I’m just going to shout out my former student teacher Matt for not only being an amazing student teacher and now amazing struggling first year teacher, but for jumping into the MTBoS from Day 1 of teaching! He’s much more active on twitter than I, but he mentioned me in a recent tweet about the meaning of radians. So, I wanted to follow it up.
I don’t think I ever learned what a radian really was in school. Somewhere along the way, I figured it out, and I love teaching it!
I usually begin by having students (in PreCalc) put masking tape around the circumference of circular objects so that it makes exactly one circumference. They then lay the masking tape flat on the desk. Next, they measure the radius of their circle. Last, they measure how many radii fit onto their masking tape. “For some reason” everyone keeps getting 6 and a little bit. Quickly, students catch on to 2pi, and they start to relate it to the circumference formula.
But that’s just the first half. Then, students trace the circle onto paper, and put the masking tape back on the circle. By now, they have all these little marks on the tape at the measurements of each radius length. We then draw a central angle that is the width of one of these radius lengths. This is an angle that is one radius wides. A RADius ANgle. A RADIAN!