Reflection: Grappling with Complexity Rotated Conic Sections - Day 2 of 2 - Section 1: Launch and Explore

 

This is a lesson that can easily go off the rails. If I did all of the calculations on the board in front of the class then 90% of students would zone out. Here are some strategies to manage the students and to manage the logistics of a such a crazy equation:

  • As mentioned in the narrative, I split up each term after we substitute so the process will go quickly. If every student does the entire problem and we go over it, it can easily take up way too much time.
  • I have one student from each third of the class write their expanded term on the board. I stress that it must be correct because if we make one tiny mistake then the whole problem will be wrong and then we will have to start over. Students were very good about checking each others' work and discussing any disagreements they had.
  • I always ditch the prime symbols once we start doing the algebra. It gets too annoying to write them out every time and they start to look like ones. I make a big deal at the end to add them back in since this equation is now on the rotated axis.

  Strategies for a Smooth Lesson
  Grappling with Complexity: Strategies for a Smooth Lesson
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Rotated Conic Sections - Day 2 of 2

Unit 10: Conic Sections
Lesson 7 of 10

Objective: SWBAT eliminate the xy-term of a rotated conic section.

Big Idea: We know this conic section has been rotated, but how do we graph it?

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Subject(s):
Math, Precalculus and Calculus, rotated conics, conic sections, ellipse
  45 minutes
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