# Exponentials Lesson 2 Episode 2 (Teachers)

### Exploring

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Stop the video above first if it is playing.

Josh and Arobindo mark in several important mathematical relationships on the timeline they created to represent the growth of the beanstalk.

### Episode Supports

Students’ Conceptual Challenges

Josh and Arobindo seemed to have some difficulty expressing the exponential relationships they were observing using groups of language [4:02 and 6:14]. This is partially resolved when the instructor asks Arobindo and Josh to be explicit about what the final group contains. In the first case, it is three groups of 1 cm heights. In the second case, it is three groups of 3 cm heights.

Focus Questions

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

1. [Pause the video at 4:29] Think about the discussion so far about the increase in height over two days. How does the idea “three groups of three copies” relate to the growth factor of 9? Josh states “then like every time you go two times, then it’s 9.” What do you think he means by two times? What do you think he means by then it’s 9?
2. [Pause the video at 6:34] Can you rephrase what Josh and Arobindo have said about the height of the beanstalk being 81 times the height of it on a previous day? Try to use groups of language to support your reasoning. Do you see anywhere else in the timeline where the growth of the beanstalk would be 81 times as big as a previous day?

Supporting Dialogue

Ask students to summarize the video. There were different growth rates discussed: 3 times, 9 times, and 81 times. Ask students to reflect on each of these by restating where they see these rates in the timeline.