Emily and Mauricio make sense of a new situation in which the length of a given garden is increased by 3 feet. They make a prediction about how this increase will affect the area of the new garden.
Episode Supports
Students’ Conceptual Challenges
The fictional student Jamal seems to face a common challenge for understanding and reasoning with two-dimensional quantities. Jamal claims the new garden will have an area of 23 ft2[1:22]. Presumably, he arrived at this value by adding the area of the smaller garden, which was 5 × 4 = 20 ft2, and the increase in the length of the garden, 3 ft. However, Jamal likely isn’t considering the total impact that increasing one dimension has on the area of the new garden. Coordinating one-dimensional and two-dimensional units is challenging for students, and understanding the relationship between them, especially as one of those units is changed, can be particularly difficult. Use prompts to draw the new garden and label dimensions and areas if your students seem to be facing this challenge.
Emily predicts the new garden will have an area of 65 ft2. She quickly backtracks and explains why she initially thought this—she added 3 ft to each of the dimensions, and then multiplied, rather than adding 3 ft only to one dimension (additionally, she might have transposed the digits of the product she found, 8 × 7 = 56).
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 2:01] Make your own prediction. First, do you think the area of the new garden will be greater than or less than 23 ft2? Next, what do you think the area of the new garden will be?
[Pause the video at 3:34] Do you agree with Mauricio? How might you use a drawing to investigate his claims?
Supporting Dialogue
[Pause the video at 1:32] Tell your partner how you think Jamal arrived 23 ft2. Do you agree with his prediction for the area of a new garden? Why or why not?
