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A K–8 resource to support deep comprehension of math skills and concepts

#### October 11, 2016 6-8-expressions-and-equations

One of the most challenging Grade 8 math topics to teach is systems of equations. Activity-based lessons are one way to go when you are trying to teach students; I also like to use online videos. But the most helpful thing I can share with you from my experience is the template that I have developed in order to help students solve a systems of equations activity using the substitution method.

## Teaching Systems of Equations

I do not remember having to solve systems of equations until I was in high school. Nonetheless, in the Common Core State Standards, it is part of the curriculum for every middle school student. In fact, it is the pinnacle of the Grade 8 algebra part of the curriculum. Students are pulling together ideas about solving equations, graphing linear function using slopes and intercepts, equations with many and no solutions, and translating word problems to algebraic models. Solving a systems of equations activity is a lot of work for a young mind!

I like the sequence that my current textbook uses to teach students these skills, which is to first solve systems of equations using graphing, then substitution, then elimination, followed by equations with many and no solutions. By using a graphing systems of equations activity first, students are able to take a visual approach to what a solution to a system is. Following it with the substitution method gets deep into algebraic manipulation (which is where the downloadable template comes in). I like its placement here because this way I still have the rest of the unit to help students who struggle with the length of the process or the algebra itself.

When students encounter the third phase of the unit, solving a system by elimination, it is like a breath of fresh air. Students sometimes say, “Why didn’t you teach us this first?” My typical reply is, “You would have never worked on learning substitution if I had taught you elimination first!” Ending with systems with no or many solutions is helpful because it allows students to compare and contrast the different methods, choosing one based on the structure of the originally-stated systems of equations activity. In this culminating part, of the unit we can have rich discussions about why students choose substitution vs. elimination.

## A Template to Help Students Solve Systems of Equations

So, let’s get back to the template. Since students struggle so much with the many steps of any systems of equations activity, I use this template to help with the process. Some students will use the template a couple of times, then set it aside because they have a good sense of the steps. Others who tend to struggle a little more with just solving one-variable equations can use the template as a guide for the process.

Within each box, they focus on one aspect of the process, then an arrow shows them whether the next box for the next step is. They can feel free to focus on the algebra task in each box (solving for y, substituting, simplifying, finding x once y is known, checking solutions) and then take a step back to see what’s next in the process.

I hope you find this template as helpful as I have. Download it when you are teaching a systems of equations activity. This template is set up only for systems of equations where you substitute for y. I always teach these first and then integrate solving for x with students who are comfortable with the process. I use the same template for students who are solving for x, and have them relabel the template.