The students revise the graph they created in the previous episode. They plot several points that relate the height of an object above the midline of a circle and its angle of rotation as it moves around a circular path.
Episode Supports
Students’ Conceptual Challenges
Early in this episode, the students start to create a graph to represent the relationship between the height of a fly traveling on a rotating fan blade and the angle of rotation of that fan blade. For points along the x-axis, they initially use equal spacing for all of the stops that they identified in the previous episode. This is problematic, though, as the new x-axis represents the continuous quantity angle of rotation, which should be represented proportionally on the axis. For example, the physical space on the axis between 2 radians and 2.28 radians should be smaller than the physical space between 2.28 radians and 3.28 radians, since the difference between 2 and 2.28 is smaller than the difference between 3.28 and 2.28. They catch this issue and correct it. Your students might do something similar (for example, just relabeling their old x-axis). The first Supporting Dialogue prompt can provide students with opportunities to discuss this.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 0:28] In the previous episode, Claire and Mary drew a graph that related the fly’s height above the midline to the stop along the circle. In this episode, they revise their graph to relate the height of the fly to the angle of rotation. Before watching the students revise their work, try this for yourself so that you can compare your ideas with theirs.
Supporting Dialogue
Pause the video at 1:43] The narrator pointed out that there is the same amount of space on the x-axis in Mary and Claire’s graph between 2 radians and 2.28 radians as there is between 2.28 radians and 3.28 radians. Tell your neighbor why you think that is problematic.
[Pause the video at 4:53] Talk with a partner to discuss what Mary and Claire have done. What purposes do the pipe cleaners serve for them? What does each axis represent? Do you think this is an accurate representation of the fly’s height in relation to the angle of rotation? Why or why not?
