Exponentials Lesson 4 Episode 5 (Teachers)


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Josh and Arobindo are given an equation that models the growth of a magical beanstalk. They explain how the beanstalk is growing.

Episode Supports

Students’ Conceptual Challenges

Josh and Arobindo seem to be on their way to generalizing how growth rates can be partitioned and composed. For example, in this episode, they draw an arc to show a growth rate of 42 between Day 0 and Day 2. When prompted, they also draw two smaller arcs to indicate a growth rate of 4 between Day 0 and Day 1 and another growth rate of 4 between Day 1 and Day 2 [5:00]. This is one of the key ideas that will be explored for the remainder of this unit, and some students may still be putting this important concept together.

Focus Questions

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

[Pause the video at 3:59] Predict what Arobindo and Josh will draw on this new timeline. What relationships might Josh and Arobindo illustrate, and how will they show them? After you make your predictions, resume the video and note similarities and differences between what you predicted and what Arobindo and Josh do.

Supporting Dialogue

Before viewing the video, ask students to pretend they need to help a classmate who missed the previous lessons. Ask them to come up with a short list of key ideas about the beanstalk context and how to represent how the height of the beanstalk on any given day. Then ask them to use those key ideas to explain how to interpret the new equation y = 3(4x).