No captions Captions Stop the video above first if it is playing.
No captions Captions Stop the video above first if it is playing.
Keoni and Sasha develop an equation that relates the x-value to the y-value for a general point on a particular parabola.
Episode Supports
Students’ Conceptual Challenges
Students might wonder how to interpret more than one symbol in a general equation. Students are often asked to isolate a variable on one side of the equals sign with a number on the other side, e.g., they “solve for x” by finding a numerical value for x. Having it make sense that the symbols are representing a general point in the parabola is challenging.
Keoni protests “but there are two variables” when Sasha writes (y–1)2 + b2 = (y+1)2[1:11-1:34]. By going back to work through a specific example 62 + b2 = 82, Sasha and Keoni identify the method to solve for b in the general case [1:47-4:50].
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 1:34]. What problem are Sasha and Keoni trying to solve?
2. [Pause video at 2:44]. Sasha and Keoni are working to solve for b. Work ahead from here. Then we will compare our work with theirs.
Supporting Dialogue
Invite students to engage in revoicing. Place a blank student worksheet under a document camera.
1. Can someone come up to the graph to draw and label the right triangle that Sasha and Keoni used in this problem?
2. Ask a student to revoice how a fellow student determined the side lengths.
Math Extensions
Use the Pythagorean theorem to represent the lengths of the right triangles described below.
1. A right triangle where one leg is half the length of the other leg.
2. A right triangle where the two legs are the same length.
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