Algebraic Expressions Lesson 6 Episode 5 (Teachers)


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The students look at someone else’s reasoning about a key difference between Amir’s and Nicole’s methods. They use this to explain what parts of the algebra equations mean in the cobblestone pattern. 

Episode Supports

Focus Questions

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

  1. [Pause the video at 1:44] Ask your students to consider what “the friend” has claimed, that x • (x + 1) = x2 + 1. Do they think this is true? Why or why not? 
  2. [Pause the video at 3:43] Prompt your students to consider the friend’s way of thinking. Ask them to annotate the cobblestone pattern to reflect the expression x2 + 1, and then ask them to compare their ideas to Haleemah’s and ET’s, which they will see once you continue the video.

Supporting Dialogue

  1. After viewing the video, ask your students to reflect on the expressions x2 + 1 and x • (x + 1). Ask them to summarize with a partner their thinking about these expressions and why they are not equivalent. Encourage them to describe at least two ways they know these two expressions are not equivalent.
  2. After students have discussed why those expressions are not equivalent, ask them to consider the expressions x2 + x and x • (x + 1). Ask them to work with a partner to determine if these two expressions are equivalent. Encourage them to come up with as many different arguments as they can to demonstrate that these expressions are or are not equivalent.