Exponentials Lesson 1 Episode 1 (Teachers)

Making Sense

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Josh and Arobindo explore the growth of a beanstalk whose height quadruples each day. They create drawings that show the growth of the beanstalk over several days. 

ET and Haleemah make sense of a swimming pool context and create a method for finding the number of tiles in the border of the pool.  

Episode Supports

Students’ Conceptual Challenges

  1. Drawing the beanstalk’s growth posed a challenge in terms of interpreting and accurately representing the quadrupling pattern visually. Initially, Josh and Arobindo drew lines to represent the beanstalk at different days, but did not attend to the relationship between the heights across successive drawings [1:24]
  2. In asking Arobindo and Josh to label each beanstalk with a corresponding day, the students were challenged to quantify days as a measure of time from when the beanstalk was first planted [3:35]. Understanding the significance of counting days from the moment the beanstalk was planted, required clarity in quantifying time not as a just a label, but as a measure of how much time has passed.

Focus Questions

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

  1. [Pause the video at 1:58 and/or 5:24] How do Josh and Arobindo visually represent the quadrupling growth of the beanstalk in their drawings? What elements in their drawings signify the increase in height each day?
  2. [Pause the video at 4:07] Arobindo described two different ways to label the days. Why might you label the first day as Day 1? Why might you label the first day as Day 0? How does the labeling of the days impact your understanding of time in the context of the problem?

Supporting Dialogue

Consider asking students to make their own drawings (either before or after watching Josh and Arobindo make theirs). As they do, encourage them to explain to a partner, and later to the class, how they are linking elements of their visual representation to the contextual representation of the story of the beanstalk.