GIMA Vs PEMDAS: Why We Changed
Leigh’s goal for students is not to blindly memorize an acronym, but rather use acronyms to build knowledge and understanding about mathematics. Thus we put a lot of thought into the acronym we use to help remember the order of operations.
There are two orders of operations that are inverses of one another.
1. Simplification of expressions (GIMA/PEMDAS)
2. Solving equations (AMIG)
GIMA/AMIG were chosen because they are broader, more global, and offer clarity.
G: Groups Includes grouping symbols such as: (), [], {} Groups can also be indicated by vincula that are part of radical symbols and used as fraction bars. Groups may also be indicated by certain functions (sometimes in conjunction with parentheses). For example sin(x + x) or f 3x+4x dx. |
P: Parentheses Suggests that only the () symbols are addressed. |
Using G instead of P reminds students that all groups must be simplified first. Some countries use B: Bracket. |
I: Index Includes an index in any operational position: exponent, radical, or logarithm. |
E: Exponent Suggests that only exponents are considered. |
Using I instead of E reminds students to consider all expressions of indices. Some countries use O: Order. |
M: Multiplication Multiplication and division have equal weight when considering the order of operations because division can be rewritten as multiplication. Multiplication and division should be performed as encountered from left to right. |
M: Multiplication D: Division While students are taught that M & D go together in the order of operations, anecdotal evidence suggests that many students misunderstand and simplify multiplication and then division. |
Using M instead of M & D reminds students that the operations are simplified together and eliminates the potential for misunderstanding. |
A: Addition Addition and subtraction have equal weight when considering the order of operations because subtraction can be rewritten as addition. Addition and subtraction should be performed as encountered from left to right. |
A: Addition S: Subtraction While students are taught that A & S go together in the order of operations, anecdotal evidence suggests that many students misunderstand and simplify addition and then subtraction. |
Using A instead of A & S reminds students that the operations are simplified together and eliminates the potential for misunderstanding. |
Solving equations requires Students are not traditionally taught the inverse of
1. using GIMA to simplify expressions PEMDAS as the order for solving equations.
2. using AMIG to solve for the variable.