# Logarithms Lesson 1 Episode 7 (Teachers)

### Reflecting

The students create two equivalent exponential expressions that both represent the height of the beanstalk any number of days after an unknown start date. They justify these expressions using a number line.

### Episode Supports

Focus Questions

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

1. [Pause the video at 0:38] Before watching Arobindo and Josh create their own number line, create one for yourself. Draw and label a number line to represent the height of the beanstalk some number of days after it has grown for some number of days.
2. [Pause the video at 2:27] Josh and Arobindo have written two expressions: 1 × 3p+3 and 3× 3e. How do each of these expressions relate to the number line? Are they equivalent expressions? How do you know?

Supporting Dialogue

1. [Pause the video at 1:33] Ask your students to examine the diagram that Josh and Arobindo have drawn. Ask them to discuss with a partner the significance and meaning for each expression in the diagram. What does p represent? What about e and p+e? Ask them to explain why the Josh and Arobindo have written 3p, 3e, and 3p+e as heights of the beanstalk at various points on the timeline.
2. After the video, ask students to consider the equation 3p+e = 3× 3e and discuss with a partner why this equation is true. Ask them if they can come up with a general rule for when exponential expressions are being multiplied.