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Mary and Claire explore how to modify the sine function to give April’s height above the ground at any angle of rotation as she travels around the Ferris wheel.
Episode Supports
Students’ Conceptual Challenges
This episode features a common challenge that students face when working with functions in general, which is how to modify the symbolic form of a function to match a given context or constraint. In this case, Mary and Claire are asked to modify the sine function they’ve already used so that it returns the height of a rider of a Ferris wheel. Claire and Mary use a systematic guess-and-check strategy, in which they offer a potential solution, check it with known values, and then revise accordingly. For example, they know that 36 • sin(1) gives the height of the rider after a rotation of 1 radian around the circle from the midline. So their first guess is to multiply the 36 by 2, which they realize doesn’t work after they check a known value [0:20].
After trying the function 2x • sin(n) + 4 and realizing that it is wrong, Mary and Claire figure out that multiplying the radius 36 by 2 would essentially be the same as exploring a different circle with a radius of 72. Check in with your students using the focus questions below to see if they understand why this is the case. Claire and Mary come back to this idea throughout this episode as they continue to guess and check to find the right function.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:14] How would you modify the sine function so that it gives the height above the ground for any point in April’s journey around the Ferris wheel?
[Pause the video at 4:04] What was the effect when Mary and Claire multiplied the radius of the Ferris wheel by two?
Supporting Dialogue
[Pause the video at 2:32] Tell a partner what you think about this function that Mary and Claire have come up with: 2x • sin(n) + 4. What does each part of this function represent?
[Pause the video at 6:02] Talk with a partner about what you think will happen when Mary and Claire multiply the sine function by 40 instead of by 36.
Captions
