I personally love to do paper mache, although I don't think I would attempt balloon anything with first graders, who probably have enough trouble just blowing up the balloons! At any rate, here are some possible solutions I have discovered over the years: First, use helium-type balloons, not cheap department store varieties, for your projects. They hold air longer and are sturdier armatures for paper mache. Second, I assume the idea is to end up with a hollow ball of paper when finished. If not, ball up some paper, tape it together, and paper mache over it, and skip the balloons all together. Use the strongest paper strips you can find, preferably office waste or drawing
paper trimmings, not newspaper if you can avoid it-- newsprint is too thin and the paper fibers are inherently weak. Several layers, in the nieghborhood of 6-8 are required to get a hard enough shell to hold up once the balloon deflates. Tissue goes on as a color layer last, because tissue alone is not strong enough to stand on its own.
Lastly, stop listening to classroom teachers and doing inane holiday projects with kids, especially since they are rarely done by the given holiday if something goofy goes wrong. If they are determined to do holiday crafts, let them do the projects- you are a fine art teacher, not a holiday craft teacher!!!! Hope this helps,