# Exponentials Lesson 3 Episode 4 (Teachers)

### Reflecting

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Stop the video above first if it is playing.

Josh and Arobindo use their timeline to create an expression that represents the height of the beanstalk on Day 100.

### Episode Supports

Students’ Conceptual Challenges

The beanstalk story is a contextual representation of the mathematical idea of exponential growth. Josh and Arobindo were asked to create a symbolic representation for this idea by creating an equation that represents the height of the beanstalk on any given day. They do so, but they use descriptive phrases instead of symbols [2:22], which illustrates the difficulty students may have transitioning from a contextual representation to a symbolic one. The use of variables and symbols is an important convention for symbolic representations, so push your students to not only use symbols, but also to define them. The teacher models this instructional move in the video.

Focus Questions

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

[Pause the video at 1:02] What does each component of Josh and Arobindo’s equation represent in the context of the growing beanstalk. What is the significance of the 3? What about the phrase “Day #”, and of the phrase “Height of the beanstalk on Day #”?

Supporting Dialogue

Josh and Arobindo have written a new equation for the height of the beanstalk: 1 • 3x = y [2:22]. Encourage your students to argue for why this equation will provide the height of the beanstalk on any given day. Arobindo provides one such explanation [3:46], and you could ask students to listen and compare his ideas with their own.