Earlier this week Michael Pershan was asked for ideas about how to introduce constructions. One suggestion was using patty paper:

It has been a while since our first Patty Paper Geometry project, so I thought we’d give it another try π

Flipping through the book last night I found a project in section 4.1 about finding the sum of angles in a polygon. I’d actually never seen this approach before and it looked really fun. We started with a triangle (and I’m sorry the pencil on the patty paper didn’t show up super well in the videos):

Next, as suggested by my younger son (and also in the book π ) we moved on to a quadrilateral:

Now we had a few conjectures and tried the same experiment with a pentagon to see if our conjectures held. It was pretty neat to hear the language (both in this video and in the last one) that the kids used to describe what was happening with the pentagon’s angles.

With that patty paper exercise as preparation, we looked at a viral geometry problem from last week. Here’s one link about the problem:

VCE Further Mathematics β50 centβ question leaves Australian students confused

The problem gave the kids a bit of trouble – here’s their conversation about it:

I wanted the kids to puzzle about the problem a bit more, but they needed to head out the door, so I decided to simplify the picture for them so help them see what was going on:

So, a fun project. Using the patty paper to see why angles in a triangle add up to 180 degrees was really neat. As I said above, I’d never see the idea presented this way before. The extension to polygons with more sides was really natural and also led to some great conjectures from the kids.

I also enjoyed seeing the kids struggle with the 50 cent problem at the end. Not being around groups of kids working on math problems all that much, I usually have a difficult time knowing when (or why) problems will be difficult. Seeing the difficulty first had is always a great lesson.