Math = Love: Cutting and Pasting to Combine Like Terms

## Tuesday, December 1, 2015

### Cutting and Pasting to Combine Like Terms

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.

File for this lesson found here (PDF and PUB).

1. What a great lesson idea! My 7th grade pre-algebra and 8th grade algebra students struggle with this concept! I can't wait to use this as a review activity next year.

I have also used one where students have a grid filled with terms, and they have to color the like terms the same. I think the actual manipulating terms and moving them around would be so much more effective!

2. My students thus year have struggled a lot with using the sign in front. This activity would be great to help with that. Thanks for sharing!

1. Thanks Kathryn!

3. I think the cutting apart is the key! It's what I finally stumbled upon myself after way too much confusion with the signs when I was just teaching kids to box and circle like terms. Physically cutting apart terms and putting them together really turned the lightbulb on for many of them.

1. Now, if only we could figure out how to cut paper without getting it all over the floor...

4. I think this is such a great idea, especially as I am a huge fan of using hands-on activities in the classroom! I would love to do this in one of my algebra classes next semester. I think physically cutting apart the terms is a great way to help with the confusion of which sign belongs to which term. Thanks for sharing!!

1. You're welcome!

5. I like that you had students use interactive notebooks and different colors throughout the notebook.

6. Great lesson! Makes me miss math! :)

1. Thanks, Nancy! You sure make teaching German look fun with your blog posts and #Teach180 tweets!

7. Sarah,

I decided to try this out with my on-grade 7th graders. I told them that this was something another math teacher (you) was using with her high school students, and that I wanted to use it now to help avoid having to spend a bunch of time on it in high school. They definitely got the hang of cutting, sorting and gluing, but since we're still working on combining positives and negatives...actually combining the groups was a challenge for them. Thanks for making this available! Oh, and I had one student call out to another "Order doesn't matter!" That made me smile.

1. I think it's so awesome that you're doing this with 7th graders!

8. Hi Sarah! As I looked through many of your blog posts of you lessons, I noticed that you almost always include activities that add some fun to mathematics. I think this is extremely important in keeping your students engaged and spicing up the content so that it is not boring for your students. As I move on to student teaching this spring semester, this is one thing I want to practice more in order to master. We also discussed the importance of including a variety of question types for your students in my math course this past semester. I think that you do a great job of this in your polynomial lesson. Students first get a hands on opportunity to manipulate the terms. In the second set of questions, you omit the +/- so that students will need to figure out what terms have the coefficients. Finally, in the additional practice, students aren’t given number strips to cut. In this case, your students adapted and made “cut lines.” I really like the lessons that you post as they give many wonderful teaching ideas and activities. I also feel like the way you teach math has a very constructivist like approach, which is how I plan to teach mathematics in the near future.

1. Thanks for the thoughtful comment!

9. For Additional Practice problems, kids can use different colored highlighters to identify/group/color like terms.

10. Thank you so much. This is exactly what I needed.

1. You're welcome!

11. Sarah I really like this activity! My students have always struggled with the meaning of "like terms" and I had run out of ways to explain it. I'm trying this in my class tomorrow. Wish I'd found this site earlier.

12. simply WOW. I loved this activity.