GEMS is an acronym to help students remember the order of operations. It stands for "Groupings"/"Exponents"/"Multiplication Family"/"Subtraction Family". I prefer the GEMS acronym over the PEMDAS acronym because the order of operations really only has FOUR steps, and the fact that PEMDAS has SIX letters often confuses my students into thinking that multiplication always comes before division and addition always comes before subtraction as part of a six-step process – NOT TRUE! The GEMS acronym has the correct number of letters to correspond with the number of steps in the process – a seemingly obvious requirement for a memory tool, and yet PEMDAS is still so widely used. Why spend extra time correcting misconceptions instead of just starting with a different tool?
This 10-page pdf file contains a student copy and a teacher copy of a two-page, double-sided foldable notes page with four flaps (one for each step in the GEMS process). The foldable contains a front page with the acronym, a detailed example problem, and a description of each step, including what is worked in each step and the order in which it is worked (left to right, inside to outside for groupings, etc.).