Students first encounter the order of operations in third grade, when they learn that multiplication and division come before addition and subtraction. The full PEMDAS framework, including parentheses, brackets, and exponents, builds out over the next several years and is typically solidified by fifth or sixth grade.
Third Grade: Where It Starts
The Common Core State Standards introduce the order of operations in grade 3 under Operations and Algebraic Thinking. At this stage, students are expected to know how to perform operations “in conventional order when there are no parentheses to specify a particular order.” In practical terms, that means a third grader working through a problem like 3 + 4 × 2 should know to multiply before adding, arriving at 11 rather than 14.
The acronym PEMDAS itself may or may not appear in a third-grade classroom. What matters at this level is the concept: multiplication and division take priority over addition and subtraction. Students need to be comfortable with all four basic operations before they can start layering on rules about the sequence, so teachers typically introduce the order of operations after students have a solid handle on multiplication and division facts.
Fifth Grade: Parentheses and Grouping
By fifth grade, the complexity jumps significantly. The standards call for students to “use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.” This is where PEMDAS as a complete acronym starts making sense in the classroom, because students now need to handle grouping symbols (the P in PEMDAS) alongside the arithmetic operations they already know.
Fifth graders also begin writing and interpreting expressions without solving them. For example, they might express the phrase “add 8 and 7, then multiply by 2” as 2 × (8 + 7), and recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without actually calculating either one. This shift from pure computation to reading and constructing expressions is a major step toward algebraic thinking.
Sixth Grade and Beyond: Exponents and Algebra
Exponents, the E in PEMDAS, typically enter the picture in sixth grade as part of the Expressions and Equations domain. Once students can work with exponents, they have every piece of the PEMDAS framework in place. From sixth through eighth grade, the standards continue building on order of operations through increasingly complex algebraic expressions and equations, reinforcing the same rules with variables, negative numbers, and more layered problems.
So while the concept is introduced in third grade, most students don’t work with the full PEMDAS sequence until around fifth or sixth grade. The progression is intentional: each year adds a new layer of complexity on top of skills that should already feel automatic.
What PEMDAS Actually Means
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It tells you the order in which to evaluate parts of a math expression. But the acronym can be misleading if you read it as six separate steps performed one at a time from left to right. In reality, multiplication and division share the same priority level, and so do addition and subtraction. Within each pair, you work left to right across the expression.
This is one of the most common sticking points for students. Research published in the journal Learning and Instruction found that only 16% of adults fully understood the order of operations, and nearly half held misconceptions tied directly to how the acronym is taught. The most frequent error is treating PEMDAS as a strict sequence, assuming multiplication always comes before division, or addition always comes before subtraction. In the expression 8 ÷ 2 × 4, for instance, you work left to right because division and multiplication are equal in priority, giving you 16 rather than 1.
The Same Rule, Different Acronyms
If you learned math outside the United States, you may have learned the same concept under a different name. In the UK, the standard acronyms are BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) or BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction). Canada and New Zealand commonly use BEDMAS. A newer acronym, GEMS (Groupings, Exponents, Multiplication or Division, Subtraction or Addition), has been introduced in some classrooms as an alternative that makes the equal-priority pairings more obvious. All of these describe the same set of rules.
How to Help a Student Practice
If your child is learning PEMDAS and struggling, the most important thing to reinforce is that multiplication and division are done together (left to right), and addition and subtraction are done together (left to right). Many mistakes come from treating the acronym as a strict six-step checklist. Writing out problems and having your child circle which operation to do first, before solving anything, builds the habit of scanning the whole expression instead of just plowing through left to right.
Start with expressions that have no parentheses, like 5 + 3 × 2. Once that feels natural, add parentheses: (5 + 3) × 2. Then layer in exponents when your child has learned them. Matching the practice problems to what your child’s grade level actually covers keeps things from feeling overwhelming. A third grader doesn’t need exponents yet, and a sixth grader should be challenged with expressions that combine all the elements.