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Second/Order Of Operations

Order of Operations Mastery

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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Prerequisites
Parentheses and Multiplication Together6 WS
Solve: (6 - 2) × 3 = ______
Three Operations Combined6 WS
Solve: (6 - 2) × 3 + 4 = ______
What to Do Next
Order of Operations Word Problems5 WS
Solve this problem: There are 2 boxes with 5 toys each. 3 more toys are added. Equation: 2 × 5 + 3 = ______

Practice Questions

  1. (4 + 5) × 3 - 12 = ?
    Show answer

    15

  2. 25 - 3 × (6 - 2) = ?
    Show answer

    13

  3. (7 - 3) × 5 + 8 = ?
    Show answer

    28

  4. 18 + 2 × (4 + 3) = ?
    Show answer

    32

  5. (6 + 4) × 2 - 9 = ?
    Show answer

    11

Teacher Resources
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