Exponentials Lesson 6 Episode 6 (Teachers)

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This episode reveals some of the difficulties students might have in understanding the range of an exponential function. Initially Josh and Arobindo decided that for the function y = 1 • 3^x, y must be greater than or equal to zero [0:16]. However, as they investigated the function through the context of the height of the beanstalk in the days prior to Jack receiving it, they realized that the height, represented by y in the equation, will never be 0 [1:30].

For use in a classroom, pause the video and ask these questions:

1. [Pause the video at 0:21] Before listening to Josh and Arobindo’s reasoning about values for y, decide for yourself what kind of values make sense for y.
2. [Pause the video at 0:45] What do you think about Arobindo’s claim that y must be greater than or equal to zero. Do you agree or disagree with that claim? Can y be negative?
3. [Pause the video at 1:33] Arobindo has just finished arguing that “when you’re going backwards, you’re dividing by three, so that’s the opposite of multiplying by three.” Can you rephrase what Arobindo has said? What do you think he means by “going backwards.”

After watching the video, ask your students to talk with one or two other students to summarize the key ideas from the last two videos. There is quite a bit to make sense of, so you may consider prompting each idea, one at a time. These ideas include what types of values make sense for both x and y in an exponential function set in the beanstalk context and the meaning of negative exponents. Afterward, ask them to reflect on their own understanding by telling their peers something they’ve figured out in this lesson and something they are still thinking about or working through.