Exponentials Lesson 5 Episode 5 (Teachers)

Reflecting

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The students reflect on how a beanstalk grows over each half day.

Episode Supports

Students’ Conceptual Challenges

The last half of this video [1:57] features Arobindo unpacking the main conceptual idea for this lesson, namely that multiplicative relationships persist over same-length time periods. This means that if you partition a time period into equal subsegments, you can similarly partition the growth into equal roots. Consider using the supporting dialogue prompt after watching the video to assess your students own emerging understanding of this challenging idea.

Focus Questions

[Pause the video at 1:15] Josh said that the reason they wrote “” across each half day is because when you multiply them, it is supposed to be the same as multiplying the height by 3 across the entire day. Rephrase Josh’s statement in your own words.

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

Supporting Dialogue

In the video [1:57], Arobindo says he knows that between Day 73 and Day 73.5, the height of the beanstalk increases by a factor of , because the opposite of a square root is squaring; so if you square the  you get 3. He also emphasizes that there is a relationship that continues forever on the timeline, saying that the relationship in growth over any two days is the same. He extends this to say there is the same multiplicative relationship between Day 73 and Day 73.5 as there is between Day 0 and Day 0.5, saying they “multiply by the same amount.” Ask your students to review this part of the video again and summarize what they think Arobindo is claiming. His summary unpacks some challenging mathematics, so provide students with plenty of time to make sense of his argument.