Tag Archives: Order of Operations

PEMDAS is NOT a Word

Here is why I believe that the PEMDAS method for remembering the order of operations should NOT be used:

1.  PEMDAS is not a word.  In general, I believe that for mnemonic devices to have the greatest impact, they should be easy to remember words.  PEMDAS is not easy to remember and PEMDAS is not even a word.

2.  PEMDAS implies to students that there are six steps in the order of operations:  Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, when in fact, there are only four steps in the order of operations.   How can we expect students to properly remember the order of operations if we are providing them with such a misleading mnemonic device?

3.  PEMDAS should not be used simply because it is the way that students want to be taught.  One student told me the other day that he was confused by the way that I was doing the order of operations simply because I was not using PEMDAS.  I told this student that he could continue to use PEMDAS if he wanted to, but he would continue to get incorrect answers (He is one of the students who thinks that PEMDAS has six steps).

4.  PEMDAS simply does not work.  If PEMDAS worked, wouldn’t students actually understand the order of operations?  The fact of the matter is that PEMDAS does not help students understand the order of operations.  PEMDAS did not work for students when they were in elementary school, why should it work for them in college?

I truly believe that my position as a college math instructor requires me to present the material differently than the students saw the material the first time that it was taught to them because whatever they were taught the first time obviously did not stick long term.  Although my ultimate goal is to help students refresh their memory, why should I refresh someone’s memory about something that is misleading and simply does not work?

Below is an example of the Order of Operations using the GEMS Procedure.  I prefer the GEMS Procedure because GEMS is actually a word and GEMS implies that the order of operations actually has four steps and not six steps.


To further prove my point, here is an example of a problem that is incorrectly done using PEMDAS versus a problem that is correctly done using the GEMS Procedure. 


I know that the GEMS Procedure is not going to become ‘mainstream,’ but I can hope, right?

Pi Day Exponent Activity

This year on Pi Day I was teaching exponents, so I created an activity surrounding many of the common errors that I see many students make when working with expressions involving exponents.  I have attached the file to this post, and I would hope that people would know what to do with it, but let me explain anyway:

1.  I printed and cut out about 10 copies of the activity (I wanted to have the students work in groups of no more than 3).  I also like to have 1-2 extra copies because it has become seemingly noticeable with my classes that there are some students who like to take the activities home with them.  Honestly, if a simple game like this gets them excited enough about math that they actually want to do play math again when they get home, I’m all for it.  By the way, it worked out best for me to place the cut out pieces in 10 separate envelopes.


2.  The activity is simple:  The students need to match the problems with the answers.  Some answers have more than one correct problem.  Some answers have no correct problems (there are two ‘whammies’).


By the way, if you notice, I created this in such a way that it could be used anytime of the year.  I hope you and your students enjoy it.


NOTE:  I noticed after the upload that you need to actually download the file for it to show up correctly.

Math Games for Integers, Multiplication, and Combining Like Terms

I have some slightly under-prepared students semester, so I suggested to them that they should try to work on their basic skills outside of class.  However, this requires me to provide some recommended resources to them, and these are what I have discovered:


  • Factoris – Tetris-style game for multiplication facts.
  • Penguin Jump – Fun Multiplication Game that can be played with up to 4 people from around the world.
  • Dad’s Worksheets – For those who just want the traditional worksheets to practice with.

Combining Like Terms

  • Combining Like Terms Quartet – This like terms game requires you to match the center term with its the appropriate like term. 
  • Matching Game – Identify the matching terms in two columns.
  • On-line Jeopardy Game – Distributive property, combining like terms, evaluating expressions, solving equations. 
Integers and Order of Operations
Other Helpful Links

GCF, LCM, and Order of Operations

In my Basic Mathematics class we just finished discussing the order of operations, and students always seem to have a problem with it, especially when division comes before multiplication (Sally has always told them otherwise).  Today we discussed finding the Greatest Common Factor (GCF) and Least Common Multiple (LCM), another topic that students sometimes seem to have a problem with.  I came up with the following problem, which sparked quite a lot of discussion in the classroom.  But more than that, I think it is the type of problem that continues to reiterate the Order of Operations, and doesn’t back students into the hole of forgetting what they have learned from one chapter to the next.


Pre-Algebra and Algebra Resources

A few months ago I had students in my Basic College Math class create a game about fractions.  One student created “Fraction Bingo”.  I decided to search the web to see if there were printable bingo sheets available.  Well, there were, along with some other activities that I found on the same website from Holt, Rinehart, and Winston.  And below is a list of a few of my favorite ones, appropriate for college-level basic math classes (organized by topic):

Operations on Numbers