Unit Circle & Exact Value of Trig Functions Review Activities

The Unit Circle is my jam. Last year, I even went to a tattoo parlor and asked them to slap one on my forearm (to which they replied that I'd need to do it much bigger if I wanted the detail I requested...so that saga continues). When I taught Pre-Calc, it was truly my favorite week of the entire year. But now that I'm teaching all things Calculus, there's less time for the beauty and elegance and just a short window for rapid fire review. My AP students are assumed to know it backwards and forwards. My school level Calculus students needed a bit more work with it based on my pre-assessments, so I did a few new things to practice with them! 

Unit Circle Hula Hoop Puzzle

I gave each group a hula hoop and had them align it with the floor tiles to form a set of axis. From there, each group was given cards with all radian measures and all coordinates of the unit circle. 

Unit Circle Puzzle (Doc)

You could go even further with this and include degrees, but I wanted to make sure the students were starting to think in radians from very early on in the year. I figured I would give them 2 minutes to try to label everything, but this turned itself into a 15 to 20 minute activity with an amazing debrief. 

As I walked around the room, I noticed some great strategies. I took note of them for next year and I want to create some kind of guiding questions displayed to lead our conversation. Here's where the convo wound up going today:

• Where did your group start? 

• Students started with quadrantal angles (which was a word they couldn't tell me before this convo, so glad it came up), then divided from there

• They were able to check themselves by thinking about the order the radians should go around the circle. I saw one group specifically calling each other out for putting ⅚π in the 3rd quadrant because it clearly had to be less than π. The idea made sense and I saw a few kiddos who'd clearly just tried to memorize their way through this in Pre-Calc have the logic behind it click. This took a huge working knowledge of fractions which is somehow still a struggle for kids who've successfully made it to Calculus. 

• What did you do when you got stuck?

• For my group, this seemed to be on the coordinates. The angles took some discussion, but they were able to reason through it together. The coordinates were a different ballgame.

• Students were at least able to sort the coordinate into quadrants. Many were able to think about the reflections that take place to make angles with the same reference angles have related coordinates. All of these ideas were integral to where we'd go after this- reviewing the circle and how to use it. 

Exact Trig Values Speed Dating

After a brief review and a few practice problems, we were ready to practice! Instead of just a worksheet or a Kahoot and trying to get my first block to wake up already, I decided to make them start wandering. No pre-planning required...this one was easy to wing! 

1) Get a whiteboard & marker

2) Find a random partner

3) Answer the random exact value question Mrs. G puts on the board with your partner

4) Boards up!!

5) Class Discussion (if necessary)

6) Find a new partner and repeat

This not only gave me the chance to get kids working and talking, but I liked that I could go over each question and check in with kids I saw struggling. 

I have a whole library of other activities I've done with Pre-Calc classes in the past, but I really liked these for a group that only has 1 day to review all of this!