Math people are discussing how to explain to non-mathematicians that a negative times a negative is a positive. I mostly follow Mr. K's approach in teaching this, but sometimes project up an image of a mysterious, intense magician and talk about how this guy controls the weather in the imaginary country of Fictionia. He has a huge black cauldron filled with hot and cold cubes, and if he adds 4 hot cubes 5 times, the temperature rises by 20 units. He can also increase the temperature by removing 4 cold cubes 5 times, and there's our negative times a negative, or at least a four times repeated subtraction of a negative.
Neither of these approaches make signed numbers immediately easy for the kids, I find, but they're both interesting enough for a conversation of some length. We return to the mathemagician of Fictionia now and again during subsequent Openers/Do Nows, so that we start a number of classes with an informal discussion of what options the guy has for, say, decreasing the temperature to some comfortable level, or increasing it just a little for some imaginary event, and gradually the ideas become more natural to the kids.
I learned this story from a co-teacher at San Quentin who was himself a Physics grad student at Berkeley but had heard the tale from either his father or one of his early math teachers.