Monday, April 14, 2014

Polynomials and Rational Functions

My polynomials and rational functions unit has passed me by and I didn't stop to post about it!  So here it all is in one post.

I started polynomials with the end behavior activity that I blogged about before.  After the activity, I gave them this foldable to summarize what they'd discovered:

End Behavior Foldable

The next day I gave them this to put in their notebook and we did this activity.

Zeroes and Multiplicity for INB

The next day we did this worksheet

Multiplicity Worksheet

We then took our first assessment over polynomials.  Up to this point, all of the polynomials we had worked with were already factored and had rational zeroes.  To prepare to work for polynomials that weren't factored and that had irrational or imaginary zeroes, we took a day to talk about synthetic division (something they have already done in Algebra II).  I gave them this for their notebook and we did a worksheet from Kuta over synthetic division.

Synthetic Division Handout

Next I gave them this to put in their notebook and we did a worksheet from my Nasco Joke Worksheet book:

Finding All Zeroes of a Polynomial

We then took our second assessment on polynomials.

Next up was Rational Functions.  Day 1 was a foldable and a little worksheet to practice using the foldable.

Rational Functions Foldable

Rational Functions Flower Activity

Our second day with rational functions found us doing this activity I got from Rebecka Peterson.  I <3 Desmos!
Rational functions day 3 was this matching activity I found on Teachers Pay Teachers.  Students worked in pairs to match up all of the cards.
Day 4 was this asymptotes sudoku puzzle, also from Teachers Pay Teachers.
Day 5 - Rational Functions Assessment

So there's a quick and dirty rundown of what's been going on in my class the last couple of weeks.  I REALLY like how I did this unit this year.  With the graphing technology available to students, I feel like things like Descartes Rule of Signs and the like are just outdated and unnecessarily confuse what should be a simple concept like the Fundamental Theorem of Algebra.  My students really seem to get that the number of zeroes a polynomial function has is determined by its degree.  They get how to determine end behavior and they get what effect the multiplicity of each zero will have on the graph.  Their first line of attack in finding zeroes is to use graphing technology and then they know they can use synthetic division and the quadratic formula if they can't get the whole picture just from their calculator.
Following polynomial functions with rational functions let them further see the value of being able to find zeroes of polynomials as the zeroes of the numerator and denominator are used to find holes, x-intercepts, and vertical asymptotes.  They were such pros at finding zeroes at this point that analyzing and graphing rational functions was a piece of cake!