Originally, when my students didn't do there homework at home, I would take their break time (i.e. recess). On top of that, if they had free time (i.e. after completing the mandatory in class assignment(s)), I would have them work on their homework during that time. That was a mistake. Don't allow students to do their homework during their free time if they didn't complete it at home.
Originally, my only thought was that I would allow my students to make up their homework during their free time because I just wanted my students to complete all of their homework. But then, I conveyed an implicit message. The implicit message that I conveyed to my students was that if they don't complete their homework, its cool because they can just work on it at school during their free time. And, if they can work on it during their free time, that is a motivator to not do their homework at home. Some students would love that because that means they have more time to play with their friends, watch TV, play videogames, or whatever else it is that my students enjoy doing.
Homework isn't just given for the hell of it. Its supposed to be extra and to an extent, independent practice. If students are allowed to make up homework in class during their free time, #1 they will be doing their homework in a distracting environment (I say that in ignorance of what their home environment is like). It's distracting because they're surrounded by friends, students that annoy them, my announcements, point systems, and probably other factors that I'm ignoring. Also, their time to make up the homework is very limited. They would literally have at best, about 20 minutes to make up their homework, which doesn't include all of the distractions.
On the assumption that their parents are caring and attentive enough, students will have more time and a more focused environment to work on their homework at home. And, for that reason, my speculation is that the quality of the homework would also be better at home than at school.
Since they aren't allowed to finish their homework during their free time, they must complete it during their break and only during their break. They should only make it up during their break because every student likes to have a break. They don't want to lose their break. So, if they want to keep their breaks, they need to make sure that they do the work. That's motivating enough for them to complete their homework. Just don't give in to letting them complete their homework during their free time.