Thanks, nice chart (small mistake on the Simplifying/npvs on the second last line) to summarize. 

I find the kids have always struggled with the difference between expressions and equations.  I have found for equations that having the kids determine a common denominator on both sides before solving has worked great. If the denominators are equal, then the numerators are equal and we can focus on solving just that part. 

As well, I avoid using the word "cancel" even though the kids loving using it, I find they have little understanding what they are doing and it creeps into other work.  "cancel" means that there is "nothing" there, which isn't true, there is 1 there.  We have a quick discussion about this and then use "divides to one". This has prevented random crossing out of terms. I also avoid the phrase "cross-multiply and divide" for the same reason: lack of understanding of what is occurring and when they can and cannot perform this shortcut.

Just my thoughts.

Mike