When a teacher assigns an objective as a class objective, only student's who haven't played it so far this year will be prompted to play it. In other words, Class Assignments are like a task list. If a student has completed that task already, the objective is checked automatically and the student moves on to the next activity. You can assign an objective to your class by selecting the class, going to 'Objectives > Assignments, and clicking 'Add'.
When a teacher assigns an objective as an individual assignment, that student will be prompted to play that objective, even if they've played it before. Students earn puzzles when they replay content this will earn puzzles for playing it, even if they've completed it previously. This is a great way to have a student review material they might need a refresher on.