First day of term 4 (which was Monday - I really am running behind at the moment!) saw the start of our Trigonometry unit with Year 9. I wanted a way to get my students to start thinking about how the angles of a right-angled triangle affect its sides, while also defining the Opposite and Adjacent sides. They already all remembered the Hypotenuse from doing Pythagoras' Theorem :)
So I took the class out to the front lawn and had groups of students form right-angled triangles by standing at the corners. (Actually, I didn't say "stand at the corners" the first time, which was a good reminder that I sometimes need to be clearer with my instructions. One group tried to form the sides of the triangle by lying on the ground.) In each group, one student was given a pink sticky note to indicate they were the right angle, and another had a green sticky note with θ written on it.
Then using different colours of party streamers, the students made the sides of the triangles, defining the Opposite and Adjacent sides as we went.
As they did this, I had the groups check the other groups around them to make sure they all had right-angled triangles. This provoked great conversations amongst the groups, as they evaluated each other's work and had to communicate clearly their reasons why a triangle was or was not right-angled.
Then I gave this challenge: make the angle at θ bigger.
As they did this, the students needed to work and talk with each other to figure out what they were going to do. Students communicating about maths to figure out a problem together! It also worked well that different groups used different solutions - some shortened the adjacent length, others lengthened the opposite - allowing us to discuss those different solutions.
Once back inside, we then worked on defining the trigonometric ratios, eventually creating this notebook page:
There was more to the lesson than that, but I'm getting sleepy now :) I might elaborate on what other work we did next time.
One more thing: as we were outside, a friend of mine happened to be driving past the school. As I was talking to him that night, he asked me two questions:
- Why did I never get to go outside to do maths at school?
- Why were you making kids stand in rectangles?
I'm a little concerned about how convincing our triangles were now...