What is likely to happen if a balloon that was blown up at a low altitude is brought to a high altitude? Why would this occur?

If the pressure is lowered, than the volume must increase. Therefore, when the pressure goes down, the balloons get larger and larger. They may even pop, depending on how full they were to start with. But if they don't pop, when the pressure went back up (you climbed back down to the classroom) ... then the balloon would go back to it's normal size.