Well with all things that we try , there is always the chance that it may fail. When I was thinking about an open middle problem and how I could create one to fit the unit we were working on, I thought decomposing a composite figure will allow students the opportunity to find their own way to decompose the shape into a way that fits their thinking . Below is a picture of the problem that I used :
I began by asking students to think about all the ways they could decompose the shape. Most responses were to draw a line and create a 2×2 at the top. After that they were really unsure if there was another way to do it . With some encouragement, some students made a line down to separate and make a 2×5 and then a larger one. After making them I asked them to consider whether there was one way that would make the area of both decomposed shapes closer to the same size. in hind sight, I wish I would have made a shape that would have encouraged the students to decompose in different ways. It was however interesting to listen to their conversations. I do feel on some level this was a failure on my part in the sense I did not create a problem that allowed the students to have a wide range of thinking but it was also successful because it did encourage my students to have some great math conversations. Below is some of their thinking.