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Order of Operations


I was lucky enough to have a true "math moment" today. The type of day when your child comes up with something so brilliant that you feel like all is right with the world, that you MUST be a good mother and that you made the right decision to homeschool. I'm 99% sure that I would feel this way even if I could claim to be objective - which, of course, I can't.

For some reason I decided to introduce the order of operations today to my 3rd grader. No one told me to. I didn't consult a scope and sequence.  I just felt in the mood to do it and I thought I would approach it and see how it worked. I thought that he was ready for something new and a bit different. It couldn't have gone any better than it did.  In fact, I'm so happy with how it went that I just knew I had to share it.  Maybe this approach will be fun for other families too.

I started the topic off with PEMDAS as a memory tool.  Each letter represents an operation and the order in which we do them. Parenthesis, Exponents,  Multiplication, Division,  Addition and Subtraction.  In 20 minutes time we had worked out several juicy math problems and my son created a math story around this topic. It was a lot of fun.  But then again....math is usually fun around here.

Here is what he did. Each operation is personified as a kid. These kids live on the same block and they work together. Their names are:

Patrick Parenthesis
Eddie Exponent
Maria Multiply
David Divide
Annie Addition
Sarah Subtraction

For EVERY problem worked out [on the chalkboard - him telling me what to do and when] I wrote PEMDAS in the top corner.  My son explained that when the kids work they do so in order.  When they are done they go off and ride bikes or skateboards.  He also reminded me that they must finish ALL of their work before they are able to leave.  Not all of the kids work on each project.  Sometimes they get the day off.  The answer of each problem is what each kid gets paid.

My son approached EVERY problem by saying "is Patrick working today"? If he was working he would do all of his work and then a check mark would be put under his initial. I created several problems with more than one set of (   ).  I used various operations within them.  Not all were simple addition.

We went through the list of kids checking them off when their work was done so they could go play.  If an operation wasn't present we just said "oh Eddie has off today" and moved on to the next in order.   Operations that were not in the problem at hand had a slash through their initial.  In this way he was able to do every problem quickly and accurately by simply checking off each item on the list. Nothing was left out or done out of order.  Even with the fun story and the embellishing we did around the characters each problem was completed in 2 - 3 minutes.  Some of the stories were pretty complex.   Others were hilarious!   Call us rebels - doing math in our PJs laughing our heads off!

This was the first time we had ever worked with complex problems that had several steps. Each time we put a character to work I modified the equation to fit that step and copied down the rest. I'm sure you've done this.  The problem gets smaller and smaller until it is reduced to something like 16 + 3. That is a pretty simple equation.  Now when I say simplify and solve this problem he knows exactly what I mean.

I'm pretty certain that introducing this concept in a workbook would have bombed with my son. This was just the start he needed to have a good foundation and move on with this concept. I may or may not create worksheets for him to do.   I'm gonna follow his lead on this one. If the processing out loud and the stories really do it for him then we'll stick with that for now.  By next week I hope to have him working independently at the chalkboard with me watching, ready to help if needed. In two weeks I hope that he can work two problems while I shower or cook or play with his little sister.  I just don't know.  I want to be flexible and open to follow his lead.  I do know that this will stick with him for years to come.  I may even hear him teaching it to my grandchildren.

If you are struggling with this concept or don't know how to introduce it I suggest you give this a thought. It may really work for your child.

Making math fun and meaningful is a high priority for me.  I didn't lose my math phobia until college statistics class - believe it or not. The right professor at the right time did the trick.  Or maybe I was just ready to stop hiding behind the old "but I'm a math dummy" whine.  Whatever the reason I am now what I laugh and call "math empowered"!  I've seen children fall in love with math and it is an amazing thing.  There is no reason why every child can not enjoy that intoxicating power.

If this works nicely for you please let me know. I 'm sure my son would be pleased to hear of other kids putting Patrick and his friends to work!  But don't forget their paychecks.  After all they might want to go to the mall :-)


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