SKILLS
(1) The student will be able explain what a radian is.
(2) The student will be able to convert between degrees and radians.
(3) The student will be able to derive and use the formula for arc length in terms of radians.
(4) The student will be able to derive and use the formula for area of a sector in terms of radians.


THE BIG IDEA
Radians while very new to these students are a very powerful concept for the future. Much of upper mathematics uses radians instead of degrees. When we look at angle based function we prefer the domain to be measurement (distance) based instead of angle based. Angles defined by a length provide a more consistent way to graph on axis based on length.

TRAPS & PITFALLS
This can be a difficult area. Students are often intimidated by the use of pi and how they are unable to visualize how big something in radian measure is... whereas they handle degrees so easily.
Teachers often teach to convert to degrees immediately and then don't worry about radians. To me this is backwards, one of the reasons we are introducing it now is that they become more familiar with radians and begin to understand their size values.
Also arc length and area formulas become much simpler when working in radians. We want to emphasize this. 

PAST CONNECTIONS
We connect similarity to circles which allows us to understand why radians can be used as a measurement for angles. Every circle is similar and thus proportional. Similarity is a powerful concept concerning why radians work.
FUTURE CONNECTIONS
Radians become the prefered way to measure angles in upper mathematics and so here we are laying the groundwork of understanding.
