Math = Love: Emphasizing Polynomial Vocabulary

Wednesday, October 7, 2015

Emphasizing Polynomial Vocabulary

Polynomials are one of my favorite algebra topics to teach.  It's the type of topic that sounds scary.  But, I love getting to show students just how un-scary these problems can be.  Every year, my explanations are getting clearer, and I'm more in tune to what students are going to find frustrating.  This year, we're flying through polynomials in Algebra 2 really quickly.  Things seem to be clicking after the first explanation.  Yay!

Here's what things look like this year:

A polynomial frayer model.  I gave students the top two boxes.  They had to come up with examples and non-examples as a class.  Next year, I want to add a polynomial/not a polynomial card sort.

Next up: Parts of a Polynomial

In the past, I've always jumped straight from definition of a polynomial to naming polynomials.  And, my kids have always struggled.  This year, I decided to add in two intermediate steps.  This added an extra day, but I think it's already paid for itself by speeding up things as we move along through the unit.

I made a poof booklet to explain how to identify the different parts of a polynomial.  Then, we did two examples together.  Students later did a few more examples on their own.

I felt like the cover of our poof book was a bit lacking.  Next year, I'm totes going to add some cute clip art.

Students were asked to underline the terms and highlight the coefficients.

Then, they circled the constant if it existed.  They rewrote the leading term below.

Then, they identified the leading coefficient and the degree of the polynomial.  We were only dealing with single-variable polynomials.  I didn't teach them to find the degree of x^2y^2 - xy + 5.

Only one student noticed my missing "L" in "LABEL."  I didn't even notice it.  Sad day...  I hate when I make typos.

Things I liked about this: students weren't confusing degree and number of terms.  This re-emphasized that terms take the sign in front of them.  This will be important throughout the year.  It was another chance to practice spotting invisible numbers.  I made them write in the invisible coefficients.  It helped set us up for our discussion of standard form!

Students did an entire quiz (only 2 questions, but still...) over labeling the parts of a polynomial.

On the same day as the polynomial frayer model + parts of a polynomial, we also did standard form.  

All of a sudden, the phrase "leading term" made sense.  Yay!

I used this to fit in distributive property and combining like terms practice.  My Algebra 2 students are still struggling a bit with combining like terms.

Then, naming polynomials.  Since I had already covered the parts of a polynomial on the previous day, I made a new naming polynomials graphic organizer.

We did naming polynomials speed dating.  I still had my set of cards from last year.  This was one of the activities featured in the audio of my NPR story.    

Here's an example of two of the cards:

Each student gets a card.  One side has a polynomial written on it in marker.  The other side has the name of the polynomial written in pencil.  Students stand up and pair up.

The goal of speed dating is to get to know something about the other person as fast as possible and to exchange information in case you later decide you want to get to know them better.  The goal of this activity is to figure out the name of the other person's polynomial as fast as possible, to exchange information (trade cards), and find a new partner to get more practice.

In this example, one player would tell the other that he/she was a linear monomial.  If correct, the person congratulates them.  If incorrect, he or she is to be coached by the person holding the card.  Repeat for the quartic polynomial.  Trade cards.  Repeat with another person.

It's fast-paced, it's loud, it's fun.  It's full of math talk.  It's everything I want an activity to be in my classroom.

Here's the front of some of the cards:

And the backs:

Naming polynomials went so much smoother this year!  Spending a day on vocab really, really helped my kids gain confidence.  

I already posted about factoring the GCF out of polynomials here.  

Up next will be adding/subtracting polynomials, multiplying polynomials, dividing polynomials, and factoring polynomials.  So much fun still to be had! 

Downloadable Files:


  1. I am so definitely going to use these when I get to polynomials with my Algebra 1 kids! THanks so much for sharing!

  2. The Parts of a Polynomial file is empty :(

  3. Sarah, so glad you posted this! I'm a few days behind you (starting polynomials on Monday in Alg 2) so I plan on using this! thanks so much!!

  4. It's such a great feeling when you teach something the second or third time and can see changes you've made helping students understand better!

    I've got to find a way to use the speed dating concept in German class...

    1. Yes! I think you could definitely use speed dating in German. I know my kids love getting out of their seats, and they end up doing a lot more practice with a lot less complaining this way!

  5. Hi Sarah,

    Is there a single word, for a monomial, without the coefficient?

    In other words, the third monomial in

    5x + 3y + 6xy^2

    is 6xy^2.

    The coefficient here is 6. But what is the product of x and y squared called? Is it just called the variable part of the monomial? Or is there a shorter term for it?

    1. That is a very good question I do not know the answer to.

  6. The standard form file only has a publisher file. Could you add a pdf file as well like the others have? I can't wait to use these ideas when we get back from Christmas break!!

    1. Should be fixed now. Thanks for letting me know!

  7. How do you fold the booklet? Thanks for sharing your resources!

    1. Instructions found on this post:

      Good luck!

  8. Thank you Sarah, I will use your work to introduce polynomials in english to my italian class. We call this CLIL = content and language integrated learning and I'm always hungry for ideas to do it. Your work is simply perfect for me. All the best, Francesca