Subtracting Isn’t Always Last! Make Order of Operations Easier

A lot of times when I post a new blog entry, I’m thinking of new teachers, who could use some quick and easy advice that would simply make their day a little easier.  I’m always looking to get the most “bang for your buck”, to maximize the very short time we have students in our presence, actually paying attention, and staying engaged.

I’m not saying that I’ve got it all figured change-signout!  Even in this 16th year of my teaching career, I spend more time than ever changing my lessons, creating new activities, and searching out better ways of teaching, to make the biggest impact that I can, given my students’ abilities (wide-ranging) and my own energy (running on empty with a 1-1/2 year old and another on the way!).

These tweaks don’t have to be earth-moving, monumental changes.  Sometimes, a little, quick change can make a big impact on the way your students understand what you’re trying to convey.  These are the kinds of things that I try to share with new teachers at my school.

One quick and easy change that we can make as pemdasMath teachers is to simply write the PEMDAS order of operations steps like I have pictured here.

Put the M above the D, and the A above the S.

The reason for writing it this way is that many of my 6th graders arrive with the misconception that addition must come before subtraction, when using the order of operations.  And I get it.  I understand that they have been taught the “Please Excuse MDear Aunt Sally” line, and that Aunt comes before Sally.  And I understand that they have been seeing the abbreviation written down in a single horizontal line, like this: PEMDAS.

But when they are suddenly faced with relatively complicated expressions that include increasingly long number of steps, they often get to the last two steps and blow it!  It’s disheartening to them (and to us!) to see students navigate through parentheses, exponents, multiplying with new symbols besides the traditional “x”, and division with a fraction bar, only to have all their work negated by an insistence that adding comes before subtracting!

So, from Day 1, I require my students to write the steps like I have pictured above.  We even draw the arrow from right to left, so students remember that multiplying and dividing are equal in the eyes of Dear Aunt Sally, as are adding and subtracting, as long as you’re moving from left to right.

It’s a small change, but it can take away some of the headaches involved in teaching the Order of Operations.

If you’re looking for a fun way to practice using the order of operations, check out my last post on the Evaluating Expressions Number Cube Games.  And if you have other ways of reinforcing the order of operations, let me know in the comments!


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