Math = Love: Combining Like Terms and the Distributive Property Interactive Notebook Pages

Saturday, September 10, 2016

Combining Like Terms and the Distributive Property Interactive Notebook Pages

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 (blog posts here and here) 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.  

Here are our finished notes on combining like terms:

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!  

Here's the outside of our foldable:

And the inside:

Before we started any distributing, I had my students specify exactly what number they would be distributing.  I gave them lots of problems like 3 - (4x + 2) to emphasize that they would actually be distributing a -1, not a 3 like students often assume.

In the next column, we carried out our distributing.

Then, in my favorite column, we took all of our terms and put them in groups like we had with our cut-out term pieces the day before.  And, in the final column, we wrote our simplified answers.

When we start back on Monday, I want to give students equations and inequalities that have parentheses and terms to be combined.  I really want to drive home the fact that we can only combine terms that are on the same side of the equal sign or inequality symbol.  I still haven't decided how I want to structure these notes/practice, though.  Something to think about this weekend!  

Because we had already talked about terms, constants, and coefficients before starting this lesson, I think my students were able to progress through this lesson much faster than my students did last year.  When we reached the last column, some of my students wanted to know why we weren't solving for x.  I told them that we could only solve for x if we had an equation or inequality.  It was awesome to see some light bulbs go off in that moment as they realized that we had just ended up with an expression!  Here's the blog post I wrote about teaching students about terms, constants, and coefficients.  

Files for these lessons are uploaded here.  Fonts are Londrina Solid, Comic Zine OT, Caviar Dreams, and HVD Comic Serif Pro.  


  1. Thank you so much for blogging about this! I saw your Twitter post and had my fingers (and toes!) crossed that you'd share your files. As always, LOVE the awesome things you come up with and LOVE that you share!

  2. Idea...what if you had a student pick a value for x and plug it into the first expression and the last? and HOLY COW they're equal! then have a student pick another value and HOLY COW they're equal! I'm not sure that I ever really focused on the fact that when we simplify, these things are still the equivalent for any value of x. Like I would focus on the "how" but not the "what we're actually accomplishing"

    Then when you get to equations, start with an equation that has a weird answer like 147. Again ask students to pick values of x (and hope they don't pick 147). Oh, wait, these sides aren't equal! It ONLY works for this one special value of x (147). Or maybe have the answer be a smaller number that they might try (3?) so it would work if they chose that, but not for others?

    I'm kind of thinking out loud here but if I had to teach Alg I again I would really want to focus on the fact that expressions are true for any x; equations are true for a limited number of x, and functions are true for a limited-but-infinite (whoa...mind blown!) set of x and y values that we can display as a graph.

    Also one of teachers at school has the Ss draw a vertical "river" below the equation sign and you only change if you cross the river. I think the vertical line visual is very useful when they're just starting out, otherwise I get students try to simplify 2 + 3x + 5 by subtracting the 2 from the 2 and the 5!

  3. Love this! I'm using the distribute worksheet today. Small mistake on the last row? Should it be -2x2 + 7x - 2?

  4. Hello Sarah! I'm a college student studying to be a Middle School or High School Math Teacher. One of my Math Education teachers encouraged us to start following Math Blogs to gain knowledge and insight for our future classrooms. I stumbled upon your blog for an assignment last semester, so I've decided to return to it to better prepare myself as a future educator.

    I really like how the first day of the lesson really gave students the power to group the terms however they would like to do so. Not only that, but you have examples for one, two, and three-variable expressions. Having students construct their own expression makes it seem fun and easier when it comes time to distribute and combine like terms.

    The foldable is a nice way to tie things together, the grouping and the distributive property. Drawing the arrows from the number that gets distributed is a nice visual representation, as well as having each column of the table be one step in the simplification process. It's very easy to follow and gives students structure to build off. My one comment/suggestion would be to maybe incorporate a variable somewhere on the outside of the foldable. A student who is used to A,B, and C being numbers may get confused when they see the variable and not distribute it otherwise.

    Overall, I think this is a fun way to combine the distributive property with like terms while still adding valuable content to the interactive math notebook.

  5. Thank you so much for this. I think it will be a great way for them to organize it and understand it as well!