# Binomials Lesson 3 Episode 7 (Teachers)

### Exploring

Emily and Mauricio choose variables and write algebraic equations expressing the area of the new garden from Episode 6 in several ways.

### Episode Supports

Students’ Conceptual Challenges

In this episode, Mauricio and Emily use variables to represent several unknown quantities in the new garden context. They use L to represent the increase in length, A to represent the increase in area, and NA to represent the total area of the new garden. The instructor tells Emily and Mauricio that when symbols are used algebraically, they need to be precisely defined [2:33]. This is something that students don’t necessarily know. Mauricio and Emily catch on, and by the end of the video, they are defining the new variable NA without prompting. Look for opportunities to encourage and require precise definitions for variables your students use.

Focus Questions

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

1. [Pause the video at 0:25] Try expressing the area of the new garden using the variables that Emily and Mauricio have chosen.
2. [Pause the video at 4:13] Can you write another expression or equation that represents the area of the new garden when its length has been increased by L ft?

Supporting Dialogue

[Pause the video at 5:05] Discus with a partner the equation 4(5 + L) = NA. What does each part of this equation represent in the context of a new garden? Is the equation true? Why or why not?