"You can only add the same things, when you add the same things, you get the same things."
This works for preschoolers to Calculus students. Stop the craziness, adding doesn't change as students get older. I've had several discussions with my students trying to convince them that 2(3)^2+4(3)^2 = 6(3)^2 or 2|x+3| + 4|x+3| = 6|x+3| is the same thing as 2 apples + 4 apples = 6 apples.
We spent a lot of time teaching what the "Things" are.
This works awesome with fractions, the denominator is the thing that is the same thing. By teaching the main principle of addition, students actually don't skip fraction problems!
Btw, subtraction is just adding the opposite.