Middle School PEMDAS Worksheets
All worksheets are created by the team of experienced teachers at Cazoom Math.
What is PEMDAS and why do middle school students need to master it?
PEMDAS is the acronym for the order of operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). This hierarchy determines the sequence for evaluating mathematical expressions, ensuring everyone arrives at the same correct answer. Middle school students encounter PEMDAS throughout 6th, 7th, and 8th grade as expressions become increasingly complex, and it forms the foundation for solving algebraic equations, simplifying expressions, and working with formulas.
A critical teaching point involves the "MD" and "AS" pairs. Students lose points on assessments when they believe multiplication always comes before division or addition always precedes subtraction. The expression 12 ÷ 4 × 3 equals 9 (working left to right), not 1 (if division waited for multiplication to finish). Worksheets that systematically present these scenarios help students internalize that operations at the same level are performed from left to right.
Which grade levels use these PEMDAS worksheets?
These worksheets serve middle school students in 6th grade, 7th grade, and 8th grade. The Common Core State Standards introduce order of operations in 6th grade (6.EE.A.1), where students evaluate numerical expressions with whole numbers and exponents. The skill continues developing through 7th and 8th grade as students work with integers, fractions, and eventually algebraic expressions.
The progression across these grades shows increasing complexity. Sixth graders typically work with whole numbers and basic exponents in straightforward expressions. By 7th grade, students apply order of operations with negative numbers and more nested grouping symbols. Eighth graders often encounter expressions that combine fractions, decimals, and variables, requiring fluent PEMDAS application while managing multiple mathematical concepts simultaneously. This scaffolded approach prevents cognitive overload while building procedural fluency.
How do students learn to expand single parentheses correctly?
Expanding single parentheses requires students to apply the distributive property, multiplying the coefficient outside the parentheses by each term inside. For example, 3(x + 5) becomes 3x + 15, not 3x + 5. Students must recognize that the multiplication distributes across all terms within the grouping symbol. This skill bridges arithmetic and algebra, preparing students for solving multi-step equations and simplifying complex expressions.
This concept appears constantly in STEM fields, particularly when working with formulas and units. Engineers calculating the total cost of materials use expressions like 12(8.50 + 3.25) to find the cost of twelve items when each includes a base price plus tax. Scientists converting temperature use C = 5/9(F - 32), which requires correct parentheses expansion. Programming and spreadsheet formulas rely on this same principle, making it a practical skill beyond mathematics class.
How can teachers use these PEMDAS worksheets effectively in class?
The worksheets provide structured practice with varied problem types, allowing students to build confidence with each aspect of order of operations separately before combining skills. The answer keys enable immediate feedback, which research shows significantly improves retention. Teachers can assign specific worksheets targeting the exact skill where students demonstrate weakness, rather than recycling generic practice that may not address the actual gap.
Many teachers use these worksheets during math centers or stations, where small groups rotate through different order of operations skills. They work well for differentiated homework assignments, allowing students who struggled during the lesson to practice foundational skills while others tackle challenge problems. The "Make Your Own PEMDAS Question" templates engage students in reverse-engineering expressions to reach target values, which deepens understanding more effectively than passive computation. Some teachers report success using these as warm-up activities or exit tickets to monitor ongoing understanding.