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Order Of Operations, One To Ten Game
Friday, October 5, 2007
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I recently had an email conversation with an elementary math teacher which reminded me of something very important. The mnemonic we use to help us remember order of operations is often misunderstood. And not just by students; many teachers misunderstand "Please Excuse My Dear Aunt Sally" (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction). And since many teachers misunderstand it, that means they don't teach it correctly.
Here's a test for you: Evaluate: 8 / 4 x 2
Was your answer "one"? If so, you realy need to keep reading, because you have misunderstood PEMDAS. The correct answer is "four".
The thing many people don't realize about Order Of Operations is that Multiplication and Division are at the same priority level, and Addition and Subtraction are at the same priority level.
In other words, if you have both multiplication and division in the same expression, you do not evaluate all the multiplication first, and then all the divion...you evaluate it from left to right.
So in the example above, since the division is to the left of the multiplication, we do it first. 8 / 4 = 2. Then we multiply by 2, giving us 4.
Similarly, how would you evalute this expression:
10 - 5 + 2
Addition and Subtraction are at the same priority level, so, since the subtraction comes first in the expression, you do it first: 10 - 5 = 5. Now you add 2 and get 7.
Someone who misunderstands PEMDAS will add 5 + 2 first, and then subtract that from 10, arriving at the incorrect answer of 3.
In order to help people out with this common confusion, I have now made the game One To Ten the featured game at The Problem Site.
This was one of the very first games on the site, and it has been used in many classrooms as part of the Order Of Operations Curriculum activities.
posted by Douglas Twitchell at
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