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Teaching Order of Operations

Lori Soard
Mother helping daughter with school work

Knowing in which order to solve a complex math problem helps students when they begin to learn algebra. However, remembering the order of operations can be a challenge. Fortunately there are some tricks that will help you teach your child in a way that he will remember. Note that you can use Adobe to download the printable on the left.

Go Over the Order of Operations

When first introducing the order of operations, explain that there is a specific order in which a complex mathematical statement should be solved. Instead of simply reading a problem left to right, the problem must be solved in the the following order:

  1. Parenthesis - Anything inside parenthesis or brackets should be solved first. You then move outside of the parentheses.
  2. Exponents - Next, any exponents should be solved.
  3. Multiplication - Solve any multiplication problems.
  4. Division - Division problems are now solved.
  5. Addition - Next, complete any addition problems within the statement.
  6. Subtraction - Finally, complete any subtractions problems.

Use simple examples to start, such as:

7 + 2 - 3 x 2 =

Using the order of operations, there is nothing in parenthesis and there are no exponents, so the multiplication would be solved first. 3 x 2 = 6, so the problem now becomes:

7 + 2 - 6 =

There is no division in this equation, so the next step would be to complete any addition. 7 + 2 = 9, so the problem now becomes:

9 - 6 =

The final step is solving any subtraction, so the student would now complete the equation and come up with the following answer:

9 - 6 = 3

Please Excuse My Dear Aunt Sally (PEMDAS)

Students who are just beginning to use order of operations may have a hard time remembering what order to solve equations in. Fortunately there is a mnemonic device that makes it easy to remember. You simply have the student take the first letter of each word in the order of operations sequence and come up with a sentence he can easily remember.

  • P - Parenthesis
  • E - Exponents
  • M - Multiplication
  • D - Division
  • A - Addition
  • S - Subtraction

Since PEMDAS is not a real word and thus not easily remembered, many people use the sentence, 'Please Excuse My Dear Aunt Sally,' to remember the first letters.

Abbreviation Operation Word to Associate
P Parenthesis Please
E Exponents Excuse
M Multiplication My
D Division Dear
A Addition Aunt
S Subtraction Sally

By learning this mnemonic device, when a student sees an equation like this, he will be able to solve it by going through the process:

(8 + 5) x 92 + 5 * 9 - (8 x 3) =

Grouping with Parenthesis

Every student learns differently. If a student is struggling with how to solve a math problem, you can teach him to use parenthesis and brackets to separate different equations. However, he must first understand the basic order of operations and should be familiar with PEMDAS for this method to be effective.

Parenthesis and brackets should be used in the order the operations occur. Here are a couple of examples:

6 + 7 * 3 -2 =

The first step that occurs in the order of operations is multiplication in this math statement, so the student would rewrite the problem like this:

6 + (7 * 3) - 2 =

6 + (21) - 2 =

The next step would be addition, so the student could then rewrite the equation like this:

[6 + (21)] - 2 =

[27] - 2 =

Finally, the student would simply solve the problem.

27 - 2 = 25

Simply using this process in the beginning stages can help the student begin to see how the order of operations is broken down step-by-step and prevent errors when longer and more complex equations occur.

Helpful Instructional Video

The following video takes the mystery out of the order of operations and is a great way to help a student grasp the concept.

Practice Makes a Difference

As with most math concepts, daily practice helps reinforce skills. If you notice the student skipping a step or mixing up order of operations, such as dividing before multiplying, then stop and go over that skill again and again until the student understands it. With mnemonic devices and taking the extra time to separate out different steps in the PEMDAS model, students will be able to solve more and more advanced math statements.

Teaching Order of Operations