# Binomials Lesson 5 Episode 7 (Teachers)

### Exploring

Mauricio and Emily express their written generalizations from Episode 6 using algebra.

### Episode Supports

Students’ Conceptual Challenges

One thing that students tend to find challenging in algebra is deciding how many variables to use for a given context. It is easy to assign a new variable to a new quantity, but far more challenging to use existing quantities and relationships between them to describe a new quantity. In this episode, Mauricio and Emily are tasked with writing a second expression for the area of a new garden that captures Emily’s method. Instead of using their existing quantities of 7 m, 3 m, and ?# (for the length, width, and unknown increase in length and width), they use new variables for the overall length and width of the new garden, ?L and ?W [6:01]. Push your students to rewrite expressions using existing values and variables by asking them to identify relationships or challenging them to use only existing variables, as the instructor does [7:25].

Focus Questions

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

1. [Pause the video at 1:09] Try this task for yourself before watching Mauricio and Emily. Draw a picture of the new garden and write an expression to show the area of the new garden.
2. [Pause the video at 2:12] Emily and Mauricio have written the symbols ?# in several places in their drawing. What do you think they mean by those symbols?

Supporting Dialogue

[Pause the video at 5:08] Talk with a partner and tell them what you think Emily and Mauricio will write when they write a new expression using Emily’s method for finding the area of a new garden.