Grade 6/Order of Operations
Three Operations Combined (592)
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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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
Prerequisites
- 591
- Basic Multiplication
- Basic Addition/Subtraction
- Understanding Parentheses
Next Steps
- Order of Operations with Division
- Expressions with Multiple Grouping Symbols
- Order of Operations: All Four Operations
- Evaluating Numeric Expressions
- Multi-Step Word Problems