Grade 5Mathmedium
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 5.
Download Free PDF
No signup required — instant download
mathorder-of-operationsG5medium
Worksheet Preview
What Your Child Will Learn
- Apply the correct sequence of operations (PEMDAS/BODMAS) to solve multi-step expressions involving parentheses, multiplication, division, addition, and subtraction
- Identify which operation to perform first in expressions containing two or more different types of operations
- Solve 10 medium-difficulty expressions by correctly following order of operations rules and showing work step-by-step
- Distinguish between expressions where parentheses change the answer versus expressions without parentheses
How to Use This Worksheet
- Step 1: Before starting, have your student write PEMDAS/BODMAS at the top of the worksheet as a reference. Review what each letter means: Parentheses/Brackets, Exponents/Orders, Multiplication & Division (left to right), Addition & Subtraction (left to right).
- Step 2: For each of the 10 problems, instruct your student to first identify and mark all operations in the expression (addition, subtraction, multiplication, division, parentheses). Have them use a colored pencil to highlight or circle parentheses if present.
- Step 3: Direct your student to determine which operation comes first according to PEMDAS rules. Tell them to write a small number (1, 2, 3) above each operation in the order they should be performed.
- Step 4: Have your student solve the expression step-by-step, writing out each calculation on separate lines. This prevents mistakes and allows you to see their reasoning process. For example: First: 3 × 4 = 12. Then: 12 + 5 = 17.
- Step 5: After completing all 10 problems, review any incorrect answers together. Ask your student to explain which operation they performed first and why. This reflection reinforces understanding of order of operations rules.
Tips for Parents & Teachers
Use the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) or BODMAS to help students remember the sequence. Have your student write this acronym at the top of their worksheet as a reference guide. Emphasize that multiplication and division are equal priority (work left to right), and addition and subtraction are equal priority (work left to right).
Watch for the common mistake of working left to right without following order of operations. For example, in the expression 2 + 3 × 4, students often calculate 2 + 3 = 5, then 5 × 4 = 20. Guide them to multiply first: 3 × 4 = 12, then add: 2 + 12 = 14. Have them underline the operation they'll do first before solving.
Many students forget that parentheses must always be solved first, even if they contain addition or subtraction. Use expressions like (2 + 3) × 4 versus 2 + 3 × 4 to show how parentheses change the answer. Have your student circle or highlight the parentheses in each problem as their first step.
Encourage students to write out each step vertically rather than trying to solve mentally. This creates a clear record of their thinking and helps catch errors. For example: Step 1: 5 × 2 = 10. Step 2: 10 + 3 = 13. This organizational method is especially helpful for medium-difficulty problems with multiple operations.
Frequently Asked Questions
Why do we need order of operations? Can't we just solve expressions from left to right?
Great question! Order of operations ensures that everyone solves the same expression and gets the same answer. Without agreed-upon rules, different people might solve 2 + 3 × 4 differently and get different answers. By following PEMDAS, mathematicians worldwide agree that 3 × 4 happens first (= 12), then 2 + 12 = 14. This is essential for mathematics, science, and engineering to work correctly.
Are multiplication and division different priorities? Which one do I do first?
Multiplication and division have the same priority level! The same rule applies to addition and subtraction. When operations have equal priority, you work from left to right. So in 12 ÷ 3 × 2, you divide first because it comes first on the left: 12 ÷ 3 = 4, then 4 × 2 = 8. If multiplication came first instead, you'd get a different answer, so the left-to-right rule is important.
What if there are parentheses inside parentheses? Like ((2 + 3) × 4)?
Solve from the innermost parentheses outward. In ((2 + 3) × 4), first solve the inner parentheses: 2 + 3 = 5. This gives you (5 × 4). Then solve the remaining parentheses: 5 × 4 = 20. Think of it like opening Russian nesting dolls — you open the smallest one first, then the next one, and so on.
Do parentheses always change the answer?
Not always, but often they do. Compare: 3 + 2 × 4 = 3 + 8 = 11 (multiply first), versus (3 + 2) × 4 = 5 × 4 = 20 (parentheses first). Parentheses force an operation to happen before normal order of operations would dictate it. Sometimes, like in 5 × (2) = 5 × 2 = 10, parentheses don't change the answer because there's only one number inside. The key is understanding that parentheses override normal order of operations.
Related Worksheets
More Math Worksheets
Related Articles
How to Teach Fractions to Kids: A Parent's Complete Guide
Learn how to teach fractions to kids in grades 2–5 with proven strategies, visual models, and hands-on methods that build real understanding — not just memorized rules.
How to Teach Ratios and Proportions: A Middle School Parent's Guide
Learn how to teach ratios and proportions to middle schoolers with step-by-step strategies, real-world examples, and hands-on activities for grades 6–8.
How to Teach Geometry to Kids: Angles, Shapes, and Lines
A practical parent guide to teaching geometry from kindergarten through 8th grade — covering shapes, angles, lines, and symmetry with hands-on activities and free worksheets.
Get Free Worksheets in Your Inbox
Subscribe for new worksheets and homeschool tips. No spam, unsubscribe anytime.