Grade 5/Order of Operations
Order of Operations Mastery (593)
This culminating mastery worksheet for combining rules features more challenging three-operation problems with larger numbers and varied formats. Students demonstrate complete understanding of order of operations by solving problems like (4 + 5) × 3 - 12 and 40 - 5 × (6 + 2). All problems require careful application of parenthesis-multiply-add/subtract sequence. This comprehensive practice prepares students for real-world applications and word problems in the next unit.
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Teaching Notes
This is an excellent pre-assessment or unit assessment for order of operations. Students who can complete this worksheet accurately are ready for word problems and real-world applications. Watch for: consistent application across all formats, accurate calculations with larger numbers, and systematic approach (not guessing). Students struggling here need targeted review of specific rules. Note Q10 has answer of 0 - good discussion point about subtracting equal amounts. Consider timing students to assess fluency vs. understanding.
Vocabulary
Parentheses: Symbols grouping parts of a math problem.
Order of Operations: Rules for solving math problems correctly.
Common Mistakes
- Calculation errors with larger numbers (especially multiplication)
- Reverting to old habits under pressure (left-to-right)
- Skipping steps mentally and making errors
- Not double-checking work on challenging problems
- Confusion on problems like 40 - 5 × (6 + 2) where result is 0
- Ignoring parentheses first.
- Incorrect add/subtract order.
- Left-to-right calculation errors.
- Misinterpreting operation symbols.
Differentiation
SupportAllow use of three-step template. Work in pairs with peer tutoring. Focus on first 6 problems only. Provide extra practice on specific weak areas identified. Consider returning to simpler two-operation problems first. Allow calculator for multiplication if focus is on operation order, not computation.
ChallengeNo step-by-step template provided - show only final answer. Add time challenge for fluency. Create four-operation problems. Design problems with specific characteristics (answer must be even, answer between 20-30, etc.). Write word problems requiring these calculations. Explore what happens with different parenthesis placements.
Discussion Questions
- Which problem was most challenging? What made it harder?
- How did larger numbers affect your solving process?
- Did you find any patterns in how the problems were structured?
- What strategies helped you keep track of three operations?
- Question 10 equals 0 - is this possible? Why or why not?
- Why is the order of operations important?
- How do parentheses change an expression?
- Can you explain PEMDAS/BEDMAS in your own words?
- When might you use order of operations outside of math class?
Extension Activities
- Create mastery-level problems for a classmate to solve
- Self-assessment: Which types of problems do you feel most confident solving?
- Error correction: Swap papers and check each other's work, discuss any mistakes
- Preview word problems: "You have 40 stickers. You give away 5 bags with 6 + 2 stickers each. How many left?"
- Challenge: Four operations: (4 + 5) × 3 - 12 + 8
Parent Tip
Ask your child to create a problem using all four operations and solve it.
Learning Path
Skill Cluster
Algebraic Thinking & Number Sense
Estimated Time
25 minutes
Skills Practiced
order operations masterycomplex multi step problemsready for applications
Prerequisites
- 591
- 592
- Multi-step arithmetic without grouping
- Basic operation fluency
Next Steps
- Algebraic expressions with variables
- Solving multi-step equations
- Order of Operations with Exponents
- Real-World Multi-Step Problems