# Logarithms Lesson 2 Episode 1 (Teachers)

### Making Sense

The students explore the growth of the beanstalk between Day 2 and Day 12. They mark in several mathematical relationships on a number line that represents this growth and write several exponential expressions.

### Episode Supports

Students’ Conceptual Challenges

The instructor asks the students if they can represent 59,049 in another way [5:30]. This number is the factor by which the plant grows from Day 2 to Day 12 (and also over any 10-day period). Arobindo writes 9= 310 but seems confused if it should be times 9 six times or five times. Soon after, Arobindo seems to conflate the growth factor over 10 days with the height of the plant on Day 10. He only counts 8 factors of 3, from Day 2 to Day 10. When he notices the discrepancy, he counts from Day 0 to Day 2. The instructor reminds them they are looking at the length of time from Day 2 to Day 12, but it isn’t clear that Arobindo has completely resolved this mix-up.

Focus Questions

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

1. [Pause the video at 1:03] Use the timeline shown in the video to show the height of the beanstalk on Day 4, Day 6, Day 8, Day 10, and Day 12. Then, label any mathematical relationships you see.
2. [Pause the video at 3:09] Can you rewrite each height that Josh and Arobindo have written as exponential expressions with a base of 3? What about with a base of 9?

Supporting Dialogue

Arobindo and Josh claim that 9= 310. Ask students to decide if this equation is true, and to craft an argument that supports their decision. If students do not agree, prompt a whole-class discussion, and ask students to provide justification for their argument that links the expressions to the context and the number line that Josh and Arobindo created.