One way to break up the routine in math class is to have the students get up and experience some of the concepts in their bodies. This is of course helpful to certain type of learners, but it helps everyone makes connections and remember things. It can also give a useful reference point when teaching a new concept.
I came across this one in The Mathematics Teacher, in an article by Maureen Macinnis, a teacher in Nova Scotia. It seems like a terrific activity, with a lasting impact.
She hands out pre-made cards, with the sine and cosine values for the sixteen “famous” angles (0°, 30°, 45°, and so on, all the way to 330°.) The sines are on orange cards, the cosines on green cards. Students are asked to pair up in sine-cosine pairs that correspond to one angle. For example, the student with an orange 3√2 needs to pair up with a green 12 or −12. (That is already a good start!)
At this point, the lesson continues outside, where the teacher has pre-drawn a large chalk unit circle on the ground, with x and y axes. Student pairs find their position on the circle. This would be a good time to review who is at what angle.
But wait, there’s more! The teacher has also drawn a pair of axes, with the y’s from -1 to 1, and the x’s marked off in degrees or radians. The next step is for the orange-card students to place themselves at the appropriate place on the graph, making a sine curve as the green-card students watch. And then they switch.
And here is the link to the same paragraphs on the Web site, where the fractions appear correctly.