If radians are introduced strictly with a formula, the meaning of the word is difficult to grasp for many students. Some years ago, I learned two tricks from a colleague, which I’ll share here:
– Tell students that “radian” is short for “radius angle”.
– A one-minute kinesthetic activity: ask students to pair up with someone of roughly the same height. Student O will be the center of the circle, and stretch out an arm, which will be the radius. Student P will stand at that distance from O, and hold an arm out in a curvy way along the (unfortunately invisible) circle. Student O then stretches out the other arm towards student P’s hand, thereby showing a central angle of one radian. (Of course, the point is not accuracy, which would be impossible to achieve, but to hammer home the point that a radian is a radius angle.)
If you have other ideas for kinesthetic activities, I’d love to hear them!