# Binomials Lesson 1 Episode 3 (Teachers)

### Reflecting

Emily and Mauricio find the area of two differently-sized rectangular pizza slices in order to determine whether each slice has the same amount of pizza.

### Episode Supports

Students’ Conceptual Challenges

1. After claiming the area is 24 inches squared (in2), the teacher says they should be able to count 24 of something. Mauricio offers the idea of counting 24 pepperonis, while Emily starts drawing lines, partitioning the slice into 24 rectangles [1:14]. However, the rectangles are not squares with side lengths of 1 inch; so, they are not square inches. Throughout the rest of this lesson, Emily and Mauricio will work to build more productive ideas and representations of a square inch, but in this episode, the meaning of a square inch is something with which they both seem to struggle.
2. In the previous episode, Emily initially said the area of the pizza slice was 24 inches, and Mauricio countered with the unit “inches squared.” In this episode, both students examine these units of measurement further. They draw a line that is 24 inches and compare it to the slice of pizza which has an area of 24 in2. While the students know that these two units of measurement differ, they struggle to put into words how they are different and what each unit measures [7:40].

Focus Questions

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

1. [Pause the video at 2:22] Mauricio and Emily have drawn lines in one of the slices of pizza, which has created 24 rectangles. How does this represent 24 in2? Is there anything you would change about their method or drawing?
2. [Pause the video at 7:45] Mauricio has just drawn a line segment that is roughly 24 inches long. In your own words, how would you explain the difference between 24 inches and 24 inches squared?

Supporting Dialogue

1. [Pause the video at 0:46] What does 24 inches squared mean? How would you describe 24 inches squared to your partner? What might you draw to show this? Once you’ve answered these questions, watch the video through 2:22 and compare your drawing or description with what Emily and Mauricio have drawn.
2. [Pause the video at 8:07] When asked how 24 inches is different than 24 inches squared, Mauricio said the line is flat and Emily said the line “isn’t finding inside something.” Turn and tell a partner what you think this means by rephrasing the students’ explanations in your own words. How are 24 inches and 24 inches squared different?