# Binomials Lesson 3 Episode 6 (Teachers)

### Exploring

Mauricio and Emily draw a picture of a new garden when the length of the original garden is increased by an unknown amount. They explore how to use symbols and letters to represent an unknown length and an unknown area.

### Episode Supports

Students’ Conceptual Challenges

Emily has written “? × 4” in the new portion of the garden. Mauricio argues that it should just be “?” that represents the area, while Emily argues that she wrote the area as “? × 4” because “?” and “4” are the dimensions of the new section. Mauricio seems to hold two different meanings for “?” in the drawing, as both the value of the one-dimensional measurement of the increase in length, and also as the value of the two-dimensional measurement for the increase in area of the new section. However, for a given context or problem, any symbol that represents a quantity must maintain the same value; so, this represents a challenge for Mauricio.

Focus Questions

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

1. [Pause the video at 0:42] Before watching Mauricio and Emily create their own drawing, try making a drawing that shows an increase in length by an unknown number. How might you represent this mathematically?
2. [Pause the video at 9:39] Why does Emily think a new symbol is needed? Summarize her argument in your own words.

Supporting Dialogue

[Pause the video at 5:45] With a partner, take turns explaining the arguments made by both Emily and Mauricio. What does Mauricio think the “?” represents? What does Emily think the “?” represents? Who do you think is right and why? What do you make of the introduction of the new “!” symbol?