Lightbulb

I love it when I am teaching and a light bulb goes on - for me!

Today I was teaching my trigonometry students about angles. We were trying to expand from the middle school concept of intersecting rays to the broader concept of a rotating ray. Things were going fine:

• Rotate the initial ray about its endpoint to create the terminal side of an angle - no problem.
• Angles are measured based on how far the ray was rotated - simple.
• One degree means the ray was rotated one 360th of a full rotation - gotcha.
• Angles can be measured in degrees-minutes-seconds - HOLD YOUR HORSES!

They weren't ready for that. They kept thinking that if an angle measure was 45 degrees and 15 minutes, that meant it rotated 45 degrees, then someone started a stopwatch and let it spin for 15 more minutes. One girl said that we couldn’t know where the terminal side ends up unless we know its velocity! I wasn't ready for this confusion. I didn't anticipate this misunderstanding.

Flying by the seat of my pants, I tried to emphasis that "minutes" and "seconds" in this context, do not refer to time, but to a fraction of a degree - blank stares. 
Completely off the cuff, I moved on to talk about that 60 was a special number for the people who came up with this crazy stuff. That's why there's 60 seconds in a minute and 60 minutes in a degree - nothing.
That they used a number system that was based on 60, not 10 - so what?
That the concept of 3.2 meaning 3 wholes and 2 tenths would not have made sense to them - kinda weird.
That they would have said something like 6 wholes and 8 minutes.

Then it happened.

LIGHT BULB!

Minutes.
Seconds.

They are the Mesopotamian/Babylonian version of decimals. A minute is the base 60 version of a tenth. A second is the base 60 version of a hundredth. I got excited, I started teaching like mad, and slowly more light bulbs started coming on all across the room.

Man, sometimes I LOVE my job!