Grade 5Mathmedium
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 5.
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What Your Child Will Learn
- Apply the correct sequence of operations (PEMDAS/BODMAS) to solve multi-step arithmetic expressions containing parentheses, multiplication, division, addition, and subtraction
- Identify which operation to perform first in expressions with mixed operations and explain why the order matters using mathematical reasoning
- Solve 10 problems with varying complexity by correctly evaluating expressions with up to 3-4 operations, demonstrating consistency and accuracy
How to Use This Worksheet
- Step 1: Review the PEMDAS/BODMAS acronym with your student and discuss what each letter means. Emphasize that Parentheses are always done first, and that Multiplication/Division and Addition/Subtraction happen at the same priority level (work left to right).
- Step 2: Have your student work through the first 2-3 problems together with you, circling or writing numbers to show the order in which operations will be performed before actually calculating.
- Step 3: Direct your student to complete problems 4-7 independently while you observe. Ask them to explain their steps aloud for at least one problem to verify they understand the reasoning, not just memorizing the acronym.
- Step 4: Review the remaining problems (8-10) together, as these likely contain more complex expressions with multiple operations or nested parentheses. Discuss any errors and help your student identify where the order of operations was missed.
- Step 5: Create 2-3 additional practice problems together (not on the worksheet) and have your student solve them independently to confirm mastery before moving forward to more advanced topics.
Tips for Parents & Teachers
Use the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) as a memory tool, but emphasize that multiplication and division are performed LEFT TO RIGHT in the order they appear—not multiplication before division. This is a common misconception at the G5 level. Practice with expressions like 12 ÷ 3 × 2 to show this works left to right.
Have students annotate each step with numbers showing the order of operations (1st, 2nd, 3rd) above or below the expression before solving. This visual strategy helps catch mistakes and shows their thinking process clearly. For example: 5 + 3 × 2 becomes 5 + (3×2)₁ = 5 + 6₂ = 11₃.
Watch for the 'left-to-right' trap where students incorrectly perform operations in the order they read them from left to right, ignoring priority rules. Create comparison problems to show why 10 - 2 + 3 ≠ 10 - 5. Work through both interpretations to demonstrate which is correct according to order of operations.
Frequently Asked Questions
Why does order of operations matter? Can't you just solve from left to right?
No, solving strictly left to right would give different answers and cause confusion in math and science. Order of operations is a universal agreement that ensures everyone gets the same correct answer. For example, 2 + 3 × 4 should equal 14 (multiply first: 3 × 4 = 12, then add 2 + 12 = 14), not 20 (if you added left to right: 2 + 3 = 5, then 5 × 4 = 20). This rule is essential for higher math, engineering, and real-world problem-solving.
My child keeps multiplying or dividing before addition or subtraction correctly, but then makes errors. What's happening?
Your child likely understands the priority of multiplication and division but may be struggling with the left-to-right rule when multiplication and division appear together, or with addition and subtraction together. For instance, in 20 ÷ 4 × 2, they need to work left to right (20 ÷ 4 = 5, then 5 × 2 = 10), not do division first everywhere. Practice mixed operation pairs separately to build this skill.
Do parentheses always change the answer?
Not always. For example, (2 + 3) × 4 = 20, but without parentheses, 2 + 3 × 4 = 14—so yes, parentheses changed the answer here. However, in some cases like (8) + 2, parentheses don't change anything because 8 + 2 already equals 10. The key is that parentheses force operations inside them to happen first, which can change the result depending on what operations are involved.
How should I help my child check their work on these problems?
Have them solve the problem a second time, but write down the order of operations FIRST (label each step 1, 2, 3, etc.). Then solve. If they get the same answer both ways, they're likely correct. You can also use a calculator to verify, but discuss why their method was right or wrong rather than just confirming the number.
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