From what I gather, you are a math teacher. Homework is essential in math. Students need that extra practice outside of the classroom. It's good that you only give 5-8 problems. That amount of work is beneficial, more than that is just overkill. As far as getting them to do it, you can start with an incentive and see if that works. If it does, you can begin slowly taking the incentive away once the students get in the habit of doing it. The incentive doesn't necessarily have to be tangible; it can be extra points on the test.

I have the same problem with my 7th graders. We have a step process which is our discipline procedures, I give students a step every time they do not do their homework. For most this works, but for some they don't care and they will continue receiving steps until they end up with an office referral. I also give random rewards. For example, I will take HW for a grade one day, but the next day I may give candy to those who did it or give them 5 points on a quiz. They never know when I am going to do it so a lot of them will do their work just to earn these rewards.

I teach 8th grade science and feel that vocabulary is crucial. I started the school year with giving vocabulary for homework. There are only 7 units worth of vocabulary, so homework was only given about every 2-3 weeks. I eventually just stopped doing homework because it was such a hassle and students would not complete the work. Now, I make students complete the vocabulary in class that way I can monitor their progress. This is easy to do for science, but maybe not so much for math. I would definitely try incentives. I have heard of homework incentives including replacing the lowest daily grade when homework guidelines were met. So if a student completes 2 homework assignments in a row, replace their lowest daily grade with a 100. Or if students complete 2-3 homework assignments in a row, allow them to skip a homework assignment and receive a 100 for that assignment. You could make the incentive be whatever your particular students will be willing to work for. It will be different for each class and possibly for each student.

Homework is a major issue for me as well. I want to assign it, but it gets done so infrequently that I wonder about the merits of it. Most of my homework now is classwork assignments that have not been done completed in class. I keep a record of all assignments turned in and show the students on a weekly basis. I continually hound them to complete their work and will do so all semester. As I show them grades, they often become more motivated to complete their work, but it is still a struggle.

I would talk to the department head and see about addressing this issue at your next department meeting. Chances are, you are not the only teacher in your department struggling with this issue. Maybe even bring an administrator into the meeting and ask for support in this area. I would suggest starting to use a system where a certain number of times that a student fails to do their homework results in a detention of some sort. You could also implement homework quizzes and increase their weight in the gradebook.

Unfortunately there seem to be a shift in rules as it relates to homework. The claim is that all students does not have the same advantage when it comes to completing homework, as their living conditions may render them completing homework a struggle. Math is a whole different ballgame because one has to practice math to be proficient. You may have to ask the administration to support instituting a flex day where the math practice can be done under supervision.

Homework is such a crucial factor for students to complete outside the classroom. You can add rewards for students to encourage them to finish it. For example, leaving the classroom 5-10 minutes earlier things like this to encourage to get their work done.