Understanding Order of Operations

Poorly Executed Mnemonics Definitely Addle Students:

In this very clever post, Bill Shillito reminds us why most of the mnemonics used to remember the rules order of operations have problems. He suggests, if you have to use anything, GEMA {grouping symbols, exponents, multiplication (first convert division to multiplying by a fraction), and addition (first convert subtraction to adding the opposite)}.

Still what kids really need to understand is that “The most compact shorthand is evaluated first.” For example exponents are just a short cut for multiplication, ex. $4^3=4*4*4$.
And multiplication is just a short cut for adding, ex. $4*3=4+4+4$.

If we keep this in mind students need to only remember two things:
     • Pay attention to grouping.
     • Shorthand comes first.


With PEMDAS so ingrained in our students heads, I had suggested that we use PEDMSA. Every time I have written this on the board the students knew this had to do with order of operation. The advantage to this is that if a student divides before they multiply it will be the same as converting the division to multiplying by a fraction and they will still get the correct answer. (The same is true for subtraction before addition, in reality you have just treated the subtracting as adding the opposite.)

Dr. Math's Order of Operations

I also have a video on the shorter version PEMA were I talk about how multiplying and dividing are related, and how adding and subtracting are related.

To see this lesson click: Order of Operations
To read the original post: http://www.solidangl.es/2014/07/poorly-executed-mnemonics-definitely.html