No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Claire and Mary use a calculator to find April’s height above the ground when her angle of rotation is 1 radian, 2.5 radians, and when she is at the top of the Ferris wheel.
Episode Supports
Students’ Conceptual Challenges
Claire and Mary quickly work through a critical step along the path of understanding trigonometric functions when they write 36 • sin(1) to find the height of a stop above the midline [1:47].They seem to understand that the sine function returns values that can be interpreted as portions of a single radius, so multiplying by the radius will yield the correct height. You should not expect your students to quickly or easily grasp this. Thus, consider having a conversation about this with your students to give them opportunities to voice their ideas.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 1:38] How would you find the height above the midline for an angle of rotation of 1 radian? How could you use that to find the height above the ground for the same spot along the circle?
[Pause the video at 4:47] Do you agree with Claire that you could subtract sin(1) from 40 to find the height of the first stop, which is below the midline? Why or why not?
Supporting Dialogue
[Pause the video at 0:53] Work with a partner to justify Claire’s claims that the top of the Ferris wheel is 76 ft high, the center is 40 ft high, and the bottom is 4 ft high. Are there any other heights along the Ferris wheel that you know?
[Pause the video at 1:51] Tell your partner why you think Mary and Claire are multiplying sin(1) by 36. What does that result in, in the context of the Ferris wheel?
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