# Logarithms Lesson 2 Episode 3 (Teachers)

The students represent the growth of the beanstalk over 101 2-day periods on a number line. They use their number line to justify two equivalent expressions that describe the growth over that period.

### Episode Supports

Students’ Conceptual Challenges

Early in the video, the pair find the height of the plant on Day 101 [0:44]. Later, this causes some confusion, as Arobindo begins reasoning about 50.5 2-day periods, instead of 101 2-day periods [1:23]. This highlights a possible challenge of re-conceptualizing the unit from one day to some other period of time and counting that period instead of single days.

Focus Questions

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

1. [Pause the video at 1:23] Josh and Arobindo have written (32)50.5. Does this accurately represent the growth rate of the beanstalk over 101 2-day periods? Why or why not? If you think it does, can you provide evidence for your thinking? If you think it does not represent that growth, how would you change the expression?
2. [Pause the video at 2:13] What does 3202 tell us about the beanstalk? How do you know?

Supporting Dialogue

After watching the video ask your students to consider the equation that Arobindo and Josh wrote: (32)101 = 3202. Ask them to rephrase what Josh and Arobindo said for each expression. What does (32)101 represent in terms of the beanstalk? Why is that the same as 3202?