A teacher at my school: Mr. Zerr is on the moon and he has a certain mass. Will his mass change when he comes to Earth?

Micheal Clark 9545 is correct only you're weight changes when you travel planets, this is due to the fact that an objects weight depends on its mass as well as the gravity acting on it so on the moon (where there is less gravity) you would have a smaller weight. On the other hand mass is the amount of matter composing an object. The amount of matter composing you're teacher does not change when you go to the moon