Mauricio and Emily apply what they learned in Episodes 1-3 (drawing a picture, finding the area of the new garden in different ways, and writing arithmetic equations) when the length of the original garden is decreased by 7 feet.
Episode Supports
Students’ Conceptual Challenges
Contextualizing—the process of applying aspects of a given context to mathematical symbols—can be tricky for students. In this episode, Mauricio tries to explain how the expression 9(12 – 7) relates to a drawing [9:11]. He initially claims that this expression represents finding the entire area, 108 ft2, and subtracting the area associated with the decrease in length, 63 ft2. However, the expression 9(12 – 7) is best contextualized as thinking about the width of the new garden, 9 ft, times the length of the new garden, (12 – 7) ft. Mauricio’s contextualization of the expression 9(12 – 7) is better suited for the expression on the right side of the equation, (9 • 12) – (9 • 7).
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 1:34] Before watching Emily and Mauricio, try this new problem for yourself. Use a drawing to find the area of Kiara’s new garden when the length is decreased by 7 ft. Be sure you can see the old garden in your picture!
Supporting Dialogue
[Pause the video at 6:14] Emily and Mauricio have written the equation 9(12 – 7) = 9 • 12 – 9 • 7. With a partner, discuss whether or not this equation is true. Then take turns pointing out where each of you sees parts of each expression in the drawing. For example, where do you see (12 – 7) in the drawing made by Mauricio and Emily?
