Order of operations is a foundational fifth-grade math skill that students use to evaluate multi-step numerical expressions correctly and consistently. Fifth graders apply PEMDAS — Parentheses, Exponents, Multiplication, Division, Addition, Subtraction — to evaluate expressions with mixed operations, understand why parentheses change results, and apply the rules to multi-step real-world problems involving all four operations.
The main challenge is that students evaluate expressions left to right without respecting operation priority, computing 3 + 4 × 2 = 14 instead of 11. Students also believe parentheses are optional, not realizing that (3 + 5) × 2 and 3 + 5 × 2 give different results. In Grade 4, students evaluated simple multi-step expressions; Grade 5 formalizes PEMDAS, introduces exponents, and requires applying the rules in complex contexts.
Our order of operations worksheets give fifth graders structured practice correcting left-to-right evaluation errors, applying PEMDAS rules to mixed-operation expressions, understanding how parentheses change values, evaluating expressions with exponents, matching equivalent expressions to their values, and solving real-world word problems that require correct operation sequencing.
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Browse all 12 printable worksheets below — click any card to open the full page.
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
What's Included in This Download
What You'll Learn
These order of operations (pemdas) worksheets help grade 5 students develop essential math skills through engaging activities.
Learning Objectives
- PEMDAS Rules: Apply the correct order of operations
- Parentheses First: Evaluate grouped expressions before others
- Exponents: Calculate squares and cubes first
- Mixed Operations: Solve multi-step expressions with all four operations
- Error Correction: Identify and fix common order of operations mistakes
Skills Covered
How to Use These Worksheets
- Download & Print: Click the download button to get the PDF. Print on standard 8.5" x 11" paper.
- Start Simple: Begin with easier pages before moving to more challenging activities.
- Daily Practice: Dedicate 10-15 minutes each day for consistent learning.
- Use Manipulatives: Pair worksheets with physical objects like blocks or counters.
- Provide Encouragement: Celebrate progress and effort to build confidence.
- Check Progress: Use the included answer key to review work together.
Common Mistakes to Watch For
- Evaluating left to right without following operation priority — students compute 3 + 4 × 2 = 14 by adding first, then multiplying. Multiplication and division must be done before addition and subtraction, regardless of left-to-right position.
- Ignoring how parentheses change the value — students compute (3 + 5) × 2 = 13 by multiplying 5 × 2 first instead of adding 3 + 5 first. Parentheses always take priority and must be evaluated before anything else.
- Confusing exponents with multiplication — students compute 3² as 3 × 2 = 6 instead of 3 × 3 = 9. An exponent tells how many times the base is used as a factor — 3² = 3 × 3, not 3 doubled.
Frequently Asked Questions
What does PEMDAS stand for and what order do I use?
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Evaluate in this order: (1) Parentheses — anything inside grouping symbols first; (2) Exponents — squares and cubes; (3) Multiplication and Division — left to right, at the same level of priority; (4) Addition and Subtraction — left to right, at the same level. A common memory phrase is 'Please Excuse My Dear Aunt Sally.' The critical rule is that multiplication and division are equal priority and evaluated left to right — same for addition and subtraction.
Why do we need order of operations rules?
Without agreed-upon rules, the same expression could give different answers depending on who evaluates it. For 3 + 4 × 2: left-to-right gives 14, but PEMDAS gives 11 (multiply first: 4 × 2 = 8, then add 3). The order of operations is a universal agreement that makes mathematical expressions unambiguous — every person following the rules gets the same answer. Parentheses allow writers to override the default order when a different sequence is intended: (3 + 4) × 2 = 14 explicitly asks for addition first.
How do parentheses change the value of an expression?
Parentheses force whatever is inside to be evaluated first, overriding the normal order. For 3 × 4 + 2 = 14 (multiply first, then add), but 3 × (4 + 2) = 18 (add first, then multiply). The parentheses moved the addition to the first step, changing the result. To make 2 + 3 × 4 equal 20, place parentheses around the addition: (2 + 3) × 4 = 5 × 4 = 20. Whenever you need a lower-priority operation to happen first, wrap it in parentheses to override PEMDAS order.
How do I evaluate expressions that include exponents?
After evaluating parentheses, compute all exponents before doing any multiplication, division, addition, or subtraction. An exponent tells how many times to use the base as a factor: 3² = 3 × 3 = 9, 4² = 16, 2³ = 2 × 2 × 2 = 8. For 3² + 4 × 2: first compute 3² = 9, then multiply 4 × 2 = 8, then add 9 + 8 = 17. For (2 + 3)²: first compute the parentheses 2 + 3 = 5, then apply the exponent 5² = 25. The exponent applies to the entire parenthetical result, not just the last number.
How do I use PEMDAS to solve a real-world multi-step problem?
Translate the problem into an expression, then apply PEMDAS to evaluate it. For 'a store sells 3 packs at $2 and 2 notebooks at $5': the total is 3 × 2 + 2 × 5 — multiply each group first: 6 + 10 = 16. For 'a baker makes (6 + 4) × 3 cookies then sells 2² × 5': compute parentheses (6 + 4 = 10), then exponent (2² = 4), then multiply each group (10 × 3 = 30 and 4 × 5 = 20), then subtract 30 − 20 = 10. Writing the full expression before evaluating keeps each step organized and reduces errors.
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Can I use these in my classroom?
Absolutely! Teachers are welcome to print and use these worksheets in their classrooms. Make as many copies as needed for your students.