# Binomials Lesson 4 Episode 3 (Teachers)

### Reflecting

Emily and Mauricio reflect on their drawing from Episode 2 and write equations to express different ways to find the area of the new garden. They explore whether or not they can distribute multiplication over subtraction.

### Episode Supports

Students’ Conceptual Challenges

1. Early in the video [1:22], Mauricio and Emily wonder if distributing (12 – 4) × 9 would give the same answer as 8 × 9. They had to actually perform the distribution of 9 across 12 – 4, which gave them 108 – 36, and then calculate to see that the result would be 72 (which is the same as 8 × 9). This is an excellent example of how students often do not “trust” a mathematical idea (e.g., the distributive property) until they have utilized it for themselves.
2. Emily and Mauricio write the equation (12 – 4) × 9 = 4 • 9 – 9 • 12 [2:22]. When multiplication is distributed over a sum, the order in which you write the resulting pairs of products isn’t important since addition is commutative. But where multiplication is distributed over a difference, the order matters. If you have students who do this, try asking them to evaluate each side of the equation to see how the equation isn’t true. Then ask them how they might change it to make the equation true and have them discuss why the order matters in this case.

Focus Questions

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

1. [Pause the video at 0:34] Mauricio and Emily have written 9 × 8 = 72 ft2 to represent the area of the new garden. Can you think of any other expressions or equations you could write that would also represent the area of the new garden?
2. [Pause the video at 3:25] Emily and Mauricio have created the equation (12 – 4) × 9 = 4 • 9 – 9 • 12. Does the equation make sense? If so, explain why it makes sense, and if not, explain what is wrong with it.

Supporting Dialogue

[Pause the video at 1:22] Emily and Mauricio wonder if (12 – 4) × 9 will result in the same answer you get if you were to distribute first. Tell a partner what you think about this—will you get the same answer either way? Why or why not?