# Exponentials Lesson 6 Episode 3 (Teachers)

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Stop the video above first if it is playing.

The students use their timeline to find the height of the beanstalk on Day ⅚.

### Episode Supports

Students’ Conceptual Challenges

In this episode, Josh and Arobindo extend their emerging ideas about fractional exponents to a new situation, one in which a day is partitioned into six equal segments. The pair work to explain why the height of the beanstalk on Day 5/6 is equal to bothand 35/6. They are eventually able to connect these expressions to multiplying the sixth root of 3 by itself five times.

Focus Questions

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

1. [Pause the video at 0:20] Create an expression that shows the height of the beanstalk on Day 5/6. Create a timeline to support your reasoning.
2. [Pause the video at 1:50] Think about the discussion you’ve just seen about measuring the beanstalk’s height on specific days. Discuss with a partner how Josh and Arobindo explain and justify the idea of a sixth root of the one-day growth factor of the beanstalk. How might you use these ideas to describe the height of the beanstalk on Day 5/6?

Supporting Dialogue

Arobindo says you can write the height on Day 5/6 as bothand also 35/6. Ask students to discuss with each other why both expressions are valid. Encourage them to connect each expression to the context of the growing beanstalk as well as to the visual representation of exponential growth given by the timeline.