Algebra tiles are a great way to teach integer addition. But I like to represent positives and negatives as members of two rival gangs.
The yellow gang member is basically the same as a yellow algebra tile (+1) and the red gang member is the same as a red algebra tile (-1). Yellow gang members get along with other yellow gang members. Same goes for the reds. But when a yellow and red meet up, bad things happen.
To a 13 year old child, this explanation is much more satisfying than some nonsense about "zero-pairs". And when one of my students is confused about an addition problem, all I have to say is "gang violence", and they know exactly what to do.
Say a student is presented with a problem like this: -4 + 7. I have to ask two questions: Which gang will win? (the positives) How many will be left? (three)
To me, this is much better than some silly rule that students have to memorize. They are visualizing the numbers. And they are seeing positives and negatives as opposites that cancel one another out. And best of all, they remember it.
Credits: Graphics are from the Smart Notebook software. I'm sure the people at Smart Technologies appreciate that I've found this use for them.