Last day of 2009

I went in on Friday, the last day of school before the winter break, and we had a half-day with only 2nd (accelerated) and 3rd (non-accelerated) hours. I wanted to try another problem of the week (POW), and I tried the "congruent rectangles" problem that was featured in the training session with the Math Forum folks. This problem definitely looks like a math problem, so I wanted to spice it up a bit, and I began by talking about money, and then about foreign money. We briefly discussed the European Union and the Euro, and then I showed the graphic, which I superimposed 5-euro notes onto. So instead of asking the dimensions of random rectangles, I was talking about the dimensions of money. The main reason I didn't use American money was because the shape was better (or more, the students aren't familiar with the shape of Euros, so I could stretch them to make them work), but I think it also gave some valuable side information - "fun facts" to break up the math tedium.

The talk about money and Europe was actually pretty good, and the students participated and were interested. When we got to the actual problem though, the students struggled. As usual, I gave them time to notice and wonder, and some of the observations included the fact that four sideways bills are the same length as three horizontal bills - which is a very important observation for setting up the problem mathematically. After listing and discussing the noticings and wonderings, I then presented the problem and asked them to see if they could solve it. The students in both classes struggled with this. They seem to not grasp the concept of area, which is something I really expected them to understand by now. So, in both classes, I ended up walking them through how to solve it, but it was more of me doing the problem and a handful of the students paying attention and following, which is not really the goal of the POWs. I sent Annie from the Math Forum an email about this issue last week, and hopefully she'll have some insights about how to make these POWs work better for our classes.