Exposing your students to many kinds of writing assignments will give you a better sense of their skills. When you experiment you will see that the writing abilities of your students vary significantly according to the task. This is because they have had more practice in some genres (like personal essays or creative writing) than others (expository writing, analytical papers).
Having a variety of assignments means that a student whose creative writing is fantastic can imagine a way to bring this expertise into their analytical paper. Their confidence in one genre can be very inspiring for their performance in others. Similarly, having a set of ungraded assignments helps students experiment with their style and tone, without worrying about their grade. Finally, you want to reinforce the feeling that writing is writing, in the world, in the classroom, in private, in public. Students often feel that their class experience is isolated from their lives. They often ask: "What is this for?" Well, writing is basically for ever, and one way to let them see this is by involving other written genres into your classroom.
Here is a short list of the kinds of writing assignments you can use in your classroom.
Reading Journals (ungraded)
Writing Journals (ungraded)
Peer Workshops, Peer Editing
Analytical Writing (graded)
Creative Writing
Outlines
Response Papers (ungraded)
Reports, Notes, Thoughts
Exam, Mock Exam, Quiz
E-mail Communication or Group Posting
Handout for Group Presentation
Technical Manual
Business Presentation or PowerPoint Show
Informal Class or Assignment Evaluation (anonymous)