Mauricio and Emily make sense of a situation in which both the length and width of a rectangular office are increased by 3 feet. They make a prediction about how these increases will affect the area of the new room.
Episode Supports
Students’ Conceptual Challenges
In this episode, Mauricio and Emily are asked to predict and then find the difference in area between two offices, one of which is 3 ft wider and 3 ft longer than the other. Their initial prediction is 9 ft, which seems to make sense to the pair, since 3 × 3 = 9. However, this product only accounts for one part of the increase in area and is indicative of a common challenge students face when multiplying binomials (and mixed numbers such as 2½ × 3¼). Later in this lesson, they use a drawing to identify the portion of the larger area (Jazmine’s office) that corresponds to 3 × 3 and also investigate the portions of the larger area that they missed.
This episode highlights an ongoing challenge of using correct units and notation. As mentioned above, the pair makes a prediction that the office will be 9 ft larger, not 9 ft2. Later [5:20] they have a brief discussion about whether the unit should be feet or square feet, and they settle on square feet since they are measuring area.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 1:34] Make a prediction: How much more area will Jazmine’s office have if it is 3 ft wider and 3 ft longer than the other office?
[Pause the video at 7:29] Emily and Mauricio predicted the difference in area would be 9 ft or 10 ft, but later found the difference to be 63 ft2. What is the difference between a foot and a square foot? Which unit of measure is appropriate for this task?
Supporting Dialogue
[Pause the video at 2:40] Talk with your partner and compare your predictions with the ones made by Emily and Mauricio: 9 ft and 10 ft bigger. Is there anything about their predictions you’d change?
[Pause the video at 6:00] Emily and Mauricio have found that the office will be 63 ft2 larger, which is not what they predicted. Talk with a neighbor to discuss why the prediction might have been so far off, and why the difference in the areas of the two offices is so large when each dimension is increased by only three feet.
