Solving Equations: Variables on Both Sides vs Combine Like Terms

It seems pretty cut and dry to me - either the variables are on the same side of the equal sign or they aren't. But I can't tell you how many of my students confuse the procedures for these equations. I find that showing one of each of these types of problems side by side helps them. 

So I would show these two equations and ask them to compare and contrast them. I also have them draw a line down the equal sign when learning how to solve equations. This really helps them to remember to keep both sides balanced using the properties of equality. 

I created these notes to help walk students through the difference between the two types of equations. I like to use gradual release with these notes. We solve the equations at the top together (I Do). Then they try the matching in the middle with a partner (We Do). Then they try to problems at the bottom on their own (You Do). I usually project these notes onto the board and have students show their work on the board. 

Like any other math topic, practice helps them to improve so I created this puzzle . I love using self-checking activities so students can self- monitor as they go. If they don’t find their answer or the puzzle doesn’t make the correct shape, they know they made a mistake. I tell them the first thing they should check is whether they correctly combined like terms or used inverse operations.  Often they will incorrectly use inverse operations when solving a problem where the terms are on the same side. They will say “I subtracted 7x from both sides.” Then it’s very easy to have them show me where they did that on the other side (spoiler alert - they didn’t) and then we can talk about a different strategy instead.