You might want to try something with a decaying activity. Start the kids working in twos, each twosome with a square piece of paper. Have them fold it in half, cut along the fold, put one half aside and repeat the process with the remaining half. Have the students repeat the process (folding, cutting, laying one-half aside, so that they are creating regions 1/2, 1/4, 1/8, 1/16, etc. the original square) until they cannot handle the piece any more. You will need paper, scissors and tweezers. You can then have some discussion about what they think might be theoretically possible as far as continuing to fold and cut even though they can't actually handle a piece of paper that small.
Some questions you could ask are: How long could you continue to do this (fold, cut, etc.)? What would the last piece look like? What would its area be? What would you call it? What would happen if you put all the pieces except for the last one (the one you could no longer handle) back together,what would its area be?
A big word of caution: while this may be a nice activity for getting the kids to talk about some things relative to infinity betwee 1 and 0, don't get hung up on trying to make them "see" anything. Let them talk about their observations and conjectures in their own way. Use the situation to allow them to play with the ideas. It will be more fun for them and you'll learn a lot about their thinking. Enjoy and good luck.
============================================================ Hannah Slovin 1776 University Ave. University of Hawaii Honolulu, HI 96822 Curriculum R & D Group (808)956-4985; FAX (808)956-4984