# Balancing equations

Feb 10, 2014 8:44am

Lately, I've been noticing that when I grade students solve for the missing variable in 2-step equations, my students are trying to isolate the variable by dividing/multiplying both sides by the coefficient (ie. they're using the multiplicative inverse) rather than doing the additive inverse 1st.

Example - If ax + b = c then they would divide both sides by "a" 1st before subtracting "b"

How do you "unteach" this? And you have time please put your 2 cents as to why are students doing this? I've always taught my students to do the inverse of PEMDAS (SADMEP) solving equations. But is there a better strategy?

• Math
• 6-12
• Assessment / Common Core / Differentiation / Planning

4

• Feb 10, 2014 9:52pm

I wish I had a good explanation as to why students make this mistake. And I teach it the same way as you, with reverse PEMDAS. It might be helpful to work through a numerical example doing it the wrong way and showing that it does not give the correct answer. Example: 2x + 4 = 10, dividing both sides by 2 first would give x = 1. Then show that x = 1 does not work. Maybe just seeing this mistake worked all the way through will stick in their minds a little more and they will (hopefully!) remember not to make that mistake again. Or you can show them that dividing EVERYTHING by 2 first will work, so that if they really want to divide first they just have to remember to do it to every term.

• Feb 11, 2014 4:51am

Hi Lauren! Thanks for taking time to respond. I definitely agree that students need to check their answers. There was a time when I would have students look for an equations truth value by guessing and checking before doing the inverse operations to look for a solution(s). So when you have them do the check do you or will you emphasize the use of the additive inverse property 1st? Thanks again.

• Feb 11, 2014 9:58am

I would emphasize it first - then say something like "let's take a look at what happens when you don't do the additive inverse first".

Another idea is to make checking their answer part of the question on a test/quiz, even worth a point or two. That way students have a little more incentive to take that step.

• Mar 2, 2014 12:21pm

In terms of just pure math, the basic principle holds. To keep things balanced, whatever you do one one side, you do to the other too. So for a simple equation in 2-steps, it doesn't matter whether you add/subtract on both sides and then divide/multiply. BUT my students are dividing/multiplying on the term with the variable but not with the constant. I mean it would be okay if they're applying it to every term but they stop at doing the division on the constant. Why? What should I do/say to let them know that they have to "undo" (by using reverse operations) to every term in that math sentence.