Park City Mathematics Institute
Lesson Study
Project Abstract
Transformations Using Matrices
Mary Pilgrim*, Jake Leibold, David Berger, Diana Braham, Adam Chawansky, Cesar Ebonia
The purpose of our lesson study was to collaboratively craft, teach, and revise a lesson for high school students learning Algebra 2/Trigonometry or an integrated 3 Common Core Mathematics class. We met an average of eight hours per week for three weeks. The lesson was first taught to 15 high school students attending a the Park City Mathematics Institute summer math camp. The second time the lesson was taught to 23 high school students attending Adella Croft's Secondary Math 3 (intensive/honors) summer school course housed at the University of Utah, in Salt Lake City.

The major objective of our lesson was for students to understand the unit circle. Other objectives were to define x and y in terms of cos θ and sin θ respectively, to connect this to an equation of a circle centered at (0,0) and radius of 1, and to connect the measure of a central angle to the radian measure of its intercepted arc. We developed an opening activity reviewing what the students know about the special right triangles (30-60-90 & 45-45-90). The students were given colored models of the special triangles that they used to create points on the unit circle.The lesson unfolded after two iterations, we were overly ambitious and the study will continue.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.