Sasha and Keoni justify how their three methods for finding points on a parabola satisfy the criteria in the definition of a parabola.
Episode Supports
Focus Questions
For use in a classroom, pause the video and ask these questions:
1. [Pause video at 0:17]. The term vertex is written in green. What is a vertex? How do you know that it is on the parabola?
2. [Pause video at 0:46]. Sasha is pointing to a line. What how does that line help her find points on the parabola?
Supporting Dialogue
When students are working on the task in class, you can support dialogue as follows:
Invite students to reflect on the problem solving process, i.e., “When you were working on constructing a parabola from the definition, where did you get stuck?”
Invite students to reflect on how they successfully struggled, i.e., “What helped you get unstuck?”
Math Extensions
These questions allow students to extend the concepts and terminology from the episode:
1. You have explored parabolas by constructing a one from its geometric definition. Parabolas have other interesting properties. Satellite dishes are 3-d parabolas. Why is the parabola used for these satellite dishes?
2. Examine your environment. Do you see other examples of parabolas around you? How do you know that the shapes you are seeing are indeed parabolas?
MathTalk