I take no credit for this. I’m teaching Precalculus for the first time, and the other teacher also teaching it has been doing this for years. We introduced the unit circle and then had students make these precious unit circle plates.
It took about 10 minutes at the end of one day, and another 15 minutes at the start of the next.
In order to make them, I gave students a sheet of paper with the unit circle on it, and dots at the relevant points on the edge. I had students draw the angles in, write down the angles in radians and degrees, and calculate the points in the first quadrant. Then I had them use symmetry arguments to get the points in the other quadrants. Then they cut the circle out, glued it to a paper plate, and stuck a pipe cleaner in the center to become the terminal angle.
Because I was rushing through the curriculum faster than I hope, I had studentsuse the unit circle plates to find the sine, cosine, and tangent of some special angles, and then I had them put the plates aside. That’s all the use we got out of them thus far. So right now, I’m not sure if the time was worth it to build them. However, I think when we get back from Thanksgiving, when we start solving trigonometric questions, I’m going to have students pull these out and use them at the very beginning… Keep things concrete. And as we progress through the lesson, ween them off.
With the plates, I can see starting simple, with questions like:
They’ll see there are a couple of solutions. I’ll give some questions with one solution, with two solutions, and no solutions!
Then a little harder:
And then finally maybe something like:
Approximate, as best you can, the solutions to:
(Which will take some critical thinking skills, and some guesstimation.)
And then we’ll figure out how to solve these without the unit circle plates… and look at the graphs… and all that good stuff.
Just a thought. And, of course, we can use the plates to construct the basic shape of the graphs of and and . If you can think of any other good uses for the plates, lemme know!