Algebraic Expressions Lesson 6 Episode 3 (Teachers)


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ET and Haleemah reflect on their generalized algebraic expression and make sense of each portion of their expression in the cobblestone context in two ways.

Episode Supports

Students’ Conceptual Challenges

Students may have difficulty contextualizing expressions for real-world contexts. For example, ET connects the expression x + 1 to the number of columns in the middle section of the cobblestone pattern. However, rather than connecting the x in x • (x + 1) explicitly to the number of stones in one column, he replies “The x is going to be the Size Number” [1:25].

Focus Questions

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

  1. [Pause the video at 3:27] Ask your students to compare ET’s explanation to Haleemah’s. What differences and similarities do they notice?
  2. [After watching the entire video] Ask students to think about the middle section of stones. One way to think about this section is to see it as five rows each containing six stones. Another way is to see five as the number of stones in each column in a section with six columns. Are these two ways equivalent? This discussion can yield another opportunity for students to think about the commutative property of multiplication in a real-world context.

Supporting Dialogue

  1. In this video, ET connects the annotations he made on the cobblestone pattern to the expression x • (x + 1) in the equation from Nicole’s method [0:52 – 2:17]. Ask your students to work with a partner to consider ET’s explanation and restate it in their own words.
  2. Do the same as above, but this time for Haleemah’s explanation [2:17 – 3:27].