What is a negative number?

I was revising the distributive property with the eleventh graders one day last term (remember, I wrote this post in the past) which they seemed to be understanding very well, as long as all of the numbers and variables were positive. If, however, they needed to add -3x + 5x, they would unanimously reply that the answer was -8x.

So I took an unplanned detour into negative numbers...

Everyone agreed that I could show them two pieces of chalk but I could not show them negative two pieces of chalk; negative numbers are something that cannot be seen.

Me: So what is a negative number? Can anyone give an example of something that's negative?
Saikou: Bravery. Bravery cannot be seen.
Therese: And love.
Me: Ummm...