Order of operations and special ed. I need drastic help!!!!

Not knowing what the kid’s problem is, I’m not sure this will help, but I just went over this with a college student and it did. Some people use “PEMDAS” as a mnemonic (or “please excuse my dear aunt sally”) — but with the caveat that multiplication really doesn’t go ahead of division.

First thing you look for are parentheses because that’s the one that the person writing the equation can use to break any of the other rules. P

AFter that, you do the operations which do the most at one time first, and the ones that are smallest, come last. So:

Next is exponents, which are like EXPLOSIONS. Sort of silly since we use those tiny little numbers when they actually get huge really fast.

THen come Multiplicatoin & Division…which are more complicated than the last ones, addition and subtraction.

The tough part is, after that, getting the kiddo to see which ones are where in the equation.

Here’s a cut & paste from another site:

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

First thing is to understand why this is important. Why do we care?

Consider a simple arithmetic problem such as

3 + 2 x 4

If we did this left to right: 3 + 2 = 5, and then 5 X 4 = 20

On the other hand, if we decided to do the multiplication first,
2 x 4 = 8, and then 3 + 8 = 11

Which one is right??

Both have perfectly correct computations, but they don’t agree!

How can we have accurate math, how can we build houses and compute taxes and all the things we do with numbers in the real world, if two people can do correct computations and get different answers?

It’s worth playing around with a few examples and seeing how many answers you can come up with for one problem with three or four computations.

Once you have developed a reason for why we have such a rule, then it helps to explain that the rule is sort of like a traffic law — it gets everybody to the same place without collisions. In this country we drive on the right; in England they drive on the left — it doesn’t matter which side you choose, as long as everybody stays on the same side in the same country. But if people drove on whichever side they chose, there would be a lot of collisions. The math rule order of operations is the same thing, an arbitrary agreement or convention.

The “Please Excuse My Dear Aunt Sally” rule is useful, but the poster above is absolutely right in pointing out that you can’t let the rules take over from the math. (a good policy in general).
Note to the student as you teach it that P for Parentheses also includes all other grouping symbols, including absolute value marks, square root signs, and numkerators and denominators of fractions; the phrase “My Dear” goes together, and multiplication and division go together; and the phrase “Aunt Sally” goes together, and addition and subtraction go together. At first this may seem to make it more complicated, but in the long run you want to avoid blind following of rules without thinking, so please take the time.

I just went thru this with my 6th grade daughter. She dances and movement really helps her. She couldn’t memorize the order and I don’t think pneumonics would have worked, but what did was the following.
We try to put together a little movement to remember the order of operations.
For instance the order of operations for algerbra are:
1) Do all problems in grouping symbols ie items in parenthesis (a+b).
2) Do all exponents 3 to the 4th power
3) Do multiplication and division from left to right
4) Do addition and subraction from left to right
5) Solve the equation.

She remembers this by saying and using her hands and body parts.
She puts her hand up for the parenthesis.
She makes a muscle and says “power” for exponents (this one she really likes)
She crosses her arms in an X for multiplication and uses her foot and fists for division and moves her hand from left to right
She then makes a plus sign with her arms and a minus sign with her arm, moves her hand from left to right
Finally she uses both arms over her head and says solve.

I tried to have her memorize the order with no results and the next night she couldn’t remember, we did the little movement above and she has it down cold, we practiced on examples and on her test she got an 87%. She taught her class this technique too. good luck.