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! 

Methods of Finding Limits Error Analysis

My AP Calculus students just took their big Limits quiz and before we dive into Continuity and IVT, I wanted to make sure we solidified some sloppy issues I saw pop up.  I designed this activity based off actual errors from student work, hoping for a little personal reflection before they ever get their quizzes handed back to them. I'm planning to use this as an intervention tool with my struggling AP kids, but then a teaching tool with my school level Calculus kids.

Limits Mid Unit Intervention (Doc)

Limits Mid Unit Intervention (PDF)

I started this by simply having students choose a technique to evaluate each limit, without actually evaluating. I hope this will be a catalyst for conversations within the group and a baseline for students as they move into the next part of the activity.

The 2nd part of the activity shows examples of mistakes from the quiz that I rewrote in my own handwriting to avoid any embarrassment. Student will need to find the mistake and then fix it. One of my favorite parts of these mistakes is that often they do not lead to an incorrect answer. My Calculus students need to get very used to attending to notational precision in their work and there's no better time than the present for that!

There's a good mix of Algebra and Calculus mistakes throughout the activity, but they definitely lean heavier on notational fluency than anything else.  

Feel free to use as is or modify as you see fit! Also, if you have any common issues that you see with your students and limits, feel free to send them to me so I can add them to this! 

Rational Functions Who Am I? Activity

Pre-Calculus has always been my first baby. As a new teacher, I was thrown into Pre-Calculus and it quickly became my pride and joy...I experimented, learned, and fell in love with teaching it. Not only was it the best preparation I could have had for when I finally got to teach my real, true love (Calculus), but it also helped me connect my knowledge of algebra, geometry, and more in a way I'd never done as a student.

This year I've started teaching a school level Calculus class and it's been so much fun to delve back into some Pre-Calculus topics that I don't normally get to review with my AP kids. This activity was a great review for my students to get them talking, factoring, and thinking. It didn't take long, but generated some good conversations. It would also be a fun extension to have students write one of these "Who Am I?" activities, which could be used for any topic in any course! 

Feel free to steal or adapt! Let me know if you make any meaningful changes! Here is the file:

Rational Functions Who Am I?

Here's some more of my thoughts about rationals from past posts, if your in the market! 

Rational Functions Slap Jack Review

Rational Functions Challenge