# Logarithms Lesson 2 Episode 4 (Teachers)

### Repeating Your Reasoning

The students use a number line to explore the growth of the beanstalk over an unknown number of 1.5-day periods of time. They develop two equivalent exponential expressions to represent this growth.

### Episode Supports

Students’ Conceptual Challenges

Some students may have trouble using the context to distinguish between 31.5n and (31.5)n. In the video, Arobindo initially claims that (31.5)n can be seen as the growth over 1.5n days [3:05], but later clarifies that for this expression, the 1.5 is a 1.5-day period, and the n signifies there are n many of those 1.5-day periods. He then argues that n many 1.5-day periods results in 1.5n many days. This is a subtle idea, but in terms of interpreting the expressions in this video, it is important to note this difference. This can help students see why the two expressions are equivalent.

Focus Questions

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

1. [Pause the video at 1:52] What significance does 1.5n have in this context?
2. [Pause the video at 2:25] Can you state in your own words what the expression 31.5n means in the beanstalk context?
3. [Pause the video at 4:09] Can you state in your own words what the expression (31.5)n means in the beanstalk context? How is it different than 31.5n? How is it the same?

Supporting Dialogue

After watching the video, ask students to restate in their own words why the two expressions (31.5)nand 31.5n are equivalent. Ask them to describe how they see 1.5n in the diagram Josh and Arobindo drew and to use that in their argument for why the expressions are equivalent.