Reflection: Coherence Converting between Degrees and Radians - Section 2: Deriving the Formulas


At some point in my teaching career, I suppose I wouldn't have thought the formula for the area of a sector had anything to do with the formula for converting degrees to radians. But now, having taught it, I understand that the big idea is not so much the formulas as it is the idea of proportional reasoning. 

Looking at it in this way has changed my approach significantly. If my only objective was for students to know the formulas, it could be a 10 minute lesson. But since I am trying to develop a bigger and more important idea of proportional reasoning, I am more concerned with their knowing how to build the formula using proportional reasoning and this takes effort. Especially because students like formulas. And if they know the formula already, good luck trying to get them to listen to the whole spiel on how the formula comes to be. It's a worthwhile struggle though, I think. 

I think that once I figure out how to assess derivation of formulas better, it will make students a lot more receptive to the teaching. Otherwise, they tend to view it as just a long drawn out way of telling them the formula which they'll never need to derive again.

  Making Connections: Proportional Reasoning
  Coherence: Making Connections: Proportional Reasoning
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Converting between Degrees and Radians

Unit 12: Unit Circle Trigonmetry
Lesson 4 of 5

Objective: SWBAT derive and apply formulas for converting between degrees and radians.

Big Idea: Currency Exchange? Students learn about the going rate between degrees and radians.

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  65 minutes
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