## Reflection: Intrinsic Motivation Name that Conic - Section 2: Investigate: Conics on Calc

I was getting a lot of questions from my students as they progressed into the second part of this activity where they needed to make generalization about the general form of each conic section. Students overall seemed unmotivated to find the generalizations, and I guess I don’t blame them. Why would they want to discover a short-cut for identifying what type of shape it is when it’s really not too difficult to just graph the general form of the conic section and then identify the shape using the calculator as a tool?

Once I noticed most of my students had completed the front side and grouped the equations on the back, I stopped the class and quickly read through the correct answers… while looking only at a blank page. I emphasized to students that they should be able to identify the type of conic sections they are looking at in general form within seconds, not the minutes it took to graph in their calculator. Their goal now was to find what rules I was using to quickly identify these. I encouraged students to find a rule that worked for all the given conic sections and to check it on some made up equations. I also told students we would be playing a speed game next. I think that helped up the ante.

Here are some sample responses from my students:

Conics on Calc, Student Response 1 – very vague answers with incorrect use of vocabulary

Conics on Calc, Student Response 2 –identifies the generalizations, but also some generalizations that aren’t always true (Also, uses ‘variable’ incorrectly… reminds me that I need to get my students writing more in math!)

Conics on Calc, Student Response 3 – Correct generalizations just not specific enough on Ellipses… a common issue for many of my students.

Conics on Calc, Student Response 4 – Three out of four generalizations correct, just missed that Ellipse again. I like how the student used the general form of a conic section to help describe the generalizations.

If there had been more time in class, I think this would have been a great opportunity for some class discussions. Did everybody’s generalizations work? Were they specific enough? Too specific? Must they always be true?

Intrinsic Motivation: Motivating Students to Find Generalizations

# Name that Conic

Unit 6: Conic Sections
Lesson 2 of 13

## Big Idea: Students develop their own system for quickly identifying a conic section in general form and then race to name that conic first.

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Standards:
Subject(s):
Math, standard form of an equation, Precalculus and Calculus, graphing calculators, conic sections, Conic
60 minutes

### Tiffany Dawdy

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