Algebraic Expressions Lesson 6 Episode 4 (Teachers)

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This video presents another example of how challenging it can be to contextual symbolic expressions, especially algebraic ones. Both Haleemah and ET are able to explicitly link numerical expressions to features in the cobblestone diagram. For example, given the expression 5 • 6, which comes from Nicole’s method, Haleemah connects the five to the number of stones in one column and the 6 to the number of columns in the second section [7:11]. ET describes how he sees the expression 5 • 5 + 5 by linking each five in that expression to features of the diagram [7:28]. However, making these connections with the algebraic expression x + 1 proves to be challenging, as ET shares it’s “very hard to explain, so it’s really hard to interpret that in Haleemah’s drawing or in my drawing” [8:32].

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

1. [Pause the video at 1:29] Ask students to compare Amir’s method to Nicole’s method. Encourage them to consider what they notice that is similar across both methods as well as what is different.
2. [Pause the video at 4:00] Display the equation (x • x) + (x • x) + x + (x • x) = x² + x • (x + 1) + x². Ask students to discuss why this equation is true (or rephrase the teacher’s question about why we can set the left side of Amir’s equation equal to the left side of Nicole’s equation).
3. [Pause the video at 8:27] Haleemah and ET have taken turns annotating the cobblestone pattern and explaining where in the picture they see each expression. Ask your students to discuss what they notice is alike in the annotations and what is different.

At the end of the video, ET says interpreting the x + 1 is difficult for both his drawing and Haleemah’s drawing [8:27]. Ask your students how they see x + 1 in either or both of the drawings.