# Algebraic Expressions Lesson 2 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

When students first begin generalizing, one challenge they often encounter is being explicit about what each variable or unknown represents in the given context. We see ET and Haleemah write an equation using the variables x and T (later changed to B) [1:52]. Notice that they do not define these variables until they are prompted to do so by the teacher [2:14]. Even then, the description for x is vague: “x is the number on the side.” Later, they change this description to “x is the number of tiles on one side.”

Focus Questions

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

1. [Pause the video at 1:35] ET asks about removing “the 15 and putting a variable in its place.” Ask students what they think ET means by this. What do they think a variable is? How would replacing the 15 with a variable help with writing an equation that would work with any number of tiles?
2. [Pause the video at 4:33] Haleemah is about to imagine a pool with a number of tiles on one side that is different from 10, 7, and 15. Ask your students to do the same and have them use their formula to determine the number of tiles there are in the border of the pool they imagined. Once they have done this, ask them to sketch their pool without drawing the tiles one by one.
3. [Pause the video at 7:04] The teacher asks Haleemah to connect each part of her equation to her drawing. Before continuing with the video, ask students to anticipate what Haleemah might say. In other words, ask your students “Where do you think Haleemah will show 25 times 4 in her picture? What about the minus 4?”

Supporting Dialogue

As students generalize and create their own equation with variables, look for opportunities to push them to be explicit about what each variable represents in the pool context. Encourage and expect specificity. You can ask pairs to review and critique the definitions they gave each of their variables.