Exponentials Lesson 7 Episode 1 (Teachers)

Making Sense

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Josh and Arobindo critique other students’ reasoning about what the height of the beanstalk should be at Day 2.5. They then use a timeline to create their own argument for what the height should be at that time.

Episode Supports

Students’ Conceptual Challenges

A fictional student named Denzel exhibits a common challenge students may face in fully understanding exponential functions, which is conflating a growth factor (in this case,  for each half day) with the functional output (in this case, the height of the beanstalk). Instead of using the growth factor and a known height to compute the height on Day 2.5, Denzel says the height on Day 2.5 is equal to the associated growth factor,  [0:56]. It would be more productive if he recognized that the height of the beanstalk on Day 2.5 is  times greater than it is on Day 2.

Focus Questions

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

  1. Pause the video at 2:35] Consider both Denzel and Isabella’s ideas. Do you agree that height on Day 2.5 will be ? How does Isabella’s argument contradict that idea? Can you connect your argument to the beanstalk context or to the timeline from the video?
  2. [Pause the video at 3:28] Denzel thinks that the height on Day 2.5 is . Is there anything productive about Denzel’s thinking? Tell your partner how you could use Denzel’s idea to correctly compute the height of the beanstalk on Day 2.5.

Supporting Dialogue

Consider pausing the video at [4:42]. This is a place where students can check in with their own understanding of the conceptual challenge voiced by the fictional student Denzel. Ask your students to discuss the method of multiplying the height on Day 2, which is 9 cm, by . Ask them to explain in two different ways why this method results in the correct height of the beanstalk on Day 2.5. Encourage your students to use a timeline (one that they’ve drawn or the one from the video) to support their argument.