First here's what led up to it:
- Did a trig intro yesterday - using sine to find a missing side of a right triangle.
- Homework examples for last night were tailored to require using sin only, like this:
But today first thing, I had them do this:
All I told them was that they could fill in whichever of the two angles they wanted, with however many degrees they wanted, but once that was done, they had to think about where they put the x and the other side length. I think about half of them got the whole opposite - hypotenuse idea right then and there. Not yesterday while I was blathering on about it!
The rest of the activity was pure gold - they worked together so much more organically, because they made up the questions, they wanted their partner to get it right, and they wanted to know that they were right in the first place!
Once they REALLY knew that sine was the opposite over the hypotenuse, the rest of the lesson, which of course was about using cos and tan, went extremely well. They were so much more aware of the significance of the sides involved. In fact Celine asked the million dollar question, "How do we know when to use cos and when to use sin?" and Kaily answered "it depends on your sides. And you use tan when there's no hypotenuse." Weeping I am.
I've taught this many times. I've never had that milion dollar question happening so fast, if at all!