# Algebraic Expressions Lesson 3 Episode 3 (Teachers)

### Exploring

No captions Captions
Stop the video above first if it is playing.

The students generalize their method and write an algebraic equation that shows the relationship between the cost per game and the total amount spent by the friends.

### Episode Supports

Students’ Conceptual Challenges

1. When asked to check their equation, ET replaces the variable c with the number 2, but initially writes 32 instead of 3 • 2 [5:40]. He resolves this challenge with seemingly little effort, but it points to a potential obstacle your students might need to overcome. The use of juxtaposition for multiplication with non-numerical symbols is a convention that is widely used in algebra and beyond. You may want to explain this convention to your students as you view this video.
2. One challenge your students might encounter that ET and Haleemah did not, is using letters incorrectly as labels or abbreviations. For example, when trying to use algebraic symbols to quantify the total amount of money spent by Danyal, students might think “Danyal bought 3 apps, and I need a variable in here, so it must be 3d, where d stands for Danyal.” Be on the lookout for expressions that might indicate students are replacing words directly with letters (for example, 2s where s stands for Suado, rather than the cost per app). To help students overcome this challenge, ask them to be explicit, as ET and Haleemah are, with writing out exactly what each variable represents in the context.

Focus Questions

For use in a classroom, pause the video and ask this question:

[Pause the video at 3:45] Ask your students “What do you think Haleemah means when she said she used the numbers they were given?” Which numbers does she mean, and what might she mean by saying they were “given those numbers?”

Supporting Dialogue

[Pause the video at 5:20] Say to your students, “Before we see how Haleemah and ET test their equation, how would you test their equation? Turn and tell your partner what you might to do to see if the equation works. After you each have shared, pick a testing method and try it.” Afterwards, let them compare their work with the work of ET and Haleemah.