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Lesson 3: Measure That Arc
• Calculate arc length given radian measure and circumference. • Calculate radian measure given arc length and circumference. • Convert between degree and radian angle measures
Lesson Narrative
In this lesson, students build on the de nition of radian measure from the previous lesson to become more comfortable with using radian measure. Students develop the idea that, just as degrees range from 0 to 360, radians range from 0 to because the circumference of a circle is times the radius. Students use comparisons of parts to the whole to calculate arc length, radian measure, and convert between degrees and radians. Students will have the opportunity to practice these skills over the next few lessons as they explore sector area.
Students make use of the structure of the circle to convert between degrees and radians (MP7) and use repeated reasoning to come up with more general strategies for doing so (MP8).
Required Materials Geometry toolkits
Rulers
Scienti c calculators String
Required Preparation
Students will be doing a problem that involves knowledge of an analog clock. If desired, nd an analog clock or a simulation of one whose minute hand moves slightly with each passing second.
Student Learning Goals
• Let’s practice using radians and measuring arc lengths. 3.1 Sketch a Circle
Warm Up: 5 minutes
The purpose of this warm-up is to strengthen the connection between radian measure, radius, and arc length. Students choose appropriate tools to make their estimations (MP5).
Look for students to use string to compare the arc length to the radius.
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Teacher Guide