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Arobindo and Josh create a timeline for a new magical beanstalk. This beanstalk’s height also increases by a factor of 3 each day, but it starts with a height of 2 cm on Day 0 instead of 1 cm. The students use their timeline to create an expression that represents the height of this new beanstalk on Day 12.
Episode Supports
Students’ Conceptual Challenges
The main challenge in this episode is how to account for an initial height that is not 1. Although Josh and Arobindo seem to have little difficulty incorporating this new value for the initial height into their reasoning, other students might not be sure how to utilize the new value in their calculations. Drawing a timeline and annotating it with relationships, as Arobindo and Josh did [1:13], can help students attend to the idea that the initial height is what is being multiplied by the growth factor over successive days.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:30] What has changed with this new beanstalk compared to the other beanstalks you’ve worked with? Make a prediction about how this change will affect the growth of the beanstalk over a period of time.
[Pause the video at 2:56] Analyze the timeline that Josh and Arobindo have drawn. What mathematical relationships do you see in the timeline? How would you illustrate those relationships on your own timeline?
Supporting Dialogue
Pause the video at [4:00] to ask students to respond to Arobindo’s explanation, “that it continues 12 times.” Specifically, ask your students to rephrase what Arobindo has just said and to describe to a partner how they might add to the drawing to make it more clear what Arobindo means.
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