Balance the meter stick on your two index fingers, with one finger initially at one end and the other finger about one-quarter of the way from the other end. Slide your fingers together (moving either one or the other or both). Your fingers will always end up together directly under the center of mass.
Try different starting points. Try adding a 100 gram weight onto either end. Try greasing your finger. It always works. Ask your students what they think will happen before doing the original experiment. Ask them again after adding a weight to one end.