We started trig last week in Algebra 2. I began this time around with a trip online to see if I could find anything new to begin the unit with. I found this great post by Riley (via Sam Shah) about having kids measure the Unit Circle. A kind of sandbox approach. Anyhow it worked fantastically. In all three of my classes we were able to have great discussions about all the stuff that was learned by measuring this all out by hand. And I don't think anyone even asked «But Roy, when are we ever gonna use this?» In one of my classes the students got into a little debate reminiscent of Name That Tune's bid a note as they tried to lower the number of measurements that were actually needed to label all the points on the circle. I was sure they would figure out the various quadrants, but when they made the connections to the complementary angles within the quadrants I knew for sure this was the perfect activity to begin trig with.
Incidentally I took Riley's picture and turned it into a worksheet. Here is the file. I began class by having my students type their data into a Google Spreadsheet that I set up with them to calculate the mean of their scores. I plan on going back to this spreadsheet in the next couple of days and adding a cosine and sine value to it.
A couple of students know we are studying trig and have asked «Roy, does this have anything to do with SOHCAHTOA?» and I have been like «What is that? It sounds similar to CAHSOHTOA! Is that what you meant?»