The Order of Operations Explained: Intro and Mnemonics

Inspired by Jimmie’s daughter’s order of operations mnemonic, I’m finally getting to the series I’ve thought about for a while.

The Order of Operations (OoO for short) is used everywhere in mathematics because it encompasses many of the foundational rules that we’ve agreed to follow.

Alas, students have been given the cheap and dirty version of it for years. “Here, memorize this thing about your Dear Aunt Sally!” What the heck?!

There are subtleties in the Order of Operations that every person over the age of seven should know.

The series begins today.

The order of operations is a set of rules – like the drivers’ handbook for math. If everyone follows the rules, we’ll all be safe. But if someone makes a bad turn, we could be looking at a crash.

But the Order of Operations is only a set of rules for arithmetic! It isn’t even the best practice when it comes to expressions involving a variable like x. I’ll cover what I mean in this weekly series.

Here are the proposed articles:

  1. Intro and mnemonics
  2. Parenthesis
  3. Exponents
  4. Exponents, Multiplication and Addition
  5. Multiplication and Division
  6. Addition, Subtraction and Conclusions
  7. (UPDATE) Exponents of Negative Numbers
  8. (another UPDATE) Another Reason to Ban PEMDAS (aka parenthesis aren’t an operation)

Mnemonics for PEMDAS

Well, there’s one: PEMDAS (pronounced just like it looks). That’s what the cool kids in high school always said. It was the same kids who said “soh-cah-toa” – which I thought sounded really goofy.

And then there’s “Please Excuse My Dear Aunt Sally.” And of course, Jimmie’s daughter’s “Piranhas Eat Mostly Decayed Antelope Skin”.

What’s your way to remember it?

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7 Responses to The Order of Operations Explained: Intro and Mnemonics

  1. I don’t use a mnemonic. I point out that addition and subtraction are low level (basic) operations taught first in school. Multiplication and division are built on the concept of repeated addition, so they are higher level operations and are taught after + and -. Exponentiation, and its inverse taking roots, are built on repeated addition. They are the highest level operations.

    The rule is to do higher level operations first. Use parentheses whenever your intention is to deviate from this rule.

    • For some things I don;t use mnemonics, you explain the logic very well. Soh-cah-toa though I was also taught (it’s sos-cas-toa in Dutch though…).

      Mnemonics might be useful in the beginning, but teaching the logic behind them would pay off much more. There is an increasing trend (in general, not just OoO) of the system putting value on memorization as opposed to understanding.

      These are the kinds of kids who are taught a “trick” and will do fine on most tests. If you however change the context or question they will be lost and have no idea what to do…

      • So true, Mentor! The tricks only take you so far before you run into something new and novel. If you understand the logic, you can adjust the tricks to fit. Or just figure out what to do next.

        Thanks for stopping by!

    • That’s a great way to remember it – and teach it, David. I wonder if they’re totally comfortable reversing it when they do algebra. I would think practicing it this way should help it stick and become internal for them. But I would love to hear if that was true.

      Thanks for your comment!

  2. I am firmly planted in the conventions field. I used an analogy to getting dressed, using underwear as the 1st thing we put on out of the bath, and so forth. I began in fourth grade and they, and later fifth graders, found mnemonics helpful. Now in middle school, I try and teach more depth. Soon they come to other grouping symbols (GEMDAS) and find old favorites need to be adjusted. when using devices I have found it useful for many to create their own personalized versions. It is important (I think) to keep in mind these are really only aids to get us started.

    • I completely agree, Tom. I’ve never tried the underwear analogy. I use pants and shoes. I think perhaps the underwear analogy will be a little funnier. I’ll give it a shot.

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