## Monday, November 22, 2010

### Trig Visualizing

Rebecca Walker and I modeled a lesson for our secondary student teachers on trigonometric equations, based on the first chapter of the Precalculus book from the very interesting CME Project curriculum.  While it has some interesting applications, this curriculum really does a good job of letting the mathematics be the context and addressing mathematical habits of mind.  The lead developer is Al Cuoco, who has a great history of interesting math and math ed work.

The lesson is a bit of a stretch, because we're just touching on one section, using a bit of information from three or four.  We did unit planning one week, lesson planning the next week, and finally the lesson.  The TAs read The Teaching Gap, so then we connected it to the idea of lesson study, and a discussion both about how to revise this lesson, and why lesson study might work as professional development.

We have two Geogebra sketches to help with visualization.

As a sketch or a webpage.  This sketch supports visualizing sine and cosine with unit circle connections.
As a sketch or a webpage.  This sketch lets you invert trig functions using the Unit Circle representation.

This is my first attempt at a WCYDWT.  When I was making these sketches (don't worry, I disinfected them before posting) I had a bad cold, so was constantly reheating my tea.  Watching it go round and round.  Thinking, "so when do we know a position and want to know the angle, with possible multiplicities...hey, wait a second."  If I was using this, I think I would start with the video, and use that to motivate the idea of solving for information based on the circle position, as well as how periodicity relates to multiple solutions.

This has to be the world's most boring video.  Enjoy!

Here's a slightly more polished version of the handout we used with the sketches.  There was some discusssion with the student teachers as to whether the inverse trig or the algebraic solutions part should come first.  I think they could be switched, depending on what you wanted to emphasize with the students and how strong their trig background is.  Also, the handout is written as if the teacher is demonstrating with the computer, which is what we wanted to model for them, (no lab is no reason to no have technology) but the ideal would be to have the students have access to the sketches.

Solving Trig Equations