Sasha and Keoni generalize their “short cut” method from Episode 3 by solving x = √(4y) for y.
Students’ Conceptual Challenges
Students often find tasks like the following challenging: “Solve x = √(4y) for y”. In part, that’s because their conception of solving the equation is to produce a numerical value for y.
By generalizing their method for solving for y when x takes on different values [see 0:42 – 1:27], Sasha and Keoni are able to rewrite the equation successfully [1:57-2:12].
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 1:27]. Summarize Sasha and Keoni’s method for solving x = √(4y) for y when x is known.
2. [Pause video at 1:50]. Sasha just said, “What?” What is different about this request to solve for y?
Ask students to relate this mathematics to other math from school by asking:
Where else in our math class have you been asked to solve an equation with two variables for one of the variables (like Sasha and Keoni rewrote x = √(4y) in terms of y)?
1. Sometimes equations can have more than one variable. Solve the equation below for x. Solve the equation for y. Which is easier?
x2 + 25y2 = 100
2. Are there some values of (x, y) that you can see will or will not satisfy the equation without solving for x or y? What are your strategies?