Algebraic Expressions Lesson 2 Episode 1 (Teachers)

Making Sense

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ET and Haleemah make sense of their previous solution and think of a way to correct their answer, creating a new method for finding the number of tiles in the border of the pool.  

Episode Supports

Students’ Conceptual Challenges

Haleemah struggles to write a new equation for the number of tiles in the border of a pool with a side length of 10. Quantifying the information from the diagram can be tricky, and Haleemah initially writes 10 • 10 to symbolize counting all four sides (with double counting of the corners) [2:11]. She also seems unsure about how to account for the double counting, and after writing “– 4” she says she is confused about the equation [3:01].

Focus Questions

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

[Pause the video at 3:57] Recall from the first lesson that Haleemah and ET initially guessed that there would be 40 tiles in the border of the pool. Now, ET and Haleemah have written the equation (10 • 4) – 4 = 36, which is the number of tiles in the border of a pool with 10 tiles on a side. Why does subtracting four work here? Would that always work for any pool? Why or why not?

Supporting Dialogue

Ask students to compare their work with ET and Haleemah’s work by talking with a partner. Encourage them to discuss what each part of their equation means, like Haleemah and ET did in this episode. For example, what in the diagram or context is represented by the 10 in the equation? The “times four”? The “minus four”? If there are differences in your students’ work and the work of Haleemah and ET, ask your students to determine if each difference is mathematically significant. For example, are parentheses required in (10 • 4) – 4? Does the order of these numbers matter, and if so, how?