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Adding and Subtracting Polynomials Activity

Today I want to share an Adding and Subtracting Polynomials Activity I created for my Algebra 1 students.

One of our objectives in Algebra 1 is that students will be able to add and subtract polynomials.  My students are usually pretty good about remembering to distribute the negative when the second polynomial is written in parentheses with a subtraction sign in front. 

The state of Oklahoma doesn’t always write the questions in this format, though.  A favorite format of theirs is to give two polynomials and ask for the sum or difference. 

If the problem asks for a difference, students must realize on their own that they need to change the signs of the terms of the second polynomial before combining like terms.

adding and subtracting polynomials activity algebra high school math

I reviewed distributing a negative through a set of parentheses with my students as bellwork.  Then, I gave each pair of students a deck of cards I had created and a penny to simulate this specific question type.   

adding and subtracting polynomials activity algebra high school math

I printed all of the x squared terms on one color of paper, all of the x terms on another color, and all of the constants on a third color of paper.  Then, I laminated them and cut out the pieces.

Each pair got a bag of pieces and a penny.  The students’ first job was to sort the cards, face-down, into three piles by color.  To begin, they would turn over one card of each color to form the first polynomial. 

Then, they would turn over another set of cards to form the second polynomial.  Finally, students would flip the penny to determine if they were finding the sum or difference of the two polynomials. 

Heads meant sum.  Tails meant difference.

After creating their problem, both students would solve the problem independently on their whiteboard.  When both students were finished, they were supposed to compare their answers. 

If the answers agreed, students would use the cards to create a new problem.  If there was a disagreement, I would come over to help the students.

What I Loved About This Adding and Subtracting Polynomials Activity

  • Students got lots of practice.  No worksheet involved.  We did the first day back from Christmas break, so I wanted an activity that would help them transition from break mode to school mode. 
  • The pace of the activity was instantly differentiated. 
    • My advanced students worked through a good number of problems. 
    • My special education students were able to work at their own pace without having to worry about how many they had finished.  Instead, they could really focus on understanding the process.
  • The randomness of what cards were dealt and the result of the coin flip led to some great conversations with students.  For example, I would probably never ask students to find the sum of two polynomials that summed to zero.  It happened to a group of my students, though.  As a result, we got to discuss what happened when all of the terms cancelled out.  

What I Didn’t Love About This Adding and Subtracting Polynomials Activity

  • A few of my upper-level students soon grew bored of the activity.
  • Some of my groups seemed to have all of the luck and flipped heads each time.  I’m pretty sure a few of these groups had more than luck on their side. 
  • The activity was not self-checking.  

I did not come up with the idea behind this activity myself.  Actually, I combined aspects of several other activities to create my own. 

Pam Wilson did a version of this activity using wooden blocks and a penny.  I didn’t have any wooden blocks, and I was planning this at the last moment. 

So, I replaced the blocks with cards similar to this activity from Joy in 6th.

Free Download of Adding and Subtracting Polynomials Activity

Adding and Subtracting Polynomials Activity (PDF) (4084 downloads )

Adding and Subtracting Polynomials Activity (WORD DOC) (1843 downloads )

I’ve seen other teachers on twitter find lots of other creative things to do with these same cards as well!

More Activities for Teaching Polynomials


Wednesday 25th of September 2019

I plan to use your cards with a die - if the student rolls a 1 or 2, add, 3 or 4, subtract, 5 or 6, multiply. Thanks for doing the hard work!


Tuesday 7th of February 2017

My students are starting Quadratic Functions. Do you have any resources that can help.

Sarah Carter (@mathequalslove)

Friday 3rd of March 2017

Check out the quadratics "tag" on the right!


Monday 7th of March 2016

I can not open the link either. Would you mind sending it to me. Thank you so much! wflutterbiinjax[at]

Sarah Carter (@mathequalslove)

Tuesday 29th of March 2016

E-mail sent!


Sunday 22nd of November 2015

Hello Sarah. How are you? I like your idea. It's simple and easy to understand. Can I use it for my students? I am also teaching Math. You must be a good teacher. I'd like to be like you... :)

Sarah Carter (@mathequalslove)

Monday 23rd of November 2015

Please use! That's why I posted it! :D


Wednesday 4th of November 2015

I am a high school para and I am always looking for manipulatives to help our identified students be more successful, expecially in our algebra II classes. Can't wait to start creating these tomorrow. Thank you.

Sarah Carter (@mathequalslove)

Monday 9th of November 2015

Glad you can use these with your students!

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