# Parabolas Lesson 4 Episode 4 (Teachers)

### Exploring

Sasha and Keoni generalize their “short cut” method from Episode 3 by solving x = √(4y) for y.

### Episode Supports 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].

Focus Questions

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?

Supporting Dialogue

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)?

Math Extensions

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?