No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
The students reflect on how to use the sine button on a calculator to find the height of an object at various stops as it travels along a circular path.
Episode Supports
Studentsβ Conceptual Challenges
While more of a procedural or technical challenge than a conceptual one, students may struggle to correctly input values for the sine function into a calculator. These struggles can include how to enter fractional values into a calculator (e.g., π/8) and how to use the degree mode instead of radians [2:00]. You can be explicit here with instruction so that students can more easily focus on understanding the mathematics rather than how to use a calculator.
Early in the episode, Mary and Claire consider the idea that to find sin(π/8), they can find sin(π/4) and divide by 2 [1:08]. Your students might have similar ideas. Use the Supporting Dialogue prompt below to elicit their ideas.
There are different ways to interpret the result of using a calculator to find the output of the sine function, and students might struggle to make sense of this. Take the equation sin(π/8) = 0.3826834324 as an example. This tells us that the height at π/8 radians is approximately 0.38 radii. In other words, the output is in terms of the radius of the circle. When the radius is 1 (as with the unit circle) then the output is exact. Students might be confused when they measure the height using a ruler or some other device and get a height that is not the same as the function output. If this happens, remind students that the sine function returns values relative to the radius of the circle. This challenge doesnβt appear in the video, but it is one to look out for.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 5:15] Before watching the rest of the episode, state in your own words why it doesnβt work to divide sin(π/8) by 2 to get sin(π/4).
Supporting Dialogue
[Pause the video at 1:08] Claire and Mary are going to explore whether or not sin(π/8) = [sin(π/4)]/2. Talk with a partner about whether or not you think this equation is true and support your claim by explaining your reasoning. Then watch Mary and Claire explore and discuss this idea.
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