Check out Khan Acadamy for this video on the introduction to radians. He shows how a radian is when the arc length of the circle equals the radian. I've never seen such a clear description. He goes on to show the relationship between degrees and radians.
The last part of the video explains why pi/180 or 180/pi is used as a conversion factor setting up to show the next video on converting between the radians and degrees. This video is a perfect set up for the topic.
This leads into having students practice converting from degrees into radians and back. Once they are comfortable, I'm going to reteach arc length using radians and again Khan Academy has a great video on it. Its only three minutes long but it is a great introduction to the topic.
So when I have students redo finding the arc length in radians, they should find it much easier to do since they've already done it in degrees and they've explored the relationship between degrees and radians.
I think this will help my ELL students tremendously. They often need these additional steps. I look forward to seeing how well they learn this. I have not taught radians in Geometry before but with the change in standards I have to teach basic trig earlier in the sequence. It used to be I didn't touch it before pre-Calculus but due to the demands of Common Core, I have to do this.
I am going to admit something to the rest of the world. I never learned what a radian was when I was in college. It was one of those things we accepted but never needed to know where it came from. I am happy to learn more about it. I love that I can still learn something new. Yeah!
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