Before we even attempt teaching complete and incomplete sentences, we always go over subject and predicate. We describe the subject as the who or what and the predicate as more about it or what it does. I've heard it called the "Who and the Do" and the "Who/What and Tell Me More."
I love the Mr. Morton Subject and Predicate song from School House Rock.
We also do a whole class sort. We pass out the cards. Students either have a subject (red) or predicate (blue). We don't tell them the colors ahead of time :). Students then find the opposite color card to make a complete sentence that makes sentence. We come back to the carpet, share our sentences, and the student has to identify if their card is the subject or predicate of the sentence. Then we tape them on a chart to create an anchor chart.
Here is a copy of the cards in Word if you would like to edit them.
When I taught fourth grade I made this simple sorting activity where students sorted complete and incomplete sentences. Although I made it for fourth grade, it really would be appropriate for second and third as well.
Do you have an great tips on getting students to recognize and write complete sentences?