Order of Operations: Prioritize the Acronym

PEMDAS problems still? Let us first admit that we may need a different tool or method to explain the order of operations. In fact, many websites and teachers treat PEMDAS synonymously with the order of operations. Below, we make the case that prioritizing the parts of the acronym can help you be more accurate and helpful for students to understand.

*Fyi, we prefer the word “Groups” over “Parentheses,” as indicated by the “G” below.

Prioritize the Acronym

When introducing the order of operations as priorities your students can assess problems in the same way: look from left-to-right for each priority category. This way, students will avoid the “in order” traps, where, for example, they think addition always comes before subtraction. The left-to-right rule applies to each priority, even the first one.

No longer must we tell students to simplify what is inside the parentheses before the term(s) with exponents. Terms with an exponent are already grouped by the exponent, so simplifying those terms is just like if the exponent was replaced with group (a set of parentheses, brackets, braces or fraction lines). When the base is made up of multiple terms, the same left-to-right principle can still apply, since the exponent is written to the right of the terms. Even a radical form can be envisioned in exponential form instead, and then the same left-to-right principle can be used.

So, by prioritizing the acronym, you can teach the left-to-right principle, while avoiding the “in order” traps often applied to multiplication and division operations, as well as addition and subtraction operations. The EXCEPTION is when an exponent has an exponent as well. In that case, you solve from the top down, the exponent of the exponent.

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