The unit circle plate is a concept that I got from my mom. When I was in high school, learning about trig, which I hated by the way, my mom had us create a plate with all the radians, degrees, and trig values (we added those after I made my plate). So I decided to do this with my students.
Basically, we folded a plate in an honors class and used the concept of pie slices to figure out the radian fractions. The kids had already learned about degrees so this helped when relating trig values to radians. But basically, you can teach this lesson using the concept of how many pie slices do you need to make 120 degrees and relate it to the size of pie slice for 30 degrees.
Oh, and it doesn't hurt to serve pie on this day :)