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