Building and Naming Polynomials Activity

The idea for this building and naming polynomials activity started out like many of my ideas do. I start thinking about the topic I’m teaching, and I ask myself “What if…?” This week, the topic was polynomials, and the question I asked myself was “What if I could create some sort of puzzle for polynomials?” I tried running the idea by my husband, but he seemed terribly confused.

So, I went ahead anyway. I typed up my idea, cut out all the pieces, laid them in the living room floor, and asked my husband to solve the puzzle. The puzzle involves the names of eight different polynomials (such as 6th degree trinomial, quartic monomial, or linear binomial) and twenty different terms which must be arranged to form these eight polynomials.

All twenty of the term cards MUST be used.

It was interesting to watch my math teacher husband tackle this puzzle. He ended up placing some cards in such a way that he later ran out of the cards he needed and had to do some shuffling to make sure that he could properly make all eight of the polynomials with the given terms.

I asked him what he thought of the difficulty level of this puzzle, and he said it was just tricky enough to be at the right level for my Algebra 1 students. After watching my students tackle this activity for the last three days (my classes are in all different places due to a talent show we had this past week), I agree that this puzzle has enough different solutions to not be too challenging but requires enough rethinking and reshuffling pieces to still engage students and get them thinking.

I printed the polynomial names on orange paper and laminated each set.

Then, I printed the polynomial term cards on a different color of paper for each set. One thing I didn’t think of when designing my cards was that the orange polynomial pieces were too big for my snack bags!

I loved listening to students discuss where to start. Many of my groups decided to start with the monomials and work their way up to the longer polynomials.

The biggest issue students ran into was trying to make a linear binomial with cards like 9x and 2x. Whenever I saw this while circulating the classroom, I would stack these two cards on top of one another and remind students that we need to always combine our like terms. 9x and 2x are the same as 11 x which meant they only had a linear monomial.

Another issue my students ran into was ending up with term cards that couldn’t fit in the polynomials they had left to create.

One of the cards students are given is “+7x^8.” The students are asked to create a 10th degree polynomial and a 6th degree trinomial as well as a host of lesser degree polynomials. This means that there is only one polynomial that could possibly hold a term with an exponent of 8. 

Many of my students did not realize this until late into the activity. I had several groups try to place 7x^8 in a linear binomial. Almost every time this happened, the other partner would speak up and say why that wasn’t allowed.

This meant my students often had to take one term from one polynomial and then another term from another polynomial to fill that spot and so on in order to make everything work.

I’m super proud of how this activity turned out. I think that my students had a much better understanding of how we name polynomials after taking a turn at creating their own.

I believe that having to build polynomials with a pre-determined set of terms (in this case, a deck of polynomial term cards) made this a much more powerful and engaging activity than just asking students to create polynomials with the terms of their choosing.

Digital Version of Building and Naming Polynomials Puzzle

Google Slides Version courtesy of Liz Mastalio