Math Atheist

Math Atheist

Wednesday, January 16, 2013

End Behavior of Polynomials - "Pharaoh Dance"

So I was teaching my students about end behavior of polynomial functions, and I realized I needed something other than a pretty chart to help them remember the different options for the end behavior (they still got the chart just in case).
I decided that I would use the 7+ years of dance class experience to good use, and I came up with a (sort-of) dance of all the end behaviors.

As I'm sure you know,  the end behavior of a polynomial depends on two things: the degree and leading coefficient.  If the degree is EVEN, both arms go the same direction.  If the degree is ODD, they go the opposite direction.  This is the first thing I established with them (Remember, odd means "different", so the arms go different ways).  The direction is dependent on the the leading coefficient.  As long as they could determine the degree and leading coefficient, the students could use these four moves to remember the end behavior.

The first is an even degree with a positive leading coefficient.  I shortened this to "even and positive".
It looks like a referee after your team scores a touch down (which is a positive thing, by the way).

Even/Positive
Next, is even and negative.  For this one, flip the "touchdown" sign upside down.  I call this one "no goal" or "no touchdown" (which is negative for your team).  It could symbolize dropping the ball before scoring.
Even/Negative

Next is odd.  This is where the pharaoh description comes in.  The odd degree polynomials look like the arms of a person doing the pharaoh dance.  You can figure out a way to help them remember that a positive leading coefficient goes up on the right and negative goes up on the left.  I told them that Ms. Avery is right handed, and I think very positively about my right hand.  Using my left hand would be a negative thing.  Of course, you can use what you want.  I would love to here what you come up with in the comments.
Odd/Positive
Odd/Negative
                                                                                 

      **Remember that your arms are a mirror image for your students, so you might want to turn around when demonstrating the moves.**








The final product is four moves that they can do on command.  The dance in order sounds like...
"Touchdown (1st move), no touchdown (2nd move), pharaoh (3rd move)...dance (4th move)"

I also called out random descriptions, and they had to show me the move.  I have a video that I might post later.

Happy Dancing!

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