After you've taught your students a rule, do they ever point out to you when published authors break that rule? It happens to me every time we review sentence fragments. As soon as we are finished practicing correcting our own fragments, a barrage of hands go up during independent reading. "Mrs. McMath, there's fragments everywhere! Don't they know the rules?!"
To know the rules is to break the rules, I encourage them. Once you know the grammar rules, you can break them with reason. The author's well chosen bending of the rules is always for a specific purpose.
This document is a handout with 5 purposes for writing sentence fragments.
Along with the reasons, I've identified 24 quotations from Lois Lowry's famous novel The Giver that demonstrate those five purposes. This handout would work well after teaching sentence fragments. It could be used with any genre of writing. Most teachers find it most useful as a resource for students to keep in their notebook.