Polynomial Operations Cut and Paste Activity Answer Key

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Combining Like Terms Activity (Version 3.0)

I modified my combining like terms strip activity that I have used for the past two years. This year, I added a box for students to write their simplified answer in. I think it really helped them organize their work better!

Close-ups of each problem:

Combining Like Terms Activity (Version 2.0)

Our third skill this year in Algebra 1 is to be able to rewrite expressions, equations, and inequalities by applying the distributive property and combining like terms.  I was able to take how I taught these concepts last year and improve them (hopefully) for the better.  

I have a few students taking Algebra 1 with me for a second time due to failing last year, and they commented that I taught this way better this year than last year.  

I was multi-tasking (aka eating lunch) while I was doing this, and I ended up making a few arithmetic mistakes.  I think I fixed them all, though.

I gave my students the three expressions on a small piece of paper.  They cut them into individual strips of expressions.

Then, one at at a time, we cut the strips into their individual terms.  After making a pile of terms, I asked students to apply what we had just learned about the definition of like terms to put their terms into piles.  I would ask students how many groups of terms they ended up with.  

Different students grouped them differently, and this led to great discussions amongst my students.  They would back up their points of view with the definition which was awesome!

Here’s a student’s work on putting the terms for the first expression into groups:

Once we were all happy with how the terms were grouped, we glued them in.

I overheard a student say “This is fun!” as she was deciding how to put the terms into groups.  It was great formative assessment for me as a teacher to see how the lesson was going. As a class, we combined the coefficients or constants to form our final, simplified answer.    

On the next day, we continued combining like terms in the context of applying the distributive property.  I wanted to do this in a way that tied directly into the “grouping” of like terms we had been doing on the day before.  

I’m pretty proud of the way I came up with to do this!   We followed up this combining like terms activity with a distributive property foldable.  

Combining Like Terms Activity (Version 1.0)

This year, I decided to really emphasize combining like terms with my Algebra 1 students.  In retrospect, I should have done the same thing in Algebra 2 because they were still struggling with what they can and cannot combine.

I thought this would be a one day lesson, but it ended up taking my students two days to work through it.  There were lots of great conversations happening, so I think it was definitely worth it!

I gave students a quarter sheet of paper that had a note box and three polynomial expressions.

We began by taking some notes over what like terms are.  I really wanted to emphasize to my students that xy and yx are like terms, so I really pushed the “order doesn’t matter” this year.

I had them copy down the first polynomial strip in their interactive notebooks.

Then, the students had to cut the strip into terms.  This led to a great discussion of what a term is.  Students had to make sure they cut the strip so that each term contained the sign in front of it.  

Students were super careful to make sure they were cutting the strips correctly which is exactly what I was hoping for.

Next, I instructed students to group the terms into groups that were like terms.  This is where the best conversations happened.  After students sorted their terms, I asked them how many groups they had.  

When students realized they had sorted into a different number of groups, they started justifying their groupings to their classmates.  It was just awesome to see them pointing each other back to the definition of like terms.  

Finally, we decided on how the terms should be grouped.  

Next, I instructed students to glue in their groupings.  I intentionally did not tell them how to group them in.  Luckily, the students glued them in different orders which let us discuss the fact the order of the terms doesn’t matter.  

Finally, we circled the groups and combined the coefficients.  Since the students glued the groups in in different orders, their terms ended up in different orders.  I emphasized that this was okay as long as the sign in front of 21x was negative, the sign in front of 2x^2 was negative, and the sign in front of 4 was positive.

Next, they proceeded to do the next two problems in their groups.

The zero coefficients and invisible one coefficients freaked some of my students out, but they persevered.

Last problem:

We finished the class period off with two additional practice problems.  The kids were quite miffed that I did not give them strips to cut because how else would they figure out what the terms were.  To remedy this, many students drew “cut lines” between the terms to separate them.

I like this activity got students actually separating terms, grouping them, and combining them.  I hope I made an abstract concept a little more concrete and understandable for my students.