# Make Equations Make Sense for Your Students: Here’s How

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This post originally appeared on the blog Make Sense of Math.

Do you feel like you are constantly teaching and re-teaching how to solve equations? Try this process and watch your students’ eyes light up with understanding.

Teaching mathematics should take the form of concrete -> symbolic -> abstract. If you just jump right into teaching abstractly, you will not reach all of your students. In this post, I will review how you can take solving equations through these 3 steps. I have used this process in my classroom, and it has proved to be very effective.

I will go through this process with the equation x – 3 = 10

Before going through the process, emphasize the meaning of the equal sign. Many students will think that the equal sign means “the answer is”. Teach that the equal signs means that both sides are the same. Many teachers relate this to a scale, which is a great visual. The scale will become unbalanced if you only add or subtract from one side of the equal sign.

CONCRETE
To concretely solve this equation, have students use Algebra tiles. Tip: Have students circle the terms separately. This will help them to not be confused with the signs. Hopefully you have already talked about the additive inverse when teaching integers. If not, teach this property. Tell students they can add or subtract anything from both sides until the variable is alone.

SYMBOLIC
Now you will move to drawing symbols for the tiles. I often still let students use the tiles if they need it to guide them in their thinking. I will have them draw a symbol for each tile. Many students start by actually drawing the blocks, but they soon change to just writing the “1” or “-1”.

ABSTRACT
Next you will move to abstract. Instead of writing “1  1  1”, students will write “+3”.

One more tip:  ALL students should start at the concrete level. Allow students to move through the progression of concrete, symbolic, abstract at their own pace. Allowing students to take the time they need at each level will help them to develop a deep understanding of the mathematics.

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After graduating with a B.S. in Mathematics, Michelle dove into teaching in the middle school math classroom. She taught for 6 years, and loved her time in the classroom and was nominated as the Teacher of the Year. She designed her classroom to consistently challenge her students’ minds in an engaging way. She took many masters classes about math pedagogy and loves to share this with other teachers. She hopes to educate math teachers to teach math in a way that makes sense to ALL students. Michelle hopes to be back in the classroom one day, but in the meantime is enjoying her time as a full-time mom and part-time curriculum writer.