# Exponentials Lesson 1 Episode 4 (Teachers)

### Exploring

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The students determine the factor by which the beanstalk is increasing over several time periods.

### Episode Supports

Students’ Conceptual Challenges

At [1:20], the instructor asks Arobindo and Josh to consider an example when the days apart are not 1. The students choose Day 0 and Day 2. They initially claim the beanstalk would be six times as tall on Day 2 as it is on Day 0. Even though Josh and Arobindo seemed to resolve this challenge quickly, it is one to consider for your own students. The growth rate in exponential functions is multiplicative over successive time periods, not additive, as Josh and Arobindo initially guessed.

Focus Questions

For use in a classroom, pause the video and ask this question:

[Pause the video at 1:25] Complete the sentence for when the days apart are not 1. Can you convince your partner that your sentence is true? How many times taller is the beanstalk on the later day compared to the earlier day? (Be on the lookout for additive thinking as Arobindo and Josh briefly illustrated at [1:20].)

Supporting Dialogue

Pause the video at [0:56] or use your own example of non-integer days. Ask students to consider how the beanstalk grows from Day 2.2 to Day 3.2 (or whichever days you’ve chosen). Encourage conversation that focuses on the tripling pattern and ask students to discuss how that pattern persists when the days aren’t whole numbers. Pay attention to answers that link the passage of 1 whole day to the tripling of the height, as this is in line with the relationship given in the context.