Mauricio and Emily reflect on the meaning of equivalence in another student’s equation: (12 − y) • 4 = 12 • 9 − y • 9. They identify what each symbol and term in the equation means in the garden context.
Episode Supports
Students’ Conceptual Challenges
This episode provides an example of a challenge that students commonly face when working with quantities in contexts, which is identifying the value of a quantity rather than the quantity itself. For example, the instructor asks where the students see any widths [1:30]. After they respond by stating “Just the 9,” they’re asked to show that width in the garden and they circle the label of 9 ft, rather than showing the actual width along the side of the garden. If your students do the same, you can be explicit and ask them things like “Can you use your pencil to draw the entire width?”
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 3:39] The instructor asked Mauricio and Emily where they see the area of the new garden on the right side of the equation, which is 12 • 9 – y • 9. This question seems to stump Emily and Mauricio. Before watching further, try to identify where you see the area of the new garden in that expression.
Supporting Dialogue
[Pause the video at 0:36] With a partner, take turns pointing out lengths you see in the drawing. As you do, connect the lengths you see in the drawing to parts of the equation (12 – y) • 9 = 12 • 9 – y • 9. Then do the same with widths and areas.
