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An engaging order of operations lesson plan

If you’re anywhere on social media, you’ve probably come across a math problem that so many people  solve incorrectly.  Chances are you think to yourself, “How are so many people getting this wrong?”  The reason is simple.  Their teacher was following the wrong order of operations lesson plan.  Simply stated, they used PEMDAS from your classic order of operations lesson plan.  Although the mnemonic can be very helpful, it can also be catastrophically misleading.  Please Excuse My Dear Aunt Sally often leads students to believe multiplication should come before division and addition should come before subtraction; however, that is not always true.  Many students come to me with this misconception; therefore, I created a lesson plan on order of operations that is built around a unique and memorable way to remember the hierarchy of operations.

Why PEMDAS is misleading

Depending on the problem, any and all of the following phrases could be true.  Please Excuse Dear My Sally Aunt, Please Excuse Dear My Aunt Sally, Please Excuse My Dear Sally Aunt or the original Please Excuse My Dear Aunt Sally.  However, the concept of sharing all of these with students is frightening and most of the phrases don’t even make any sense!  However, if you were to use this mnemonic tool, you would be doing your students a disservice in not telling them all the other possibilities. 

Multiplication and division should be solved from left to right, as should addition and subtraction.  A new way of teaching the order of operations is needed to ensure understanding and to put these common misconceptions to rest. 

What to teach instead of PEMDAS for your next order of operations lesson plan

Last year I was tired of fighting the battle of misconceptions my students had from PEMDAS.  I don’t totally disregard the helpful hint; but I got to thinking.  There has to be a better way to get students to understand that subtraction and addition are solved based on whichever one comes first in the problem.  I was fighting this battle for years and it hit me…let the operations do the fighting.  If you were to ask anyone that has any background knowledge about mathematics which operation is faster and stronger between multiplication and addition, chances are they would argue that multiplication is the stronger of the two operations.  It can build up numbers at a much faster rate.  Similarly, division can break down numbers at a much faster rate than subtraction. 

What about addition and subtraction?  Which operation is superior?  Which one would win in a fight?  Once you can get students to realize a match-up between the two would be a tie, you have won the grueling battle of misconceptions brought on by PEMDAS.  That’s why I use a strength rating hierarchy in my lesson plan for order of operations in math class.

How I started teaching order of operations differently

I start off my lesson talking about two individuals going head to head in a battle of strength.  I show the students the individuals’ ratings and ask the students who would win.  This hook gets students interested in the conversation while math is out of the picture.  Even my students that claim they “can’t do math” are always willing to participate in the discussion.  As a class we go through a series of matchups and discuss who will win along with a supporting argument to quiet any naysayers.  For fun, every once in a while I’ll throw in teachers’ names to further engage students.  However, I always include at least one example that contains multiple people (to later on simulate the idea of parentheses) and a matchup that would result in a tie. 

Next, following the “story” and non-math related scenarios, I start to introduce mathematical operations.  The students follow similar reasoning they used from the opening activity to determine which operation would win in a “fight” or would be considered to have more “strength”.  I allow and encourage students to discuss with peers and as a class decide the victor.  (The winner should always be the operation that comes first in the order of operations.  Be sure to sway students in this direction if they do not come up with this solution on their own.)

How students benefit from this instruction

Some of the insight and discussions my students have are refreshing to say the least!  They use math related terms to justify their reasoning.  Usually my students will say addition and subtraction result in a tie; however, sometimes they need convincing.  I refer to these operations as having “equal strength”.  I inform the students in the result of a tie, we simply go with the one first in line.  Similar to how people would be announced based on rank.  If two have the same ranking, they would most likely be introduced from left to right.  

Following the group discussion, in small groups, my students organize or rank the following operations:  parentheses, exponents, multiplication, division, addition, subtraction by ordering them from “strongest to weakest”.  Once all groups have time to discuss and come up with their final list, we share thoughts as a group and determine the order of operations as a class based on the strength comparisons.

Can your students easily recall the Order of Operations?

In presenting the material in this way, I found my students less likely to forget the order in which to solve.  Furthermore, students were able to tackle the common misconception that multiplication comes before division and addition comes before subtraction.  To assess my students and provide additional practice and support, I use a variety of order of operations games and activities.  With this order of operations lesson plan in place, I no longer need to worry that my students will have the common misconceptions brought on by my dear Aunt Sally.  Please excuse her, the misconceptions were not intended.