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
In this episode, Mauricio and Emily have decided to find the area of each slice of pizza so they can evaluate the fairness of the proposed trade. Emily uses the unit “inches” while Mauricio offers the unit “inches squared” [1:55]. The pair settle on inches squared, but it isn’t clear that they have a full understanding of what that unit of measurement means. This episode presents an example of students who seem to have a procedural understanding of how to calculate area but may need more work to build conceptual understanding of that measurement.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 2:31] What did Mauricio and Emily calculate just now? What do you think area means? Why did Mauricio use the phrase “inches squared” and what does that mean?
Supporting Dialogue
Emily and Mauricio point out that the two slices are different—they have different lengths and widths [3:05]. However, the two students say it is a good trade because each person will get the “same amount of pizza they are going to eat.” Can you rephrase their argument in your own words—why is this a fair trade? Why will each person get the same amount of pizza even though the two slices look different?
