On Monday I had my first Year 9 lesson since introducing New Things Thursday last week. While I’d had a few positive reactions, I was still a little nervous about how the class felt about the whole thing. As it turned out, they were asking if we could do New Things, and were disappointed that they’re going to be away on Thursday. I was also disappointed, so I’d already decided to New Things on Monday anyway 🙂
As I put my New Things slide up on the IWB, my students were immediately excited about being able to share their new things – well, most of them were. It was only then that I realised two of my students were away last Thursday and had absolutely no idea what was going on. Oops. I told them to just go with it and found a gap in the conversation to explain it all to them.
Proving Pythagoras’ Theorem
Last week explained Pythagoras’ Theorem, and while I mentioned that theorem’s should be proven, I’d only hinted that the proof was still to come. This was Monday’s task. Like last time, we’d do this with a “New Things Page”.
I wanted to make the proof as simple to follow as possible. I also decided to use cutting and pasting of triangles and squares rather than just drawing diagrams – I hoped to help the kinaesthetic learners as well as the visual ones, and make it obvious that all the triangles are the same. The end result (well, my version of it) is below:
(I tacked on the algebra proof after the class – it’s my personal favourite proof, but we haven’t covered enough algebra yet for me to teach it. Also, I think my arty skills have improved since last time!)
The key point that makes the proof work is realising that the areas not covered by the triangles are the same on both large squares. When I asked the class which area was bigger, they debated with each other for a few moments before declaring it a stupid question because they were the same. (Hooray!)
I’m pretty keen to make New Things Thursday a permanent feature, but I’d like to see if the class stays enthusiastic about it once it’s, well, not a new thing. I asked a few students if they thought it was a good idea or if they thought I’d gone crazy. “Both,” was the answer. I guess that’s good?