As a new teacher, two things that I don’t feel the most comfortable with in my teaching are:
- teaching theorems by name. For example, opposite angle theorem (OAT), corresponding angles, etc. I know how they work, but I’m not very good at remembering the names.
- review. I am still fairly new to teaching, and it’s been difficult figuring out exactly how much detail I need and how fast I should be going when I review material from previous years. I’m always a bit anxious and eager to start the new material (in this case, one of my favourite units, trigonometry.) Usually I end up doing too much or too little. This is something that will hopefully get easier for me with time.
On this particular day, I ended up doing both of those things.
Personally, I don’t think it’s even really necessary to teach all of the angle theorems along with all of their names. You really only need 1 or 2 rules. The rest can be derived from the first 2 to solve for any missing angle. But because my class was one of seven Grade 10 academic math classes running that semester, I thought it was important for consistency that they learn the names. We also have the same tests for all 7 classes on the same day, so I needed to make sure that if knowing theorems by name was on the test, students would know the names.
Based on what other teachers had done in the past, I began with a warm up review of some common terminology that students would be using later on in the trig unit:
The students didn’t seem to have too much trouble with it, and we were able to take it up quickly.
We did a bit more practice with ratios and other odds and ends:
(If none of this seems like it really goes together, please forgive me. New teacher syndrome.)
Then we got to the main part of the lesson: the angle theorems. Instead of going over each rule individually (all 9 of them! So many names!), I wanted to see if my students could derive the theorems themselves. So I put up this diagram and told my students that all 9 angle rules appear in the picture:
We did the first one together:
I then gave the students some time to work with a partner and told them to find all 8 other rules:
When we took it up, my students got all 9 rules on their own! Some of them remembered the names of the rules, the others they told me which angles made the rule and I helped them with the names (I may or may not have had the names written on a sticky note on my laptop to remind me of what each theorem was called). I took a picture of the board and posted it on our Google Classroom as a summary of what we learned:
(Usually I have another column for who came up with the rule, but I cropped it out for the sake of my students’ anonymity online.)
The rest of the lesson we spent doing practice questions.
This was one of my favourite lessons of the year: student-focused and student-driven. Bring on the trig!