I’ve been reading on-line conversations lately about scaling and dilation (which are two terms for the same thing, I think). Repeatedly I’ve seeing questions from various people on scaling activities. This confused me at first, not the concept itself, but why did there seem to be such an interest in methods of teaching dilation? Turns out that this idea of proportional change is a key concept to grasp in math, and the nuances of it are tricky to teach. After thinking about it I thought about how artists and designers use scaling all the time, and I mean all the time. So, this week, when I was working with first grade students, I decided that I would present the decorative part of their project as an a math lesson, as an exercise in scaling.
Each student picked six strips of paper, which were 1.5″ x 3″ each. I told them that these strips are the shape of two squares on top of each other, and I knew that because they are twice as high as they are wide. I don’t think they understood that part, but that was fine. I just wanted them to hear the language, as I think that it conveys a sense of importance. I then showed them how if they lined up the papers so that they made an “L” they could see a square, which they could then cut, as in the photo above. From there we talked about how they could use the square for decoration. Since a plain square is,well, not too exciting I tilted the square for a more interesting look. Next I showed them what happened when the square was cut in half, corner to corner -one cut, two triangles! We then looked at what happened when the triangle was cut in half again, and then again.
I also showed the students that to make a scaled down square that they had to cut the original square twice, once in both directions. There is something about making “baby squares” that particularly captured their interest.
Baby triangles were a big hit too.
Their project, by the way, was making a book for their animal reports.
Students have done their research, now they’ve made their books, next they will be adding writing to the books. This elephant will eventually be flanked by facts about his habitat and other interesting facts.
These students will be able to continue with these embellishments as they complete the rest of the books, I won’t be there for that part, but I think they’ve got the idea and these books well become even more wonderful.