When we both moved to 5th grade, one of our team members shared with us the idea of using GEMS rather than PEMDAS for Order of Operations and simplifying expressions. Our minds were blown! It was so much more effective. Here's why:
We all probably grew up learning the common acronym for order of operations: PEMDAS or "Please Excuse My Dear Aunt Sally" or "Parenthesis, Exponents, Multiply, Divide, Add, Subtract". Although it does help remember the order, we found that our students were confused because they would follow the acronym too closely forgetting that you multiply and divide and add and subtract going from left to right. Also, they would get confused if they saw brackets or other types of groupings. It seemed like a common mistake that they forgot the left to right groupings.
So, in comes GEMS! GEMS stands for "Groupings, Exponents, Multiply/Divide, Subtract/Add". Why do we like it better?
The G stands for groupings so it includes parentheses, brackets, braces, and fraction bars.The E stands for exponents just like in the old PEMDAS acronym.
The M stands for both multiplication and division, in order from left to right.
And the S stands fro subtraction and addition, in order from left to right.
By grouping the M/D and A/S into single letters, it solidifies the idea that either operation can be performed first. It depends solely on which comes first in the expression.
We love incorporating music into our instruction, but we couldn't find any songs online using the GEMS acronym. When in doubt, create your own! Feel free to use this fun song with your class! Click the image for a printable file.
