Discovering The Unit Circle

In Pre-Calculus, a HUGE HUGE HUGE chunk of the curriculum is trigonometry. With this, students must know and understand the unit circle and how it applies to the trigonometry we are learning. When I was in high school, the unit circle was put on the board and we were told to copy it down and memorize it. Over the years, I've tried different activities.. paper plate unit circle, colored pieces of paper, and so on. It seemed to me that still telling them the circle and what to write down was not allowing the students to truly understand the unit circle and all of the patters associated with it. So, I decided to try something new with my lovely group of juniors.

I first split the students up into groups based on where they are sitting. I placed 3 students in a group and had them circle up so they could see one another. I then gave each group a blank unit circle in a sheet protector along with a dry erase marker. Then, I explained the modified version of "Save the last word for ME" that we used.

"I will be the timekeeper and 1 student in each group will be the facilitator. Students will number off 1, 2, 3, etc. Person number 1 will have a set amount of time to start labeling what they know of the Unit Circle. They will have to explain why they labeled what they did, however the other 2 members may not speak. After the time is up, the other two members have a set amount of time to discuss, agree, or fix what the first member added. Then, we will go to member 2 and follow the same protocol. This will be done through the following key ideas.
*Label Degrees (1 minute; 1 minute)

*Label Radians (1 minute; 1 minute)
*Label 1st Quadrant Coordinates (2 minutes; 2 minutes)
*Label 2nd Quadrant Coordinates (2 minutes; 2 minutes)
*Label 3rd Quadrant Coordinates (2 minutes; 2 minutes)
*Label 4th Quadrant Coordinates (2 minutes; 2 minutes)

*** COORDINATES MUST BE EXACT! NOT ROUNDED! ***
** Students should look for trig function relationships during this time **"

These rules were displayed and each task was displayed on the SmartBoard one at a time. 

At first, students freaked out when they saw they had to complete the entire unit circle. They felt better when I told them they would fill it out piece by piece. Students were great in the silence and focused on watching what the writer in their group was doing. I could tell it was hard for some students to just sit without being able to correct their group mates right away. Some students got ancy and were dancing in their seats when they had to remain quiet. The labeling of the degrees and radians went well overall. Students noticed the patterns easily, especially since we had discussed the quadrant angles before. The coordinates were a little more difficult. Some groups had absolutely no idea, and they didn't know how to find the exact coordinates (the coordinates are irrational... they can't easily be converted into pretty fractions). I had to guide the groups along a little bit (by giving them hints about drawing right triangles and do a mini-lesson on simplifying radicals), but again they quickly saw the patterns and were able to continue with the process.

I really liked this process for students discovering/learning the unit circle. It really required them to think about how the things we had learned applied to the unit circle. They were tired and had headaches after, but that means they really worked hard in class that day. A few of them even said they liked that better than just seeing and copying the unit circle.