Grade 5/Order of Operations
Parentheses and Multiplication Together (591)
This worksheet introduces the full order of operations by combining parenthesis and multiplication rules. Students learn that parenthesis comes FIRST, then multiplication. Problems are structured so the parenthesis result is then multiplied by another number. Two formats are presented: (a + b) × c and a × (b + c), both using addition and subtraction within parenthesis. This builds understanding of the complete PEMDAS sequence for Grade 3.
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Teaching Notes
This is a critical transition worksheet combining both major rules. Emphasize: "Parenthesis is the BOSS - it always goes first, then multiplication." Students who mastered each rule separately may still struggle combining them. Have students identify BOTH operations before solving: "Circle the parenthesis, underline the multiplication, which goes first?" Use PEMDAS mnemonic: Please (Parenthesis) Excuse (Exponents - skip for Grade 3) My (Multiply) Dear (Divide) Aunt (Add) Sally (Subtract). Focus on P and M today.
Vocabulary
Parentheses: Symbols ( ) that group numbers or operations.
Group: To put numbers or operations together.
Common Mistakes
- Multiplying first instead of solving parenthesis: 2 × (3 + 4) done as 6 + 4 = 10
- Forgetting parenthesis entirely and working left-to-right
- Correct order but calculation errors (multiplication facts)
- Not writing down parenthesis result before multiplying
- Multiplying before solving parentheses.
- Incorrect arithmetic within parentheses.
- Ignoring parentheses entirely.
- Confusing addition with multiplication order.
Differentiation
SupportUse only (a + b) × c format initially (parenthesis clearly first). Circle parenthesis with one color, box multiplication with another. Reduce to 8 problems. Provide multiplication table. Work problems together: "What do we do first? Circle it. Now what?"
ChallengeAdd three operations: (2 + 3) × 4 - 5 or 20 - (2 + 3) × 4. Include larger numbers: (12 + 8) × 3. Try nested thinking: What if we had ((2 + 3) × 4)? Create word problems requiring this structure.
Discussion Questions
- Why does (2 + 3) × 4 give a different answer than 2 + 3 × 4? Calculate both ways.
- Which is stronger: parenthesis or multiplication? How do you know?
- What happens if you multiply first? Try (3 + 4) × 2 the wrong way.
- Can you create a real-world problem for (5 + 3) × 2?
- Why are parentheses important in math?
- What happens if we multiply first?
- Can you write a word problem?
- How is this like a recipe?
Extension Activities
- Compare three versions: (2 + 3) × 4 vs 2 + 3 × 4 vs 2 + (3 × 4) - discuss differences
- Use manipulatives: Show (2 + 3) groups of 4 objects physically
- Create problems: Write your own (a + b) × c where answer is exactly 20
- Preview: What if we had (2 + 3) × 4 - 5? (Three operations - coming soon!)
Parent Tip
Have your child explain what parentheses mean in a math problem.
Learning Path
Skill Cluster
Number Operations and Algebraic Thinking
Estimated Time
22 minutes
Skills Practiced
combined operation orderPEMDAS basicsthree number problems
Prerequisites
- 585
- 586
- 587
- 588
- 589
- 590
- Single-Digit Multiplication
- Two-Step Addition/Subtraction
Next Steps
- Order of Operations: Division
- Expressions with Multiple Grouping Symbols
- Parentheses and Division Together
- Order of Operations: All Operations
- Multiplication and Addition Order of Operations