No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Mary and Claire begin to create a graph that relates an object’s angle of rotation, measured in radians, with its height above the midline, measured in radii, as it travels along a circular path.re make their graph more accurate by plotting several more points.
Episode Supports
Students’ Conceptual Challenges
Before watching the video, check in with your students to gauge their prior understanding of functions. You can introduce the idea of the sine function by describing it as relating the height (the function’s output) to the corresponding angle of rotation (the function’s input). For now, this is all your students need to understand about the sine function, but it is worth checking to make sure they understand what functions are more generally so they can best utilize the opportunities in this and future episodes to make sense of the sine function.
In this episode, students are asked to label the heights of each stop around the circle [2:30]. Without units, this might be hard for students, and they might ask for help coming up with exact answers. Resist the temptation to get sidetracked into discussing how to calculate using sine (e.g., talking about “opposite over hypotenuse”). Instead, encourage them to use what they know or create their own stand-ins for the quantities they are finding. You can redirect their curiosity by posing questions about relationships between the heights (e.g., Between which two stops is the height growing faster? Growing the least?). Mary and Claire explore one productive pathway for this challenge by scaling their circle to match their graph and copying heights directly from the circle to the graph.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:37] Label each eighth of a rotation on the circle with its corresponding angle measure in radians. Then compare your work with what Mary and Claire do.
[Pause the video at 2:30] Claire and Mary are about to label the height at each of the stops along the circle. Before they do, try it for yourself. Make note of any challenges you encounter.
[Pause the video at 3:58] Try making a graph using the values you’ve generated for this task so far. Plot the angle of rotation along the x-axis and the height that corresponds to those angles of rotation along the y-axis. Then compare the graph that Claire and Mary make with yours.
Supporting Dialogue
[Pause the video at 5:38] How long are the green line segments that Mary and Claire have marked on their graph? How could use what you know about circles to figure this out? Discuss this with a partner.
[Pause the video at 7:44] Tell a neighbor what you think Claire and Mary are talking about right now. They are discussing making the circle bigger and/or the graph smaller. What purpose would this serve? What would that help them accomplish?
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