Emily and Mauricio discuss the meaning of distributivity in the equation and drawing from Episodes 5 and 6.
Episode Supports
Students’ Conceptual Challenges
This episode features Emily and Mauricio reasoning about the equation (y + 4) • (y + 3) = y2 + (4 • y) + (y • 3) + 12 to identify where they see the distributive property. This is challenging work! Binomial multiplication utilizes the distributive property, but it might not be easy for students to see. In the equation above, one might see the distributive property in several ways, or being used multiple times. For example, one could think of (y + 4) as being distributed to each of y and 3 from (y + 3), yielding (y + 4) • y + (y + 4) • 3. Each term on the right side of that equation could then have the distributive property applied again to result in the expression y2 + (4 • y) + (y • 3) + 12.
Focus Questions
For use in a classroom, pause the video and ask this question:
[Pause the video at 6:08] Can you use reasoning that is similar to Mauricio’s and use the distributive property to find the missing areas? Try to connect your ideas to the picture of the new fabric.
Supporting Dialogue
[Pause the video at 0:57] Examine the equation and the drawing. Talk with a partner to identify what looks like “distributing” and then listen as Mauricio and Emily share their ideas.
MathTalk