he was so focused on some 30-60-90 triangles, but what prevented me from helping him get unstuck is that I was so focused on some equilateral triangles. Hopefully I can learn from this and come up with some better questions next time.