Recently the other 7th grade teacher told me she wanted to do a day of origami math. We had been learning the relationship between the sides of special right triangles (30-60-90 and 45-45-90). We had also started talking about the volumes of prisms.
With that in mind, my co-teacher showed me a project she was going to do. She was going to have her students build an origami cube, and then use their knowledge of these special right triangles to determine the volume of the cube.
We said that the side of the original unfolded sheet of origami paper was “x” and then using that, they needed to find the volume of the cube in terms of “x.”
Although I’m never quite convinced that these sort of hands-on activities really bring about understanding (see recent NYT article questioning the relationship between the concrete v. abstract in math), we had a day to spare and so I decided to do it in my class too.
I made a website with the step-by-step instructions to project on the SmartBoard so my students could follow along. I also had a giant square which I folded in front of them. I had each student do only one step at a time.
Since the day, I found a number of videos on YouTube explaining how to make the origami shapes. Here’s one:
Overall the students seemed to have an okay time with it. They really liked the cube itself. When it came to solving the problem, I let them float on their own. (This is an advanced class, so I wanted to see where they would go.) Many got to the point where they unfolded their origami sheet and saw the creases which formed the side of the square. And it was this point — where they had to notice a relationship between the side of the original origami sheet (“x”) and the diagonal of the square (“x/2”) that was key to the solution. With a little prompting, they got there.
We still needed an extra 5 or 10 minutes for this lesson to go more smoothly and to give students time to mull and go astray. Two of the four groups working on it got the answer, or very close to it. I stopped the investigation 7 minutes before class ended and we went through the solution as a group.