# Binomials Lesson 5 Episode 2 (Teachers)

### Exploring

Emily and Mauricio create a drawing to find the area of the new garden from Episode 1. Then they write several arithmetic equations to represent the area of the new garden.

### Episode Supports

Students’ Conceptual Challenges

1. As seen in the previous episode, Mauricio forgets to add in the part of the new garden that corresponds exclusively to the new length, in this case a square with length and width of 2 m. In this episode he discusses how he forgot about that “isolated piece” and uses the drawing to revise his thinking [4:50].
2. As Emily and Mauricio work to create expressions that represent the new area, they write 7 + 2 × 3 + 2 [11:00]. They do not include parentheses, which are needed for this expression to be accurate. Notice how the instructor asks about writing it so someone else doesn’t get confused by what to do first. This is a great way to help students become more aware of the conventions we use in mathematics and why we use them.

Focus Questions

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

1. [Pause the video at 0:42] Before watching Emily and Mauricio create their drawing, try this for yourself. Draw a picture that you can use to find the area of the new garden and see the original garden. Recall the original garden is 7 m long and 3 m wide and the new garden has a length and width that is each 2 m longer than the original garden.
2. [Pause the video at 9:38] Mauricio and Emily have written two ways to express the area of the new garden: 9 × 5 and 21 + 14 + 6 + 4. Can you think of any other ways to express the area of the new garden?

Supporting Dialogue

1. [Pause the video at 2:20] Mauricio says he “forgot the little square.” Discuss with a partner what you think he means by that. Recall his prediction was 41 m2.
2. [Pause the video at 4:41] Revoice Emily’s method in your own words. How does it compare to your prediction or method for finding the area of the new garden?