G-C.2.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

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Formative Assessments
Formative Assessments
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Students are asked to find the lengths of arcs in two different circles.
Arc Length
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Students are asked to explain why the length of an arc intercepted by an angle is proportional to the radius and then explain how that proportionality leads to a definition of the radian measure of an angle.
Arc Length and Radians
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Students are asked to write a formula to find the area of a sector of a circle and then explain and justify that formula.
Deriving the Sector Area Formula
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Videos of Expert Instruction
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Where should we make a horizontal cut so we have equal amounts of cheese?
Lucky Cow
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Use Real Link and Title
Math Literature
Math Literature
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You may want to begin with students working as a whole class to agree on a certain set of password requirements and then calculate the total number of potential passwords based on those requirements.
How Can We Make Stronger Passwords?
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This lesson is useful as a context for finding arc lengths or for developing conceptual understanding of circumference as measuring a circle’s perimeter using infinitely many infinitely small line segments.
How Far Apart Are Exits On A Ring Road?
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