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 investigate the radian as a unit of measure. They start by estimating the measure of two angles in radians.
Episode Supports
Students’ Conceptual Challenges
Claire’s initial method for estimating radians is to create a radian protractor using circular patty paper. This is an effective tool for the task, but Claire decides it won’t work [3:00]. She thinks that her method won’t work since the circular patty paper is larger than the circle the arc is part of. She claims that they won’t be “equal radians” because they are working with larger and smaller circles. However, radians scale proportionally according to the size of the radius/circle, and her method would work, as Mary eventually points out.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:40] Before hearing ideas from Mary and Claire, decide for yourself how you would determine about how many radians each angle is for the given arcs. What tools or methods would you use? How would you check your work?
[Pause the video at 7:39] What do you think about the claim made by Mary (and later echoed by Claire) that every radian has the same angle measure? What would you say to someone who claims that since radians are based on the radius of a circle, different circles would produce radians of different sizes?
Supporting Dialogue
[Pause the video at 1:49] Talk with a partner and discuss Mary’s method for finding the radian measure of the given arcs. What purpose did the pipe cleaners serve? Why is she measuring the arc when she is finding an angle measure? How does her method compare with yours or your neighbors?
[Pause the video at 4:09] What do you think: When measuring in radians, does the size of the protractor matter? Talk with a partner to share your ideas.
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