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Grade 5/Order of Operations

Multi-Step Challenge Problems

This challenging worksheet presents complex real-world scenarios requiring multiple operations and careful attention to order of operations. Problems involve larger numbers and more sophisticated contexts like libraries, farms, stores, and parking lots. Students must read carefully, identify all operations needed, write the complete equation, and solve using proper operation order. Some problems require three or four operations, building on all skills learned throughout the unit.
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#WorksheetQuestionsActions
Easy
1
10 questions
2
10 questions
Medium
1
10 questions
2
10 questions
Hard
1
10 questions
2
10 questions
Prerequisites
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 = ______
What to Do Next
Division Before Addition6 WS
Solve: 12 ÷ 3 + 2 = ?

Practice Questions

  1. A library has 8 shelves. Each shelf has 6 books. If students borrow 15 books, how many books are left on the shelves?
    Show answer

    33

  2. Maya had 12 flowers. She gave 3 friends 2 flowers each. Then she picked 7 more flowers. How many flowers does Maya have now?
    Show answer

    13

  3. A farmer planted 5 rows with 7 corn plants in each row. Birds ate 8 plants. How many corn plants are left?
    Show answer

    27

  4. There are 40 students. They form 6 groups of 4 students each. How many students are not in a group?
    Show answer

    16

  5. Jake collected 9 rocks on Monday and 6 rocks on Tuesday. He gave his friend 3 bags with 4 rocks each. How many rocks does Jake have left?
    Show answer

    3

Teacher Resources
Teaching Notes

This worksheet is significantly more challenging due to larger numbers and more complex scenarios. Some problems involve three operations (Q2, Q7, Q11), requiring students to apply order of operations multiple times. Calculator may be appropriate if focus is on operation order rather than computation. Encourage students to: 1) Read problem twice, 2) Underline key numbers and circle operation words, 3) Write complete equation, 4) Number the operations 1-2-3, 5) Solve step-by-step, 6) Check answer makes sense in context. Excellent for gifted students or enrichment.

Vocabulary
Challenge Problem: A problem requiring multiple steps to solve.
Equation: A number sentence with an equals sign.
Common Mistakes
  • Calculation errors with larger numbers (especially 8 × 7, 9 × 8)
  • Missing one operation in complex three-operation problems
  • Writing partial equation instead of complete equation
  • Solving in wrong order when multiple operations present
  • Not re-reading to verify answer makes sense in context
  • Incorrect operation order
  • Missing a step
  • Misreading scenario details
  • Calculation errors
Differentiation
SupportStart with only two-operation problems (Q1, Q3, Q4, Q6, Q8, Q10, Q12). Allow calculator for multiplication. Provide graphic organizers with boxes for each step. Work in small groups with teacher guidance. Break longer problems into parts: "First find total flowers, then subtract shared flowers." Extended time on fewer problems better than rushing through all.
ChallengeRemove equation prompts - students determine equation independently. Add problems with four operations. Include problems requiring estimation first ("About how many..."). Challenge: Create problems where different parenthesis placement changes answer. Write problems with intentionally confusing wording that students must decode. Time challenge: Complete worksheet in under 25 minutes.
Discussion Questions
  • Which problems required the most operations? How did you keep track?
  • What strategies help with larger numbers?
  • Did any answers surprise you? Why?
  • How do you check if your answer is reasonable?
  • Which problem was most challenging? What made it difficult?
  • What information is essential to solve?
  • Which operations do we need, and in what order?
  • How can we check our work?
  • Can this problem be solved another way?
Extension Activities
  • Create your own multi-step problems with answers between 30-50
  • Compare Q2 vs Q7 vs Q11: What's similar? (all have three operations)
  • Reverse engineering: Given answer 36, create a word problem (note: Q6 and Q8 both = 36)
  • Act out problems: Use classroom objects to model the scenarios
  • Challenge: Write a problem needing four operations: (a + b) × c - d + e
Parent Tip

Have your child create a story for a given math equation.

Learning Path
Skill Cluster

Problem Solving & Operations

Estimated Time

35 minutes

Skills Practiced
Complex problem solvingAdvanced applicationsMulti step reasoning