No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Claire and Mary create several circles of various sizes. On each of the circles, they trace out an arc whose length is the radius of the circle. They create angles at the centers of the circles that cut out these arcs. They compare those angles. A new unit of angle measure is defined: the radian.
Episode Supports
Students’ Conceptual Challenges
Understanding radians can be challenging. For example, Mary seems unsure about what exactly a radian is or what it measures. When asked to describe a radian, she points to the radius, then the arc length, and finally to one of the wedges that has been drawn [6:50]. It isn’t clear if she recognizes the radian as a measure of angle rotation or as a slice of the circle. You can help students by providing opportunities for them to discuss the idea of a radian and by asking them to point out a radian on a diagram or draw their own picture of a radian.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 1:04] Before continuing the episode, create a circle with a given radius. Then, trace an arc on that circle that has the same length as the radius of the circle. After you’ve done this, play the episode and compare your circle and arc to the ones created by Claire and Mary.
[Pause the video at 5:03] Can you restate what Mary and Claire said about why they get about 6 arcs with a length equal to the radius for each circle they drew?
Supporting Dialogue
[Pause the video at 2:31] Show your circle and arc to a neighbor and compare your work with theirs. Then compare your work with what Mary and Claire did. Talk with your partner about what you notice among all the examples you see. Are there any similarities or characteristics that stand out to you?
[Pause the video at 6:22] What similarities and differences do you notice between degrees, radians, and gips? Talk with a partner to share your ideas.
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