# Algebraic Expressions Lesson 5 Episode 4 (Teachers)

### Exploring

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Haleemah and ET generalize Amir’s method that relates an unknown Size Number and the number of gray stones in the cobblestone pattern.

### Episode Supports

Students’ Conceptual Challenges

In this episode, Haleemah and ET are challenged to precisely define their variables. Defining variables can be tricky, but doing so with specificity is an important part of generalizing. Haleemah and ET initially state that their variable x represents the unknown number of gray stones [2:57], but they use x to represent the Size Number or the number of stones in a column. Later, as they work to more precisely define their variable x, Haleemah states that it could be the gray stones, or “any gray stone” [5:28].

Focus Questions

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

1. [Pause the video at 1:08] Ask your students “What do you think it means to generalize Amir’s method? What do you expect Haleemah and ET will do in this video?”
2. [Pause the video at 4:22] Haleemah stated that x is the unknown number of gray stones, and ET agrees. Ask your students what they think—does anyone disagree with ET and Haleemah? If someone disagrees, ask them what they think x means in the equation.

Supporting Dialogue

After viewing the video, ask students to reflect on ET and Haleemah’s equation and definitions. Ask them if they would write the equation in the same way, or if not, how they might write it differently. Students may say they would use a different variable, but they also might attend to the fact that x • x = x2, or that there are 3 copies of x • x which can be rewritten as 3(x • x). Use this discussion as an opportunity to build on ideas about equivalence.