# Algebraic Expressions Lesson 1 Episode 3 (Teachers)

### Exploring

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Haleemah and ET generalize their method and write an algebraic equation that shows the relationship between a border with any number of tiles on one side and the total number of tiles in the border.

### Episode Supports

Students’ Conceptual Challenges

Haleemah and ET initially write an equation with three variables: (x • 2) + (y • 2) = B [2:09]. It can be challenging for students to recognize when one quantity is related to another, which means fewer variables will suffice. Later, Haleemah and ET realize that y = x – 2 [6:12]. Then they are able to express their equation with just two variables: (x • 2) + (x – 2) • 2 = B [9:34].

Focus Questions

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

1. [Pause the video at 2:09] Haleemah has written the equation (x • 2) + (y • 2) = B, which contains three variables: x, y, and B. What do you think each variable means in the pool context?
2. [Pause the video at 5:04] Are the variables x and y related? If so, how are they related? Turn and talk with a partner about how you might express one variable in terms of the other.

Supporting Dialogue

1. Ask students to generalize their own methods and encourage them to express their generalizations by using an algebraic expression or equation.
2. As you monitor students working, look for opportunities to push students to make clear any relationships between quantities they are using in their equations, particularly if they have used two variables or defined two quantities to describe the number of tiles in the border. Ask “I see you have two variables here. What can you tell me about the relationship between these?” or “I’m wondering how you might write this equation using only one variable to describe the number of tiles in the border.”