When a teacher assigns an Objective as a class assignment only, only students 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'.
All objectives assigned as a class or individual assignment count toward a student's percent progress, but only objectives part of a student's journey count toward their Journey progress. For information on both metrics visit: What is the difference between Puzzle Goal Progress and Journey Progress?
Class assignments appear under Class assignments, and individual assignments appear under Just for me. For steps on how to assign class or individual assignments visit: How do I assign, edit, or reorder class and individual assignments?