The Line on the Floor — How do you split something fairly? (I cut, you choose)

The fairest way to split something between two people is for one of them to divide it and the other to pick first, because then whoever holds the knife has to make both halves equal or lose. Try to cheat your little sister out of half a bedroom, find out why you cannot, discover the strange part where you BOTH end up with more than half, and then build the rule yourself for the things that will not cut in half at all.