L.A.
Good suggestions already..
More thoughts.
I would also suggest each class that wins, gets to put their class name in a year long drawing. At the end of the year one class name is pulled out of all of the winners and they win a Pizza Party the last week of school.
Each week the winning classroom gets to display the Spirit "Trophy"
The "Spirit Stick" Or "spirit Sign" In their room for the week. You all decide.. Maybe a banner that hangs in the room? Or on the door to that classroom?
You could hand out school stickers, School spirit ribbons, School buttons, Put their "Class name" on the school sign out front of the school.
"1 Free homework pass." Not able to use on special projects.