Mauricio and Emily reflect on their drawing from Episode 2 and write equations to express different ways to find the area of the new garden. The idea of distributing multiplication over addition comes up.
Episode Supports
Students’ Conceptual Challenges
Early in the episode [1:12], Emily and Mauricio start writing an expression to represent the area of the new garden. The students grapple with two different related ideas.
First, they discuss whether parentheses are needed to enclose 5 + 3, if they are wanting to multiply that entire quantity by 4. This illustrates the need for students to know of and be able to use mathematical conventions. The order of operations is a convention; so, look for opportunities to discuss that convention.
Second, they question where the 4 should be placed: before (5 + 3) so the expression is 4 × (5 + 3); or after (5 + 3) so the expression is (5 + 3) × 4. Since multiplication is commutative, the choice doesn’t matter, but it seems to make sense to Mauricio and Emily that the 4 should come first. The distributive property works either way, however, and Mauricio and Emily might not realize that in this episode.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 2:27] Do you agree with Mauricio and Emily that 5 + 3 should be in parentheses? Why or why not? Do you agree with Mauricio and Emily that the 4 should be front of (5 + 3) in order to distribute? What would happen if instead the expression was (5 + 3) × 4?
Supporting Dialogue
Pay close attention to the connections Mauricio and Emily discuss starting at [5:49]. After finishing the video, pick one of those connections and tell your partner about it in your own words.
