## Thursday, February 28, 2008

### Technology in Math

This lesson didn't begin with technology. Initially the students were working with three triangles from tangrams and creating polygons. Five regular polygons can be made with those triangles. They then had to find the area and perimeter of the shapes. The goal is for them to realize that shapes can have the same area but different perimeters (or the other way around). It was harder for them than I had anticipated, but they enjoyed it.

We ended up writing the perimeters of the shapes as algebraic expressions based on the sides of the triangles. Actually measuring was not working well and this was good practice for them writing expressions. Plus, that pushed some of them to finally realize that the areas of the shapes were all the same. Once they recognized that the sides of the triangles remained the same no matter what shape they created, they were able to realize that the areas of each triangle did so as well.

As we neared the end of the lesson we realized that we needed to look at some of it a bit more deeply. I gave each student some fresh graph paper and asked them to try and create shapes with areas greater than perimeters, perimeters greater than areas, and equal perimeters and areas. (I know we are comparing apples and oranges to an extent here because we are comparing units with units squared, but they had a lot of preconceived notions that needed to be questioned.)

Then I wanted to be able to look at some of what they found together. So I pulled up grid paper on my smartboard.

They drew several different shapes to show how each of the possibilities might look. Some students were just amazed that you could have equal perimeter and area or that the perimeter could ever be a larger number than the area. It was interesting to hear their discussion. Then Mr. B opened up Geometer's Sketchpad with a shape that he could manipulate so they could watch the perimeter and area change. This allowed them to test some theories quickly without having to do a lot of tedious computation (which would have caused them to not test their theories). They were enthralled.

This was the best on-the-fly use of technology I've done all year. I was so glad to have the smartboard and Geometer's Sketchpad at my fingertips. The one depressing piece was that I hadn't originally thought to do these things as a part of the lesson.