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Second/Order Of Operations

Three Operations Combined

This advanced worksheet challenges students to apply all three order of operations rules in a single problem: parenthesis first, multiplication second, then addition or subtraction. Problems include formats like (2 + 3) × 4 + 5 and 20 - 2 × (7 - 3), requiring students to carefully sequence three operations. Detailed three-step solutions guide students through the complete PEMDAS process appropriate for Grade 3.
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Prerequisites
Parentheses and Multiplication Together6 WS
Solve: (6 - 2) × 3 = ______
What to Do Next
Order of Operations Mastery6 WS
Solve: (7 - 3) × 5 + 8 = ______

Practice Questions

  1. (2 + 3) × 4 + 5 = ?
    Show answer

    25

  2. 3 × (4 + 2) - 8 = ?
    Show answer

    10

  3. (6 - 2) × 3 + 4 = ?
    Show answer

    16

  4. 20 - 2 × (7 - 3) = ?
    Show answer

    12

  5. (3 + 4) × 2 - 6 = ?
    Show answer

    8

Teacher Resources
Teaching Notes

This is the most complex worksheet in the unit and may require multiple class periods. Teach students to work methodically: "1-2-3: Parenthesis-Multiply-Add/Subtract." Have students NUMBER the operations before solving (write 1 above parenthesis, 2 above multiplication, 3 above final operation). Common struggle: remembering the final add/subtract step after focusing on parenthesis and multiplication. Consider demonstrating with color coding: red for step 1, blue for step 2, green for step 3.

Vocabulary
Parentheses: Symbols that group numbers and operations.
Order of Operations: Rules for solving math problems step-by-step.
Common Mistakes
  • Forgetting the third operation after completing parenthesis and multiplication
  • Wrong order: doing final add/subtract before multiplication
  • Calculation errors accumulating across three steps
  • Left-to-right on problems like 20 - 2 × (7 - 3) instead of parenthesis-multiply-subtract
  • Not tracking which operation is next
  • Incorrect operation order
  • Calculation errors
  • Skipping parentheses
  • Rushing multi-steps
Differentiation
SupportStart with only format (a + b) × c + d (clearest sequence). Work first 3-4 problems together as class. Use colored pencils for each step. Provide step-by-step template: "1. Solve ( ) = ___, 2. Multiply: ___ × ___ = ___, 3. Add/Subtract: ___ ± ___ = ___". Reduce to 8 problems.
ChallengeAdd fourth operation: (2 + 3) × 4 + 5 - 2. Include double parenthesis: (2 + 3) × (4 + 1). Add division (if covered): (8 - 2) × 4 ÷ 2. Create word problems requiring three operations. Design problems with specific target answers.
Discussion Questions
  • Why is it important to do operations in the exact order? What happens if you skip a step?
  • Which step is easiest? Which is hardest? Why?
  • How would (2 + 3) × 4 + 5 change if we added more parenthesis: ((2 + 3) × 4) + 5?
  • Can you create a story problem that needs all three steps?
  • Why is order important?
  • What happens if you ignore parentheses?
  • Can we do multiplication first sometimes?
  • How is this different from simple addition?
Extension Activities
  • Error analysis: Show wrong solutions (wrong order) and identify where mistake occurred
  • Create your own: Make problems where answer is exactly 20 using three operations
  • Compare formats: (2 + 3) × 4 + 5 vs 5 + (2 + 3) × 4 - same or different?
  • Challenge: Add fourth operation: (2 + 3) × 4 + 5 - 10 (preview for next worksheet)
Parent Tip

Ask your child to explain the order of operations using a real-life example.

Learning Path
Skill Cluster

Operations and Algebraic Thinking

Estimated Time

25 minutes

Skills Practiced
Three operation sequenceComplete PEMDAS applicationMulti step problems