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.
1 comment:
You wrote:
"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."
I'm not sure you could have planned this because when you started the lesson you didn't know what your students knew. You had an idea where they were at and the paper models might have been enough. To me this lesson was pure teaching and learning! Using the technology was a reaction to what your kids were doing. Technology was a tool to make it better for your students as you realized the concrete materials would only go so far. Chalk one up for the experience teacher. For some students it might have been enough to use the paper models. As it turned out, seeing the transformations and measurements change electronically on a smartboard and using software was the perfect tool to take them to the lightbulb stage. Yeah! I think you used the technology just right... doesn't matter when the idea came. Seemed pretty seamless to me. Great lesson!
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