Student+work+samples+and+analysis+of+students'+misconceptions.

These are both samples from day 2. This was activity 19.13 from //Teaching Developmentally.// In the first example the students created two parallelograms. When I asked them about this, they told me that they were different shapes because they were going in different directions. I'm very curious to revisit this idea in a couple of weeks when we study rotations, reflections, translations and flips. In the second example, the students created one shape whose sides were different (bottom right corner). I think this was an honest mistake. They knew they had enough triangle to make six shapes, and I think they were struggling to find a sixth shape. In both of these examples, I had the students write down their conjectures about the area of these shapes. I was pleased with their initial understanding of this concept.



These are some examples of the students exploring the virtual tangrams. I was surprised at how quickly some students were able to complete these tangrams. It took me multiple tries and frustrations to figure these out. I have two students that solved three in 10 minutes. Most of my students solved one in 10 minutes. There were a few students who really struggled with this. I allowed them to use one "hint" to help them understand how these shapes were suppose to fit. Several of my students wanted to continue playing this "game" at home, so I linked it to my webpage.



This is the poster we made from Day 3. The students came up with the 2 conjectures: 1. A shape may have the same perimeter but a different area. 2. A shape may have the same area but a different perimeter.



This set of pictures is from day 5. Students were asked if the formula for finding the area of a rectangle and square, A = b x h, would work for parallelograms. After testing and then counting, they realized that this formula would work. I thought it was interesting that the first picture shows that the child eliminated the "half-squares" from one side and made up for them on the other side. In the second picture, the child tested the formula, then counted the squares. The third child began by counting the squares, marking her halves, and then tested the formula. This child was so excited about this activity and was actually the first to discover our formula A=bxh on Day 4.