Solving equations is foundational for middle and high school math. Students actually have been doing this since first grade! However, students can make careless errors or struggle when it comes to following the many procedural steps required to solve an equation.
The Standard
Why the struggle?
Solving equations is very revealing. If your students struggle with integer operations, then it will show up again when solving equations. If your students struggle with rational number operations, then it will show up again when solving equations.
Here are some other misconceptions:
- Combining like terms incorrectly
- Dividing/multiplying a negative coefficient. Students trying to add instead.
- Not distributing when they should. Example: 5 – 2(x + 2) = 10 simplifying to 3(x +2) = 10
- Students completing inverse operations on the same side of the equal sign instead of combining like terms (see below for picture)
Does this sound familiar?
Use Algebra Tiles (No, really, use them!)
I was resistant! Manipulatives can cause undue stress (tiny items + 30 children); it is a lot! However, I think that if I had used algebra tiles in my classroom, students would have been way more engaged! I occasionally drew a model to demonstrate solving equations, but then Noelle showed me all the ways algebra tiles could be used to combine like terms, distribute, and solve two-step equations (even quadratics). I was on board!
Before using algebra tiles to introduce students to solving equations, use algebra tiles to demonstrate combining like terms. Combining like terms can be challenging for students, but when you ask students to combine all of the long green tiles (x), the long red tiles (-x), the small yellow tiles (+1), and the small red tiles (-1), it provides excellent concrete practice. It will also assist with zero pair understanding, which will be essential to solving equations with algebra tiles.
What would you rather combine as a student? The terms or the algebra tiles?
Let’s move on to solving equations. Look at the following example:
Before exposing your students to two-step equations with variables on both sides, let them practice with one-step equations first. Scaffolding is key. I chose this example to show you how versatile algebra tiles are (variables on both sides and negative values)
To isolate the variable, students would need to recognize that they needed to get rid of positive 2. To do this, they would add two negative tiles to make a zero pair. Adding negative 2 to one side would mean they would add to the other side to keep the equation balanced.
After students have removed the two zero pairs on the left side of the equation, they might be a little stuck. They are exploring, after all. Remind students that we want all variables on one side, since we want to find out what one x is equal to. Students would then add a negative x to both sides to create another zero pair.
Lastly, to get the solution for one x, students would divide the remaining red tiles among the two x tiles: X = -4.
Students are actually solving for x by undoing the problem, by using inverse operations (adding -2 to both sides and dividing by 2), and by keeping the equation balanced (they are adding tiles to both sides). All the procedural steps that might mean nothing to students in a traditional problem have meaning when students have been exposed to practicing with algebra tiles.
Remember that algebra tiles (like most manipulatives) exist to make the math visual. They provide conceptual understanding. Eventually, students will move into the algorithm. When students are exploring, make sure all of the solutions are integers (you can’t break the tiles into pieces).
To learn more about students making the jump from concrete to abstract, please check out our posts about the CRA Framework – Part 1 and Part 2.
Another tip I recommend is to have students write out what is happening as they are using algebra tiles to solve an equation. If they are combining 3 green tiles with two red tiles, then they would need to write 3x-2x with evidence of only 1x remaining.
If you don’t have access to algebra tiles, students can use this website.
Be sure to grab our Getting Started with Algebra Tiles freebie to learn more about using algebra tiles to tackle simplifying expressions, the distributive property, solving linear equations, adding and subtracting polynomials, multiplying and dividing polynomials, and factoring polynomials.
Helpful Tips
These teacher tips might help your students:
- Draw a line to separate the two sides of the equation.
- Do Undo Line – this is another strategy that can help students.
- Color-coding to help with combining like terms
- Making sure to actually say (and make students say), “2 times x equals 5” as opposed to “2x = 5.”
For more resources, check out these units and bundles.
What additional tips do you have? Do you use algebra tiles in your classroom?
