I remembered last night while lying in bed (in those 30 seconds that it takes me to get to sleep because I'm always so tired from getting up at o'dark-thirty) that today we were starting trig in precalc class. Which means radians! Which meant I needed to find my favorite pi shirt (and earrings) to wear today.
So that set me on a scramble this morning to find that box that had all of my random clothes in it. Because we've moved since my last opportunity to wear a pi shirt.
I don't know how much trig my precalc class has seen. I have students coming from 3 different places (Honors Algebra 2, Honors Math 3, and Trig w Functions (which does very little trig, btw)) so I'm going to go through my normal trig unit like I have in the past. If I see that they "got" it I'll adjust on the fly.
Today we started with a quick warm up with adding and subtracting fractions - I'm sure they were like, "Seriously?!" and then went over the little special right triangle review that I'd given them Friday. Then we moved into the idea of measuring angles... why is this one 120 degrees and not 240? Why not 480? Enter the coterminal angle.
And now, just for fun, what if we throw in another unit of measurement? Who needs to stick with degrees anyway. I pulled out my "very expensive, very accurate measuring tool" (aka The Smartees) and had the kids measure a variety of circles. Then we took those smartees and placed them along the arc of the circle to create an angle. That, my friends, is one radian. Now do it again. And again.
Have we gotten halfway through the circle? Almost. (Some kids had. They must not be very well trained in the art of smartee-arc measuring.)
This brought us to the idea of pi radians equaling half of the circle... and off we went from there. I also showed the radian gif that's on this site that looks a little nicer.
Anyway, my class went on from there. We labeled some angles we "think" we might use in the near future and talked about coterminal angles in terms of radians. And then the bell rang. (ugh)
However, on the way out, the kids were talking about the next class they were going to. One of the girls said she's not a fan of her next one because it's boring. And then she said, "This (precalc) is the only class where I have to think. But I'd rather think than be bored."
I think I'm doing my job.