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Learning and Teaching the Order of Operations

written by: KellenKautzman • edited by: Patricia Gable • updated: 8/2/2012

Can you get to work before you drive your car? No, there are steps you need to take. The same goes for teaching order of operations problems; specific steps have to be taken before you can come up with the end result.

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    Lesson Plan

    Order of Operations "Please Excuse My Dear Aunt Sally." That is probably how most of us have learned how to complete order of operations problems. That means to complete these problems you do parentheses, exponents, multiplication, division, addition, and subtraction.

    In today’s changing world a little change needs to be made.

    • Instead of saying parentheses, it is necessary to call them grouping symbols because [brackets] and {braces} are also commonly found in these types of problems.
    • Instead of using a mnemonic device for trying to remember this, frequently review the correct order with the students.
    • Also, reinforce that multiplication and division are done in the order of whichever comes first, the same goes for addition or subtraction.

    You might consider free worksheets about the order of operations to help you teach the class with extra practice.

    To get students excited about learning which operations to perform first, you will want to start by having them relate to something they know, like sending a text message. For this, the teacher will write the steps of texting scattered on the board, and of course out of order (press the send button, type text message, select a person to send the message to.) You will want to keep this simple so all of the students will get the correct order. Have the students write the steps in the correct order on either their whiteboard or paper. You may want to do a few more examples, ask the students for suggestions, and do this for no more than 5 minutes. Remember it is only an introduction. Once that has been finished, it is time to talk about order of operations.

    Write the steps for order of operations on the board and have the students copy in their notebooks. Remember not to use the term parentheses; call them grouping symbols. Depending on the grade level of the students, you may not need to do any problems with exponents, because they typically aren’t introduced until seventh grade or so. After the students have copied the steps, have them repeat the steps orally several times and possibly write the steps several times as well. The more times they hear and see the steps, the better they will remember it. Let the students do this for at least 10 minutes to allow the instructions to really sink in.

    It is very important for the teacher to do a few problems first for the students to see. Whenever I teach order of operations problems, I make the students underline the part they are working on to keep track of what they have done, then they replace the underline part with the answer and copy the rest of the problem, this is done until they have one single answer. The below example will show how this works. Ask the students to tell you what part to do next. Do at least 3 examples with the students before you let them try on their own.

    Teacher Example:

    {30 ÷ 6} x 2 – 8 + 9

    {30 ÷ 6} x 2 – 8 + 9

    5 x 2 – 8 + 9

    10 – 8 + 9

    2 + 9

    11

    If you are using a textbook, that will be a great source of problems to do with the students. Have them do at least 10 examples on their own. Write problems on the board for them to do on their whiteboards. As the students are working, walk around to check for progress, making certain they are underlining and rewriting the problem as they work; this really helps.

    Before the class is over, have the students recite the order of operations, or write it on a small slip of paper before leaving. The key to retaining information is repetitiveness and exposure; the more students say or see something, the better they will remember.

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    Image References

    Equation Order of Operations Problems