# Logarithms Lesson 1 Episode 3 (Teachers)

The students create an expression that represents the height of the beanstalk any number of days after Day 2, and create a number line to represent this expression.

### Episode Supports

Students’ Conceptual Challenges

1. At 1:00, Arobindo describes x as being the number of days after Day 2, but then goes on to say that it’s “x days.” It is unclear if he still meant “x days after Day 2” or something different. Clearly defining variables might be a challenge for some students. For the beanstalk context from the previous unit, the variable was typically defined as the number of days the beanstalk was growing, but here it represents the number of days after Day 2.
2. The instructor asks Josh and Arobindo where they see the expression 2+x on the number line [1:35]. Josh draws an arc spanning from Day 0 to Day 2, another arc spanning from Day 2 to Day (2 + x), and finally a large arc spanning from Day 0 to Day (2 + x). Some students might not readily see 2 + x as a distance on the number line. They may point out the label, for example, or be imprecise with where 2 + x is. Continue asking them to draw or indicate with their writing instrument or finger until they indicate that 2 + x can be seen as the length or distance of a line segment on the number line.

Focus Questions

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

[Pause the video at 0:17] Before watching the episode, create your own expression for the height of the beanstalk any number of days after Day 2 and represent it on a number line.

Supporting Dialogue

Josh writes × 3x (times 3x) instead of × 3x [2:52]. Ask your students to consider each expression and then argue for why × 3x is not correct. What does 3x mean and how is that different than 3x?