The students draw a picture of a new garden when the length of the original garden is decreased by an unknown amount. They explore how to use algebra to express their two general methods for finding the area of the new garden.
Episode Supports
Students’ Conceptual Challenges
Early in the episode [1:46], Emily tries to add on to the garden while Mauricio argues they should draw a line inside of the old garden. It isn’t clear if Emily misunderstands the directions or if she is unclear about what it means to decrease by an unknown length. Look for opportunities to have your students clarify the task for each other as Mauricio does for Emily.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:46] Before watching Mauricio and Emily, try this task for yourself. Draw a picture to help you find the area of the new garden when its length has been decreased by some unknown number of feet.
[Pause the video at 7:34] Can you argue for why the segment that Mauricio points to with an arrow has a length of 12 – L?
Supporting Dialogue
[Pause the video at 4:12] Using the variables Emily and Mauricio have chosen, talk with a partner about what expressions and equations you think the pair of students will write.
[Pause the video at 9:09] Before listening to Emily and Mauricio, talk with a partner to describe where you see each part of the equation 9 × 12 – 9 × L = NGA in their drawing. Where is the 9? What about the 9 × L? Why is there a minus sign?
