No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
The students solidify how many radians are in various amounts of rotation and think about how that relates to degrees.
Episode Supports
Studentsβ Conceptual Challenges
Claire and Mary are unsure if 2π can represent a quantity of radians [0:25]. Claire claims you canβt say β2π radians.β Recognizing π as a number is challenging for students. Check in with your students to see what they think about using 2π as a valid number for counting radians. Look for opportunities to connect the idea of circumference (which is 2π times the length of the radius) with the notion that an arc length equal to the radius determines a radian.
Claire is unsure about how to express one third of a rotation using radians [3:30]. She seems to be confused by the fact that you can find the exact number of degrees in a circle, but there isnβt a whole number of radians in a circle. Her uncertainty with using π as a number for counting radians also seems to contribute to this challenge.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:20] Before listening to Mary and Claire, explore this on your own: How many radians are in a full rotation? Does it matter what size the circle is?
[Pause the video at 3:20] How many radians would one-third of a rotation be? Try this for yourself; then watch Mary and Claire discuss their ideas.
Supporting Dialogue
[Pause the video at 1:06] Tell a partner what you think about the idea that there are 2π radians in a full rotation.
[Pause the video at 6:35] Mary and Claire have landed on 2π/3 for the number of radians in one-third of a full rotation. Talk with your neighbor about this idea. Is it correct? Is it exact?
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