In order to emphasize the similarities and differences of the equations for conic sections, I created this flow chart that the students filled out and used once they had learned all four conics. Before the flow chart, every time a kid would say, "Mrs. Peterson, is this a hyperbola?!" I would go through the same questions with her:

"Are both variables squared?"

"No."

"Good. So you know it's not a...?"

"Parabola."

"Awesome. Now are the squared terms being SUBTRACTED?"

"Yes. Oh! Yeah, it IS a hyperbola."

I got tired of going through these questions over and over and over. Also, I don't think the kids realized the order in which I was asking the questions, which didn't do much for them except answer the immediate question.

So, now, instead of answering their question with a string of my own questions, all I have to say is, "Do you have your flow chart out?" Much less work for me. A little more work for them. And they're

**reading**.

The wording isn't perfect. I don't know how to succinctly differentiate between the ellipse and the circle in standard form. This is the best I came up with. Of course, then kids think as soon as an equation has fractions in it, it can't be a circle. That's not really what the wording says, but I totally understand the confusion. I combated the confusion the lazy way: all our circles' centers were (m,n) when m and n were both integers.

Another good thing: this flow chart can be easily changed to classifying conic sections in general form. I just had the students take a few extra notes on the side (such as changing

*different denominators*to

*different coefficients*), and they were good to go.

All in all, conic sections went very smoothly. And now onto exponential and logarithmic functions!

Would it be any better to ask: "Are the co-efficients of the variables the same?"

ReplyDeleteMaybe so. I went back and forth on that one. The kids seemed to respond well to "look for differences," but maybe I will word it the other way around next year and see if that changes anything.

DeleteSue

DeleteThat is certainly how I've approached it and I point out that fractions are coefficients just like integers are.

Hey - I have a question for you. My school is starting a STEM initiative and our director has an idea for a Saturday math open house for elementary and middle school kids. Sam Shah suggested that you might be a source of wisdom on an issue like this one. Any advice?

Thanks in advance

Jim Doherty (jdoherty@wyomingseminary.org)

Oops, I didn't mean to change the same/different part. I meant to change denominator into co-efficient. I still have no idea whether that would work any better.

ReplyDeleteI'll email you, Jim. (I'm at mathanthologyeditor on the g mail system.)

Ah, I see. :) Yes, yes, I agree.

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ReplyDeleteGreat blog I enjoyed readinng

ReplyDelete