> We have to teach order of operations in fifth grade. Does
> anyone have any good ideas on how to teach this? My
> students are a little confused. I have searched in several
> places, but most of the lessons I have found are for
> secondary students. Thanks for any help!
Sherry, 10/13/00

Real Examples, "PEMDAS," Game

I always start with a numeric problem on the board:

Evaluate: 2 + 3 x 4

Then ask for answers. There are always a bunch who give me 20 and others who say 14. Then we analyze it. What word problem could this describe? For instance: what if you work for 3 hours (mowing lawns, babysitting...) and you normally get $4/hour. But this time the people tip you an extra $2. How much did you earn? They all know that this is $14. How can we write this as a number sentence? 3 x 4 + 2. Isn't that the same as 2 + 3 x 4? Well, shouldn't it be?

Then elicit that mathematicians devised this "agreement" called Order of Operations so that everyone would do the operations in the same order, all of the time. Then state them. Remember that exponents (powers) is an operation, but parentheses are used when we want to change the normal order of things. PEMDAS (they can come up with their own mnemonic device or use the famous standby, "Please Excuse My Dear Aunt Sally."): [ Parentheses / Exponents / Multiplication & Division / Addition & Subtraction ]

You will have to stress that this is a hierarchy listing things in order of importance. But multiplication is just as important as division, so sometimes division comes first. And addition and subtraction are equally important, so sometimes subtraction comes first.

Practice a few with just the four basic operations. Then add in exponents and parentheses.

Next, give them a set of numbers: 4 x 6 + 2 + 3 x 6 = 50 and ask them to insert parentheses to make this true.

Ans: 4 x(6 + 2) + 3 x 6 = 50

I purchased a set of "Number Jumblers" from Discovery Toys (they have a website [ http://www.discoverytoysinc.com ] and an 800 number [ (800) 426-4777] ), and I have the kids work in pairs generating random sets of numbers that they then have to insert operation signs into to come up with the target number. (It looks like a flower, but in each "petal" is a color die (one black) and in the center there is another black one. Roll it on the palm of your hand and the dice turn. Add the two black dice to get the target number to hit or at least get close to. Then start with the die to the right of the black one and write the numbers as you go clockwise. Then add the operations to come close to the target number). I love this toy. There are no loose pieces. There is one with letters also and they use it like Boggle.)

Or, make up your own: Use one + and two - to make this true: 1 2 1 2 1 2 = 8

Ans: 1 + 21 - 2 - 12 = 8.

This only uses two operations, but they can merge the numbers in two - digit numbers. Make up ones where they must use all four operations, even parentheses and exponents.

DSF/NJ, 10/14/00 on teachers.net math board

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Web lessons

You can see my entire approach by viewing my interactive lesson on this topic at:

http://www.mathgoodies.com/lessons/vol7/order_operations.html

This lesson uses whole numbers only. I have another lesson which builds upon the first one, and uses exponents at:

http://www.mathgoodies.com/lessons/vol7/operations_exponents.html

For order of operations with integers, visit:

http://www.mathgoodies.com/lessons/vol7/operations_integers.html

Gisele, Math Goodies 10/14/00 on teachers.net math board

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"PEMDAS"

Go with Pemdas -- I've used it with my sixth grade, and it works quite well -- point out that in math, the important thing is to have a logical step-by-step problem-solving approach. Pemdas is the instruction book to go by.

g, 10/18/00 on teachers.net math board

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PEMDAS can be dangerous as they progress in math!

Make sure that your students understand that multiplication and division go together; multiplication does not take precedence over division. I teach high school, and too often kids think that multiplication comes before division because M comes before D in PEMDAS. It's a great place to start, but don't let the mnemonic device replace the actual mathematics going on.

George James, 10/19/00 on teachers.net math board
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