Exponentials Lesson 7 Episode 3 (Teachers)

Repeating Your Reasoning

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Arobindo and Josh use their timeline to find the height of the beanstalk on Day 11/3.

Episode Supports

Students’ Conceptual Challenges

As Josh and Arobindo are making sense of the timeline partitioned into eleven sections, each of which represents one-third of one day, Josh writes  as the growth factor for one such section instead of  [2:50]. Arobindo questions this, and Josh changes it to , but only links this symbolic representation to the Day 1/3. The instructor points out that this should make sense because is the number you multiply by itself three times to get 3. This illustrates how, even though students may seem to grasp the complexities of the symbolic notation for fractional exponents, it is hard work to ground those symbols in the mathematical concept. Look for opportunities to assess your own students’ understanding through the focus questions and supporting dialogue prompts for this lesson.

Focus Questions

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

  1. [Pause the video at 0:19] Work with a partner to find the height of the beanstalk on Day 11/3. Illustrate your work on a timeline.
  2. [Pause the video at 2:11] Josh and Arobindo are going to describe what is happening with the height on each of the eleven 1/3 days. Before they do so, make a prediction for what Arobindo and Josh will say. How would you illustrate this on the timeline?

Supporting Dialogue

After watching the video, ask your students to examine the timeline Josh and Arobindo have drawn and to share their thoughts with a partner about how Arobindo and Josh visualized and marked the height changes on the timeline. Ask them to state where they see in the timeline and to link with the expression 31/3.