Free Order of Operations Worksheets (Grades 5-8)
Practice order of operations (Grades 5-8) with free printable PDF worksheets. 4 pre-packaged classroom sets with 100% verified step-by-step answer keys, plus an unlimited live customizer for teachers and homeschoolers.
PDF + Answer KeysMultiplication Times Tables 50-Worksheet Master Workbook
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How to Create & Print Custom Worksheets in 3 Steps
Every generated sheet includes student name, date, score lines, and a complete answer key!
1. Set Options & Count
Select difficulty (Easy, Medium, Hard) and choose your exact problem count (8, 12, 16, or 20 problems per sheet).
2. Generate & Review
Click "Shuffle" to generate fresh randomized questions. Student name, date, and score blanks are added automatically.
3. Print with Answer Key
Print clean 8.5"×11" pages. Includes a detachable verified answer key for 1-minute grading or student self-checking!
Recommended Classroom & Homeschool Uses
Versatile math practice formats designed for busy educators and parents.
Explore Interactive Tools for Order of Operations Worksheets (PEMDAS / BODMAS)
Master this math concept across all PanMaths learning verticals:
Common Mistakes to Avoid
The #1 misconception students make is thinking Multiplication ALWAYS comes before Division, or Addition ALWAYS comes before Subtraction. In reality, Multiplication and Division hold equal priority and must be solved from left to right. The same rule applies to Addition and Subtraction.
Worksheet Customization by Grade
Select Easy for Grade 5 introduction (2-step problems without exponents), Medium for Grade 6 (includes single parentheses and multiple operations), or Hard for Grades 7-8 (includes exponents, squared quantities, and nested operations). Every sheet includes an instant printable answer key.
💡 Work Left to Right for Multiplication & Division
Multiplication does not outrank division. When both appear, evaluate them in order from left to right: 12 ÷ 3 × 2 = 4 × 2 = 8 (not 12 ÷ 6).
12 ÷ 3 × 2 = 4 × 2 = 8💡 Parentheses Grouping First
Always simplify everything inside parentheses or brackets before applying outer exponents or operations.
3 × (4 + 5) = 3 × 9 = 27💡 Addition & Subtraction Tie-Breaker
Just like multiplication and division, addition and subtraction share equal priority and are solved strictly left to right.
10 - 3 + 2 = 7 + 2 = 9 (not 10 - 5)Worksheet Facts by Grade Level
| Grade Level | Common Core Standard | Target Operations & Complexity | Recommended Drills |
|---|---|---|---|
| Grade 3 | CCSS.MATH.CONTENT.3.OA.D.8 | Two-step word problems with +, −, × | Set A (Standard) - Basic addition/multiplication |
| Grade 4 | CCSS.MATH.CONTENT.4.OA.A.3 | Multi-step whole numbers with parentheses | Set A & Set B - 2-step parentheses equations |
| Grade 5 | CCSS.MATH.CONTENT.5.OA.A.1 | Parentheses, brackets & nested braces | Set B & Set C - Multi-nested grouping symbols |
| Grade 6 | CCSS.MATH.CONTENT.6.EE.A.2 | Whole number exponents & algebraic variables | Set C (Challenging & Exponents) |
| Grades 7–8 | CCSS.MATH.CONTENT.7.NS.A.2 | Negative signed integers, fractions & powers | Set C & Unlimited Studio custom counts |
Mastering the Order of Operations: PEMDAS vs BODMAS
The Order of Operations is the foundational mathematical rulebook that ensures everyone evaluates algebraic expressions to the exact same correct value. Without a standardized order, an expression like 8 + 2 × 5 could yield either 18 or 50.
PEMDAS vs BODMAS: What Is the Difference?
Different English-speaking countries use different mnemonics for the exact same four-step hierarchy:
- PEMDAS (US & Canada): Parentheses ➔ Exponents ➔ Multiplication & Division (Left-to-Right) ➔ Addition & Subtraction (Left-to-Right). Mnemonic: "Please Excuse My Dear Aunt Sally"
- BODMAS (UK, India, Australia): Brackets ➔ Orders (Powers/Roots) ➔ Division & Multiplication (Left-to-Right) ➔ Addition & Subtraction (Left-to-Right).
- BIDMAS / GEMDAS: Indices or Grouping symbols (brackets, braces, absolute value bars).
The 4 Core Steps of Order of Operations
- Step 1: Grouping Symbols First (P / B) — Simplify innermost parentheses
( ), brackets[ ], braces{ }, and radical radicands first. - Step 2: Exponents & Roots (E / O / I) — Evaluate all powers, square roots, and indices from left to right (e.g.,
3² = 9,√16 = 4). - Step 3: Multiplication & Division (M & D / D & M) — Perform all multiplications and divisions as they appear sequentially from left to right. Neither operation has priority over the other!
- Step 4: Addition & Subtraction (A & S) — Perform all additions and subtractions as they appear sequentially from left to right.
Common Student Pitfalls & How to Avoid Them
Over 80% of student calculation mistakes on standardized math tests come from these two common misconceptions:
- Mistake 1: Forcing Multiplication before Division
Incorrect:20 ÷ 4 × 5 = 20 ÷ 20 = 1
Correct:20 ÷ 4 × 5 = 5 × 5 = 25(Divide first because it appears first on the left). - Mistake 2: Forcing Addition before Subtraction
Incorrect:15 - 5 + 3 = 15 - 8 = 7
Correct:15 - 5 + 3 = 10 + 3 = 13(Subtract first because it appears first on the left).
Benefits of Mastery
📐 Pre-Algebra Mastery
Order of operations is the critical prerequisite for solving one-step, two-step, and multi-variable linear equations.
🎯 Error Prevention
Step-by-step unravelling trains students to write intermediate mathematical proofs without skipped logical steps.
⚡ Standardized Test Confidence
Directly aligns with Common Core State Standards (CCSS) 5.OA.A.1 and 6.EE.A.2 for state exam success.
🖨️ 100% Free Photocopy Rights
Teachers and homeschool educators have full permission to print, photocopy, and distribute all sets.
Frequently Asked Questions
Why do we need order of operations in math?
Without a standardized order of operations, mathematical expressions would be ambiguous. For example, 10 + 2 × 3 could equal 36 if added first, or 16 if multiplied first. Standardizing PEMDAS ensures that scientific formulas, financial calculations, and computer programs produce identical, verifiable results.
Does multiplication always come before division in PEMDAS?
No! Multiplication and division have equal priority. You solve them in whichever order they appear from left to right. In 12 ÷ 3 × 2, you divide first to get 4 × 2 = 8.
Are these worksheets free to print and photocopy for classrooms?
Yes! All PanMaths worksheets, answer keys, and generator tools are 100% free for teachers, homeschoolers, tutors, and students with no sign-up or registration required.
How does the Step-by-Step Answer Key help teachers and students?
Our answer keys provide intermediate evaluation lines (e.g. 1. Parentheses -> 2. Multiply -> 3. Final Answer). This allows teachers to grade student work in seconds and helps students immediately diagnose where an order-of-operations mistake occurred.