The students reflect on the meaning of the equation from Episode 5: (y + 4) • (y + 3) = y2 + (4 • 7) + (3 • y) + 12. They let y = 2 inches and create a drawing that shows both the original and new piece of fabric. Then they reflect on the meaning of the equation in terms of lengths, widths, and areas.
Episode Supports
Students’ Conceptual Challenges
Emily seems to conflate lengths and areas in this episode. For example, when asked about where she sees the expression 12 (which is the product 3 × 4, and is an area in square inches), she draws a line indicating a length along part of the new rectangle [9:36]. Keeping track of units and measurements in both one and two dimensions is challenging. To help, redirect students to the picture and ask them to point out where they see particular expressions and values. Ask for clarification as needed.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:49] Make your own drawing before watching Mauricio and Emily make theirs. If the original square fabric has a length of 2 inches, what will the new rectangle of fabric look like if the length of the original square fabric is increased by 4 in and the width is increased by 3 in?
[Pause the video at 8:22] Where do you see y + 4 in the picture? What about y + 3? What about the other expressions in the equation (y + 4) • (y + 3) = y2 + (4 • y) + (y • 3) + 12?
Supporting Dialogue
[Pause the video at 3:20] Mauricio is about to connect parts of their equation with their drawing (for example, by stating where he sees 2 + 4 in the picture). Before he does so, talk with a partner about the connections you see between the equation (2 + 4) × (2 + 3) = 22 + (4 • 2) + (2 • 3) + 12 and the drawing.
