Exponentials Lesson 5 Episode 3 (Teachers)

Repeating Your Reasoning

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Josh and Arobindo use their timeline to find the height of the beanstalk on Day ¼.

Episode Supports

Students’ Conceptual Challenges

An overarching challenge for this lesson is made visible in this episode, namely that of equally partitioning (splitting up) the multiplicative growth over a similarly partitioned period of time. In this video, Arobindo and Josh must partition the known growth factor of 3 over the period of one day in order to determine how tall the beanstalk is after growing for only a quarter of a day. Although Josh and Arobindo deftly utilize the exponential notation from their previous equation to predict that the height of the beanstalk will be 3¼ at Day ¼ [0:33], other students might struggle to make this connection. If this is the case, your students might need help seeing the entire growth factor of 3 being equally partitioned into four smaller growth factors, which, when multiplied together, yield 3.

Focus Questions

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

  1. [Pause the video at 0:25] Predict how Josh and Arobindo will find the height of the beanstalk on Day ¼. How might you use a timeline to represent that height? What do you think the decimal approximation for this height might be?
  2. [Pause the video at 3:58] Summarize Arobindo’s method for approximating the fourth root of 3. Why do you think he is raising his guesses to the power of 4? How does that relate to the fourth root? Arobindo explains that raising something to the power of 4 is the same as multiplying that number by itself four times; how does Arobindo’s explanation relate to the fourth root of a number?
  3. [Pause the video at 6:37] What is happening with the time between each successive segment in the timeline drawn by Josh and Arobindo? What about the height of the beanstalk? What does this mean for both the height and time over several consecutive segments?

Supporting Dialogue

After watching the first two minutes of the video, consider pausing at [2:07]. Ask your students to articulate what they think the fourth root means. Ask them to discuss with a partner how it relates to finding the height of the beanstalk on Day ¼. Ask them to share how they might explain this idea to someone else, and if they have anything they would add to Arobindo’s explanation for what the fourth root of 3 means.