# Question Detail

# Balancing equations

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

Try this. 2x + 5 = 11

Cover up the 2x and say,"Some number + 5 equals 11. What must that number be?

Students will say 6.

You say "so 2x must equal 6."

What times 2 equals 6.

They see that x must be 3.

P

4

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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.

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.

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.

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.