Keoni and Sasha reflect on why increasing the p-value results in a wider parabola. They engage in algebraic reasoning to support their argument.
Episode Supports
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 1:03]. How did Sasha get the equation y = 1/p?
2. [Pause video at 2:17]. What does a smaller y-value have to do with the shape of the graph?
Supporting Dialogue
Provide opportunities to revoice the mathematical ideas of others:
1. Revoice what Sasha and Keoni noticed and justified about how a change in the p-value impacts the y-value of a coordinate with a fixed x-value.
2. Revoice what Sasha and Keoni noticed and justified about how a change in the p-value impacts the shape of a parabola.
Math Extensions
1. Find the coordinates of points on each of the three parabolas when the x-value is 1.5.
2. Considering the ordered pairs that you found, what do you notice about the y-values when the p-value increases? How does that impact the shape of the parabola?
MathTalk