If a teacher wants broad, pre-defined "folders" for types of posts, then categories are a good choice.
Teachers can create or delete categories via Categories page in the settings of their class (Settings -> Categories). Note that deleting a category does not delete posts, just the label.
You might use categories for certain subjects like "Math" or "Book Clubs." You can also use categories for students in small groups like "Blue Group" or "Lego Team 5". Categories would allow those students to easily filter posts to find other members of their group. Each post can be assigned to more than one category.