In this lesson, students find sector areas and arc lengths for central angles with radian measure. They justify the formula for the area of a sector, and they observe that radian measure simplifies arc length calculations. As students explain why the expression \(\frac12 r^2 \theta\) gives the area of a sector with radius \(r\) units and central angle \(\theta\) radians, they are reasoning abstractly and quantitatively (MP2).
Lesson overview
 13.1 Warmup: What Fraction? (5 minutes)
 13.2 Activity: A Sector Area Shortcut (15 minutes)

13.3 Activity: An Arc Length Shortcut (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 13.4 Cooldown: Calculate It (5 minutes)
Learning goals:
 Interpret radian measure as the constant of proportionality between an arc length and a radius.
 Justify (in written language) why the formula \(\frac12 r^2 \theta\) gives the area of a sector with central angle \(\theta\) radians and radius \(r\) units.
Learning goals (student facing):
 Let’s see how radians can help us calculate sector areas and arc lengths.
Learning targets (student facing):
 I can calculate the area of a sector whose central angle measure is given in radians.
 I know that the radian measure of an angle can be thought of as the slope of the line \(\ell=\theta \cdot r\).
Standards:
 This lesson builds towards the standard: CCSS.HSGC.B.5MS.GC.5MO.G.C.B.4MO.G.C.B.5
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