Modeling Addition Algebraic Equations

The last couple of weeks, my classes have been learning to solve equations using the different operations. The first type of algebraic equation we learned was equations involving addition. As you can tell by my other posts, I love to use hands-on manipulatives. I love to have my students model problems. I love to have my students draw pictures of them. I find that when I use this process, I can keep ALL of my students engaged, excited, and ready to learn when they get to “play.”

Here is how my students learned to solve addition algebraic equations…….

First of all I am giving you a packet of printables that I made for all of this. The first few pages in this packet is an equation mat, and two different sets of a cup and counters. The first set are blank and the second set has positive signs and negative signs…… Here is a picture of the equation mat and counters that I made. I printed the equation mat on red paper and the cup and counters on blue paper (I buy them in reams at Sam’s).

Equation Mat and Counters

There is also a page that has a template for an envelope to hold the cup and the counters. I had my students glue it to the back of their equation mat. I three-hole punched the equation mat so that my students could put them in their math binder (that’s a whole other post that I need to type up for you).


The concept of using the cups and counters is not new at all, in fact our text books used that method for modeling. Last year, I used actual little bathroom cups and two-color counters. This year, I chose to have the students cut their own out so that they could keep them and take them home with them.

Basically, you use the cup as the variable and the counters as the numbers. For addition equations, make sure students understand that what they do to one side, they must also do to the other side. If they a cup and two counters on one side of the equation sign and ten counters on the other side. To know how many are only in the cup, they must take away the two counters on the side with the cup and also on the other side. This leaves them with the cup equals eight. That is a very quick, short version of the lesson. In the packet, there is a page of example equations for the students to solve using the cup and counters. After doing a few examples using the cup and counters (the number of examples depends on the understanding of my students), I have my students get out a sheet of paper and we do some examples with the students drawing the models. After they get the hang of it for sure, then we start doing it without drawing.

Included in the packet are also a couple of models for setting up word problems. These worked extremely great for my students. Here are some pictures of how I used them.

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 Click on the image below to get your free packet!!

Cup and Counters Picture I hope you find these handy and useful! I am currently in the process of making many more games and activities for students to practice and reinforce these skills. Let me know what you think about all of this in the comments below!!

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