Normally I start off the year with a boring going over the rules/syllabus the first day. I decided not to torture the students this year but to start with a hands on activity. So I tried the making the rectangle activity on the first day with my two 8th grade technology classes. By the way I changed it into a theme for a complete geometry unit if you are interested. I also made a chart for students to fill in with their data.
The students were interested in the pictures. They really had no idea about the construction processes. When we went outside most of the students immediately made the mistake of confusing area for perimeter. I asked lots of questions to re-direct them and to get them to re-think about the difference. Then the groups staked out quadrilaterals, some more square than others. One of my favorite parts was watching a student lay down on the ground to estimate six feet instead of using the tape measure. I challenged them to consider if their shape was a “perfect” rectangle.
At the end of the hour the students measured the sides and the diagonals. I had to go to each group and help with this. At first every group just wrote down the measurements that they thought they had measured. I told them that they must measure what their sides actually were and write down their imperfect measurements not what they meant them to be.
The next day we discussed how to determine whose was the best rectangle. We ended up having to define a rectangle which was a good activity for the students. I then showed them how the diagonals of a true rectangle are congruent and we talked about Pythagorean Theorem. I then showed them this video of an area proof:
We then talked about 3-4-5 triangles and I had students come to the front of the room and create a perfect 90 degree corner by holding three tape measures at 3,4, and 5 feet.
I was disappointed in the student’s prior knowledge about the Pythagorean Theorem. None of them had heard of it even though a few of them had Algebra last year. I will repeat this on the first day of my class for the next three quarters. I will be curious to see if students do better later in the year after they have been exposed to more background knowledge in math class.