Exponentials Lesson 1 Episode 2 (Teachers)

Making Sense

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The students watch a video of the beanstalk growing. They describe what they notice about how it is growing.  

Episode Supports

Students’ Conceptual Challenges

The use of the applet introduces a visually-dynamic model of the beanstalk and its growth. Josh and Arobindo note that the growth of the beanstalk is “slow at the beginning” but then “it grows faster as it progresses” [1:09]. Later Arobindo claims “the growth rate is growing.” These statements reflect the challenge of understanding a new kind of growth rate, one that maintains a common factor of growth over equal time periods.

Focus Questions

For use in a classroom, pause the video and ask this question:

[Pause the video at 1:29] Arobindo and Josh mention that the growth of the beanstalk changes, initially saying it starts out slow and then grows faster, and then claiming “the growth rate is growing.” What do you think Arobindo means when he uses the term growth rate? Do you agree or disagree with Arobindo that the growth rate is growing? Explain why you think that way.

Supporting Dialogue

If you use the applet, ask students to discuss their observations about the growth of the beanstalk. Encourage them to discuss which parts of the beanstalk they notice are growing and, if necessary, point out the “poofing” leaves versus the continually-growing brown part of the stalk. Ask them to decide which is the part of the stalk that is continually growing. If you are not using the applet, pause the video at [1:39] and hold this same discussion before hearing the instructor’s explanation of this idea.