# Logarithms Lesson 3 Episode 1 (Teachers)

### Making Sense

Josh and Arobindo create a number line to model the growth of mold on a pizza slice. They estimate when the pizza will have 50 grams of mold, and mark this in on their number line.

### Episode Supports

Students’ Conceptual Challenges

1. To help determine when there would be 50 grams of mold on the pizza, Arobindo and Josh find two quotients, 50/27 and 81/50. Arobindo seems to quickly understand that dividing the two quantities of mold will yield the growth factor between the associated times. Some students might not see this so quickly. Consider using the last two Focus Questions, as well as the Supporting Dialogue prompt, to help students make sense of Arobindo’s method.
2. One additional consideration is that this method yields the growth factor, but it does not provide the exponent. To put this in the context of moldy pizza, the method does not yield the specific time at which there is 50 grams of mold. Be on the lookout for students who overextend the usefulness of finding the growth factor instead of finding the exponent.

Focus Questions

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

1. [Pause the video at 1:04] Examine the diagram provided to Josh and Arobindo. Can you use the diagram to make a guess for when there will be 50 grams of mold on the pizza? How does your guess compare to the reasoning of Arobindo and Josh?
2. [Pause the video at 1:35] Do you think the time will be closer to Hour 3 or Hour 4? How could you determine this?
3. [Pause the video at 2:34] Arobindo has written 50/27 = 1.851851851. What did he find?
4. [Pause the video at 4:30] Arobindo has written 81/50 = 1.62. What did he find this time?

Supporting Dialogue

Ask your students to summarize the discussion from 4:30 until the end of the video, in which Josh and Arobindo talk about both 50/27 and 81/50 as growth factors. What do those expressions tell us in the context of the moldy pizza? How can they be used to help us determine when there is 50 grams of mold on the pizza?