One reason to avoid dangling modifiers is the unintentional humor they sometimes bring to a sentence. For example, if someone writes "Items for sale included a blue woman's sweater." While the author of a sentence like this probably means that the sweater for sale is blue, the sentence literally suggests that the sweater in question is meant for women whose skin is blue. Ask your students to come up with a sentence that includes a dangling modifier and have them draw a picture to accompany it. This appeal to humor will help to cement the absurdity that dangling modifiers often bring to sentences.
Another activity that allows you to highlight the importance of avoiding dangling modifiers in a humorous fashion is to have your students write an otherwise grammatically correct sentence that uses as many dangling modifiers as possible. Present it as a contest to see who can write the most awful sentence and offer a point or two of extra credit to the winner. An example of the kind of sentence your students should write is the following: "The man in the garden took a stroll with his dog in his underwear covered in mud." This sentence contains three examples of dangling modifiers (it should properly run "The man in his underwear took a stroll in the garden with his dog covered in mud.)
Rewrite four or five sentences from literature so that they include dangling modifiers and show them to your students. Make sure they are familiar with the original sentences first, then ask them to explain why the dangling modifiers undercut or obscure the meaning of the original sentences. For example, if you change the first sentence of Toni Morrison's "Paradise" from "They shoot the white man first" to "They shoot the first white man," you suggest that the shooter is seeking out one particular white man out of a group rather than white men in general as opposed to members of other races.
A little friendly competition always helps to motivate students in the classroom. Divide your students into groups and give each group a dry erase board, marker and eraser. Write a sentence that includes a dangling modifier on the board and ask the groups to write the answer on their boards. Each time a group writes a correct answer, it receives a point. Use the chalkboard to record the groups' points. Present between 20 and 25 sentences. At the end of the game, the group with the most points on the board wins.