Mauricio and Emily reflect on another student’s equation: (5 + x) • 4 = 5 • 4 + x • 4. They discuss how this equation is similar to and different from the equations they wrote in Episode 7. They also reflect on the meaning of equivalence in the garden context.
Episode Supports
Students’ Conceptual Challenges
This episode represents a critical point in understanding the distributive property of multiplication over addition. Mauricio and Emily work to show that two different expressions each represent the total area of a new garden. One expression shows that you can find the area by identifying the new length first (5 + x) and then multiplying that by the width to get (5 + x) • 4. The other expression shows you can find partial areas first, including the area of the original garden (5 • 4) and the area of the extension (x • 4), and then add those two areas together. This idea seems tricky to Mauricio and Emily, which is a common challenge for students. The distributive property is relatively straightforward to represent symbolically, but understanding how it can be utilized in contexts and drawings isn’t as straightforward.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 0:40] Take a minute to examine the drawing Mia made. What connections between the drawing and the equation do you notice?
Supporting Dialogue
[Pause the video at 5:25] In your own words, tell a neighbor what Emily and Mauricio just said about the expression (5 + x) • 4. Where in the drawing is the 5 + x? What about the 4? What does that expression mean in the context of the new garden?
[Pause the video at 6:16] In your own words, tell a neighbor what Mauricio and Emily just said about the expression 5 • 4 + x • 4. Where in the drawing is 5 • 4? What about the x • 4? What does this expression mean in the context of the new garden?
