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Mary and Claire explore another student’s reasoning who thought that you could use arc length to determine the angle of rotation. They compare two arcs with different lengths. or not you can use arc length to measure the angle of rotation.
Episode Supports
Students’ Conceptual Challenges
This episode features a common conceptual challenge, which is voiced by a fictional student. The task in this episode can help students examine the problematic idea that arc length alone can be used to compare or measure angles. Claire and Mary recognize that more information is needed to accurately determine which angle is bigger when given two different arcs. They realize that the smaller arc (in terms of length) is coming from a smaller circle, but still represents a larger angle. Use this task and the questions and prompts below to help your students examine this idea and form their own conclusions about the relationship between arc length and angle measure.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:28] Before listening to Claire and Mary talk about the student’s claim, decide for yourself if Arc D represents a larger angle because it has a larger measure than Arc C. What do you notice or look for when making your decision?
[Pause the video at 5:52] How does your way of estimating the two angles compare to the ways described by Mary and Claire? Did you come to the same conclusion that they did regarding which angle is bigger?
Supporting Dialogue
Pause the video at 2:00] Talk with a neighbor and restate in your own words the arguments you just heard from Mary and Claire. Do you agree with their conclusion that Arc C represents the larger angle?
After watching the episode, consider this statement: Given two arcs, the one with the larger length represents a larger angle. Tell your partner whether you agree or disagree with this statement. Are there any circumstances in which this statement is true? Are there any circumstances in which this statement is false? How would you modify the statement to make it always true?
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