180 Days of Ideas for Discussion in Math Class.
(as of 9July2014, we're in overtime!)
You can do something similar with integers even. If my number line I draw on the board has units of length one foot and yours has units of length two feet, what's one plus one? If we just translate the units, it's more than two on my number line and less than two on yours.
This problem is the same as "what is 2 oranges plus 3 apples?". The correct answer is "two quarters".