I'm trying something new this year both in AP Calculus and in Precalculus when the students go over their homework, and I think it's a win for me/my class/my students.
For the past several years in precalculus, I would work out the homework, place the key on the document camera, and we would painfully and slowly go over the answers while the students corrected in a different colored pen. I grade on completion since I think homework should be a time to practice. I understand (obviously) there are different philosophies on this, but I feel this works in my situation. I do watch for kids sneakily copying things in pencil and passing it off as their own. I do look over the homework later to see if they attempted all problems.
Anyway, this always took way too much class time, and most likely, students were probably not looking as closely as possible to solutions, and everyone most likely had different problems they were confused about, so some were sitting around needlessly while they waited for their particular problem to be shown on the document camera.
This year, I take my key and make enough copies for 1 per 2 kids. They silently glance over the key and correct their work. This has gone MUCH faster than before. Also, kids can see how I lay out my work and have the time to concentrate on the particular problems they need to see and have good examples of process and thoroughness (or maybe I'm just being idealistic).
I've also done this in calculus. I used to just collect the homework, then put the worked out key on the LMS site for them to check later. I'm guessing that by the time they got back the homework by the following class and had more homework to deal with, they never checked the old homework. This year in my flipped class, they have the key on their table and can carefully go over it and ask questions right when it is still fresh in their minds. Again I like the fact that they have constant reminders of how the work should look if it's thoroughly done.