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Mary and Claire measure the angles they have created in their drawings of the boy rotating. They measure the angles in degrees.
Episode Supports
Students’ Conceptual Challenges
Throughout this video, Mary and Claire make use of the idea of a full turn. They seem to have in mind one turn is the same as 360 degrees of rotation. You can take advantage of their ideas by pausing the video to ask your students what they think one third of a turn or 15/16 of a turn is. You can also ask them what they think two full turns might look like. This is a good opportunity for students to begin confronting a common conceptual challenge when learning trigonometry—the idea of angles describing rotations (particularly in the unit circle), and why, for example 3𝜋/4 radians results in the same final position on the unit circle as 11𝜋/4 radians.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 1:55] Claire and Mary claim the angle is about 145 degrees, or just over a third of a turn. First, do you agree or disagree with the students? Second, what do they mean by a third of a turn? What would be half a turn, or a full turn? What would two full turns look like?
[Pause the video at 3:59] Mary and Claire claim the next angle would be “15/16 of a turn.” What do they mean by this? Do you agree with them?
Supporting Dialogue
[Pause the video at 3:00] The students use angles with measures of 270 degrees, 45 degrees, and 22.5 degrees. Talk with a partner about where you see those angles. How do you think they came up with those measurements?
[Pause the video at 5:07] Talk with a partner: Why do you think Claire thinks the circle they are using is better than a typical protractor? How are the students using that tool to help them complete this task?
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