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.  

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