The usual activities teachers do with Oreos don't actually teach much about the phases of the moon. For example, they don't explain why the phases have the shapes that they have. Instead, try something more experiential:
In an otherwise dark room, set up a bright light bulb in the center representing the sun, and let students explore how a ball (or any round object, like an orange) shows different phases when looked at from different angles and as the ball moves around the "sun."
Then, on a day when the moon is visible in the sky, give them each a small ball or orange, take them outside, and have them hold up the ball in the direction of the moon. The ball will show the same phase as the moon -- and for the same reason! (See attached photo.)
To understand why the phases have the shapes they do, they need to see light falling on a sphere. You don't get phases like crescent and gibbous from light shining on a flat (Oreo) disk.