The students mark in an object’s height above the midline of a circle at several stops along its circular path. They coordinate these heights with the object’s angle of rotation and mark these in as well.
Episode Supports
Students’ Conceptual Challenges
Mary and Claire marked a point along the circle as being the highest point, and they labeled a segment associated with that point as y [3:00]. When asked if y represents the highest point, the students said yes. However, y seems to be the difference in height between the highest point and the height of the first stop at 1 radian, which the students labeled as x.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 1:05] Consider the drawing Mary and Claire have made. How would you label the heights at each “stop” that is indicated by radii along the circle?
Supporting Dialogue
[Pause the video at 3:33] Claire and Mary have labeled two distances, x and y. When asked if y represents the highest point, they say yes. Is there anything you would say to them about this? Are they correct? Why or why not?
[Pause the video at 5:35] Mary and Claire disagree about how many radians the third stop represents, with Claire claiming it is 2.28 radians and Mary claiming it is 3.28 radians. Who is correct? Why? Share your thoughts with a partner.
