Solving Equations – Do/Undo Method

I dearly love to teach solving equations. I could spend the entire year on just this one concept. Wait a minute…isn’t solving equations, of any type, 80-90% of the algebra curriculum already? Well, that might explain my love of algebra.

 I do love solving equations and I look forward to teaching this at the beginning of the school year. An algebra student typically comes in with equation solving knowledge. However, we have all experienced students in our classrooms who had not mastered the prerequisite desired of a beginning algebra student. In this segment I want to talk about the ways that we can vary the instruction in the beginning so that students master the concept of solving equations, even if they did not come to you class with the desired prior knowledge. 

 There are many methods of teaching equation solving, including buying expensive manipulative materials such as equation boards and balance beams. I personally have not experienced any product out there that does a comprehensive job of teaching students to solve equations. That’s not to say that I do not believe in using manipulatives during the instruction process. Everything that you’d need to teach students to solve equations is within your classroom or school. Balance beams from your science teachers may be helpful in addition to white boards/laminated papers, markers/color pencils and two color counters or even simple object such as textbooks and binders. Using manipulatives will allow your tactile and visual learners to grasp what is going on during the solving process. Lastly, I cannot discount the wonderful websites out there that have applets that provide students reinforcement of understanding the solving process. I will share those with you in a bit.

 I will start with your most challenging algebra student, those who do not come to your class with the desired equation solving ability. Start with a review of basic integer operations as well as the definition of subtraction. For this method it will be essential for students to recognize situations such as x – (-2) is really x + 2 and x + (-3) is x – 3. To evaluate an expression it is essential to follow the proper order of operations. To solve an equation is to undo the order of the operations that were done to the unknown value. To do this we must reverse the order of operations. While this method does not take care of all the types of equations students will be solving algebra, this will assist in students understand the concept of opposite operations while maintaining equality. It works nicely to use a “Do/Undo” table. When given an equation, students fill in the left side of a table that explains what has been done to the variable. Then they simply fill in the right hand side of how to undo the operations that were done initially. See the attached file for examples and explanations to this method.


This table is essential for students to be successful with solving equations. It breaks down the steps into smaller parts, more manageable for students who are not the strongest algebra student. As students master solving basic multistep equations, other strategies for solving equations can be introduced. The underlying theme in solving equations is that what is done to one side of the equation must be done on the other side as well. This will call for the use of the distributive property in many cases. I will look at more sophisticated methods of solutions in further posts. If there is one thing that I can leave you with on this post, I would stress to students that there is more than one way to solve an equation. Flexibility and strategy are key elements in solving equations.

 Online Resources

National Library of Virtual Manipulatives

A wonderful resource and an easy to use app; however, I’m not such a fan of “throwing away” blocks from both sides to show division. Division to me is a regrouping. There’s no opportunity to show that regrouping aspect here.

 MathsNet: Interactive Algebra


            This is a great app for students to use at home when practicing. I find it very easy to use and following the natural solving process, even with the variability as to what step you take first. What I like most about this app is that it takes on the direction the student wishes to take. The one drawback is that there is an assumption that what is done to one side is done to the other side of the equals sign by simply typing in one command, such as +6x or ÷2. I’d personally like to see students enter this information under particular terms on each side of the equals sign to reinforce the properties of equality.

 Explore Learning


            This site has wonderful apps for students to manipulate across the pre-algebra curriculum, including the basic one and two step equations. They also have integer applets that can be utilized beforehand to sharpen those skills. The equation apps follow similar strategies and the integer practice problems. The drawback to this is that it costs. Check with your site technology person and see if your school has a site license for this product and if not, check into seeing what it would cost for both your science and math teachers to use with your students.

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