Only assign what's necessary to augment instruction. If you can get sufficient information by assigning only five problems, then don't assign fifty.
Focus on practice and review. Give students a chance to try new material, further practice skills they have recently learned, and review something they already know.
Take students' age into consideration when determining the amount of homework to assign. Recommendations from Helping Your Students With Homework: A Guide for Teachers (PDF), published by the U.S. Department of Education, lists the following:
Remember, this is a cumulative amount. If you are only one of five teachers assigning homework, you should adjust accordingly.
Share a list of homework rules before handing out the first assignment. A written explanation of expectations will increase the likelihood that assignments are completed. Let students know that homework is important, and that not doing an assignment will have consequences, which may include lower grades.
Let students know ahead of time when homework will be assigned. Some teachers always assign homework on specific nights—every Tuesday and Thursday, for example. This lets students and parents know when to expect homework.
Designate a Homework Collector. Assign a student to gather the papers at the start of class while you take roll or attend to other administrative tasks.
Have a weekly prize drawing. Students get a ticket for each homework assignment they complete, and at the end of the week, a winner is randomly chosen. (Plus, this activity can serve as the motivation for a probability lesson!)
Employ a "While You Were Out" form for students to fill out indicating any class periods they missed. (Leave blank copies of this form in a location accessible to students.) When students return these forms, fill out the form indicating the class work, homework, or tests that students missed, and return the forms to students. When students complete the make-up work, they should attach the form. Having a system for missed work will help you with organization, and it will reduce the number of last-minute assignments turned in at report-card time.
Give constructive feedback. Students are more apt to complete assignments and advance their learning when they get consistent and constructive feedback. Make an effort to provide written comments on student work that lets them know what they did well and what they need to improve.