[ Warning, if you are neither a teenager nor a math geek, you might not understand this story... ]

I was teaching a group of 8th graders this morning and one of them referred to PEMDAS. PEMDAS is a widely used acronym for remembering the order of operations: 

This was a perfect opportunity to try-out an approach to teaching this topic that I had been discussing with other Math teachers recently! 

I started by writing PEMDAS on the board, and then began thinking aloud... 

1. since subtraction is better done as the addition of the additive opposite (for example, instead of subtracting 5, add negative 5: if you don't subtract, you'll save yourself from a ton of errors!), so the S goes away...
I erased the S and the students shouted "PEMDA?"

2. since division is best expressed as multiplication by the multiplicative opposite (for example, dividing by two becomes multiplying by 1/2), division is no longer an issue... 
I erased the D and they shouted "PEMA!"

3. what about absolute value?
The students responded that the P actually referred to groupings, not just parentheses: I changed the P to a G, "GEMA!"

4. but what is multiplication? If I write 9 * 3, what I mean is 9 + 9 + 9, ...right?
A student commented, "Multiplication is just repeated addition, so the M can go away, too."
Another student asked "Isn't multiplication more like a way of grouping addition...?" (I didn't respond.)  

5. So what's 9²?
"OMG! Exponents are grouped multiplication and multiplication is grouped addition, so the whole order of operations can be reduced to the concept of grouped addition!! So now we just have GA!!" 

Yeah, a student said all that. . .  :-) 

When the class was done testing all of the different ways they could say our new acronym, "GA," we talked about how so many teachers and students use PEMDAS, that we can't get away from it.

I pointed out that that was okay, because now we understand it, and we know why it works, so we can just go ahead and use it.