I just graded my algebra 1 tests over Solving Systems by Substitution. Oh my. The kids generally knew what they were doing, but their sloppiness got in their way. Some couldn't read their own handwriting and dropped negatives or made 3's into 13's and such. Some wavered all over the place and then misread their work that way.
Today we had a lesson on neatness and how part of your job as a "mathematician" is not just to get the answer but to communicate to others how the problem is done, so they can just follow along by reading your work and you don't have to be there to interpret the "doctor handwriting" as I call it. I implored (ordered) them to write each step and keep it all lined up going down the page and not all higgeldy-piggeldy every which way.
We practiced. We practiced some more. We refreshed our memory on fractions. We refreshed our memory on the fact that "3x/4" means the same thing as "3/4 x". We refreshed our distributing skills of "5 - 3(x - 2)" types of situations.
We discussed how to check our work (plug (x,y) back into BOTH equations).
"But why do I have to check both?"
"It could be right in one but your previous mistake makes it wrong in the other. Check both!"
"But I'm not going to be a mathematician. I'm going to be a doctor."
"Well, after surgery you don't just want to check ... 'did I leave the scalpel in the body? No? Good, sew him up' and meanwhile, you didn't check that you left the saw in the body."