Math = Love: What in the World is a Polynomial?

## Friday, March 3, 2017

### What in the World is a Polynomial?

My Algebra 1 students are currently working through our unit on polynomials.  Whenever we begin working with polynomials, the first thing my students want to know is "What is a polynomial?"  I try to answer that before we do anything else in the unit.

The Oklahoma standards don't require that my students be able to classify expressions as polynomials or not or name polynomials, but I like to include these in my unit anyway.

We began with a frayer model about polynomials.  I told students exactly what to write in the "Definition" box and the "Characteristics" box.

After finishing these two boxes, we skipped the "Example" and "Non-Example" boxes.  This really stressed my students out.  But, I assured them that we would come back to them.

Last year, I had the idea to make a polynomial or not card sort, but I never carried the idea out.  This year, I read my blog post about last year's polynomial unit and saw my note to myself about making a card sort.  I wasn't really in the mood to make a card sort, so I decided to turn it into a coloring activity.  Students had to color in the boxes that contained polynomials.  If a box did not contain a polynomial, the students would have to write down what rule it broke that kept it from being a polynomial.

I was a bit tricky with some of them.  For example, my students unanimously agreed that x to the four over two power was not a polynomial because it contained a fractional exponent.  When I told them that it was a polynomial, they were flabbergasted.  Then, I challenged them to figure out why it really was a polynomial.  After a few moments of critical thinking, one student in the class would realize that four over two simplified to just two.  They knew that x squared was a polynomial.

After classifying these 12 as examples and non-examples, my students were finally ready to write their own examples and non-examples on their Frayer model.  I found that my students came up with much better examples and non-examples than in the past thanks to the intermediate coloring/sorting activity.

Next, we glued in a book that has definitions for the different parts of a polynomial.  Our copy machine at school likes to put black streaks on everything.  So frustrating!

Some of the definitions were familiar to students because we have been talking about them ALL year long.  For example, we learned about terms and coefficients during our very first unit of the year!

We've also been talking about constants for the entire year.  "Leading term" was a new vocab word for my students, though.

Also new were the terms "leading coefficient" and "degree."

I gave students two polynomials to write in their notebooks.  They went through each page of the book and wrote down the appropriate facts about the polynomial.  Students had to underline each term, highlight each coefficient, and circle each constant.  Then, they had to write down the number of terms, the leading term, the leading coefficient, and the degree of each polynomial.

Now that we have reviewed what terms are and learned what degree means, that means it's time to name polynomials!

As we were filling out this chart in our interactive notebooks, I was asking students to predict what would go in certain boxes.  One student started sharing answers which shocked the ENTIRE class.  They couldn't figure out how he already knew these weird words.

It turns out he had noticed the "Naming Polynomials" poster I had created and hung on the wall.  So, he already had the ENTIRE sheet of notes filled out.  The file for this poster is uploaded here.

I am pretty pleased with how this naming polynomials practice sheet I made for their interactive notebooks turned out!

Many of my students adopted this same format when naming the polynomials on their quizzes.

I think that the process of writing out the degree and the number of terms as well as the name of the polynomial helped my students to make more sense of what we were doing.  In the past, I have just had them write the name without the intermediate step.

After we practiced naming polynomials in our notes, we did a favorite activity of mine: naming polynomials speed dating.

I haven't turned this activity into a shareable digital file yet, but I definitely should do that in the future!  Right now, I'm just using index cards with polynomials written on the front and names written on the back.

My Algebra 1 classes this year are quite a bit larger than my classes in the past, so I had to write up a bunch of new index cards this year.

I give each student an index card with the polynomial facing up.  I instruct them to figure out the name of their polynomial.  When they have it figured out, they may flip over the card and check their answer.

Then, I instructed each student to stand up.  Here's where the "speed dating" comes in.  Students pair up.  Each person holds their index card so the polynomial is facing their partner and the answer is facing them.  Students take turns quizzing and coaching their partners.  When both polynomials have been named correctly, students switch cards and find a new partner.  The goal is to practice naming as many polynomials in as short a time as possible

It can be a bit chaotic, but the classroom is full of kids talking about math.  So, I couldn't be any happier than that!  Here's a few pictures of my students.  I had to block out the faces which made me sad because they always look so happy when doing this type of activity!

Files are uploaded here.