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:
- Intro and mnemonics
- Parenthesis
- Exponents
- Exponents, Multiplication and Addition
- Multiplication and Division
- Addition, Subtraction and Conclusions
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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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.
…woops. I meant to say exponentiation is built on repeated multiplication. …
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!