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.

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.   

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.