At TMC13 I was a member of the PreCalculus morning session that worked on Inverse Trig Functions. You can read about the fruits of our labor on Sam Shah’s blog.

For the **very first day of learning and first task** in Functions/Trig (our pre-calc for A/B) my class tackled the first portion of what the group developed at TMC13. Here is what I gave the students: Analyzing Circles On The Coordinate Plane formatted to be taped into the composition book students will used for their notes and classwork.

After a brief discussion on how to use a protractor and going through the directions that set up the rotational system, I set students to work and collaborate in their groups. For the next 75 minutes I circulated around the classroom showing how to use the protractor (again), reviewing how to estimate, working with students whose answers were WAY off, and clarifying directions. Most students were comfortable on the “forward problems” but questions began to fly when it came to the “backwards problems”. Most common misunderstandings were x=0.30 is a vertical line and slope = 1 can be turned into a fraction. Once students had these clues, they were able to complete the “backwards problems”. The sixteen problems presented took most students a full 75 minutes. Only a few completed the reflection questions, so that became their homework for next class. Of those that did answer the questions, very few noticed anything, and the wondering was mostly “why are we doing this?”

We will revisit this activity in a few classes once we learn about the trigonometric functions on the unit circle. At that time we will compare their estimated values to the actual and see if any noticing, wondering, or “ah-ha moments” can be gleaned. I think there will also be a non-candy prize for the student with the closest estimations … any suggestions??