No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Mary and Claire think about whether or not you can use arc length to measure the angle of rotation.
Episode Supports
Students’ Conceptual Challenges
This episode introduces a key idea in trigonometry, namely that arc lengths and angles are closely related, and one can be used to find the other. This idea is the foundation of the unit of measure called radians, and it can be very challenging for students to understand what exactly radians are. In this episode, Claire seems convinced that arc length and angle of rotation are not related [e.g., 0:40]; while Mary seems open to the idea.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 1:01] Claire argues that measuring the arc length only measures the distance someone would walk around a circle, not the angle of rotation. Do you agree with this? How does her claim compare to your ideas about using arc length to measure an angle of rotation?
[Pause the video at 2:58] Mary seems to argue that the length of an arc would correspond to what a person in the center of a circle would see as they rotated, which means you could measure the angle of rotation using arc length. Do you agree with Mary? How does her claim compare to your ideas about using arc length to measure an angle of rotation?
Supporting Dialogue
[Pause the video at 0:29] Decide for yourself if you agree with the statement that you can determine the angle of rotation by measuring arc length. Then talk with a partner to share your ideas about this claim before listening to Mary and Claire talk about their own ideas.
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