Exponentials Lesson 2 Episode 3 (Teachers)

Repeating Your Reasoning

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The students explore what segments of various lengths on the on the timeline represent in terms of both the passage of time and height.

Episode Supports

Students’ Conceptual Challenges

Although Arobindo and Josh seemed able to extend their understanding of the context to coordinate time periods and heights, some students may struggle to reason simultaneously about three different quantities: length of a segment on the number line, amount of time that has passed, and multiplicative change in height of the beanstalk over that period of time. The next episode presents a task that can drive a conversation to help students coordinate these three quantities. 

Focus Questions

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

Pause the video at 0:40] What do you think a 1-inch segment on the timeline represents in terms of both time and height? What about a 5-inch segment? An n-inch segment?

Supporting Dialogue

[Pause the video at 2:27] Arobindo has argued that a 5-inch segment starting on Day 0 of the timeline corresponds to a 243 times increase in the height the beanstalk. Ask students to discuss if that conclusion can be generalized for any 5-inch segment. Ask them to use a diagram and/or groups of language to support their claims.