October 8^th, 2008

Today, I wanted to begin my lesson with a warm up activity to get students thinking about numbers and how to represent numbers. I asked students to think of as many as they could to represent the number 56. I gave them five minutes and then we began talking. I gave students the opportunity to come to the board and write some of their representations. I was expecting that after the first four or five students had written their responses, most of their answers would have been written. Well, was I surprised? An hour later, and a board full of math, and we called it a class.

After about the tenth or eleventh representation was drawn, written, colored, or symbolized, students started coming up with more and more ways to represent this number. The more students wrote and talked about the numbers, the more ways students came up with. We talked about the different ways students represented that number, got students to explain their reasoning behind their representations and once all was said and done, we were able to represent the number 56 in 56 different ways!!

I used one of the suggestions on how to create open ended tasks to come up with this activity. I was not expecting students to be as engaged as they were. They were actually racing to the board to grab a marker so they could write yet another way to show how they thought about the number 56. At one point, I think almost all students were at the board. What was interesting to note about this particular activity, was how little I did to facilitate this conversation. I stood back and let things unfold. I noticed that students were thinking about how others had represented the number and some even questioned these representations. For example, one student drew a digital clock with the time 8:04. One student looked at this and asked how this represented 56. The other student answered by saying that there is 56 minutes left before 9:00. Settled! The questioning student then drew an analog clock using the same reasoning as the time read 8:56, 56 minutes after 8:00.

We all agreed that this was one of most enjoyable math classes yet!