One of the responses to the rather large thread on PEMDAS got me thinking about this. I teach middle school math, and we always teach order of operations to 6th graders. I have always explained that PEMDAS is just the set of rules for evaluating mathematical expressions; no student has ever asked me "why are these rules the way they are?"

Is it just arbitrary that multiplication and division come before addition and subtraction in PEMDAS, or is there a reason? In algebra, when we get to 2-step equations (3X + 12 = 24), I have always suggested undoing addition and subtraction first, then undoing multiplication and division. But PEMDAS teaches "doing" multiplication and division first. No wonder many kids get confused.

When you **evaluate** an expression, you "do" PEMDAS (mult and div first), but when you **solve** an equation, you "undo" (add and sub first). Is there a logical way to explain this to students?