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 involving parentheses, multiplication, division, addition, and subtraction
- Distinguish between expressions that require different operation orders and explain why performing operations out of sequence produces incorrect answers
- Evaluate expressions with two or more operations by correctly identifying which operation to perform first, second, and third
How to Use This Worksheet
- Step 1: Review the PEMDAS/BODMAS acronym with your student (Parentheses/Brackets, Exponents/Orders, Multiplication & Division left-to-right, Addition & Subtraction left-to-right). Create a reference poster they can see while working.
- Step 2: Before solving each problem, have your student identify all the operations present and circle or underline which operation should be performed first according to the order of operations rules.
- Step 3: Work through the first 2-3 problems together, verbally explaining each step: 'I see parentheses first, so I'll calculate inside them. Then I see multiplication, which comes before addition, so I'll do that next.'
- Step 4: Have your student solve problems 4-7 independently while you observe, noting where they hesitate or make mistakes. These will reveal which rules need reinforcement.
- Step 5: Review the remaining problems together, having your student explain their reasoning for the operation order they chose rather than just checking if answers are correct.
Tips for Parents & Teachers
Emphasize that multiplication and division have equal priority and should be performed left-to-right as they appear, not always multiplication first. Many Grade 5 students incorrectly believe multiplication always comes before division. Use concrete examples like 12 ÷ 3 × 2 to show this matters: going left-to-right gives 8, while doing multiplication first gives 2.
Have students physically underline or box the operation they'll perform first before solving. This creates a visual checkpoint that prevents impulsive calculation and helps them internalize the hierarchy. For expressions like 5 + 3 × 2, having them mark the multiplication first reduces careless errors.
Relate order of operations to real-world contexts Grade 5 students understand, such as calculating the cost of multiple items with a discount, or determining points in a game with bonuses and penalties. This helps them see order of operations as a logical system rather than arbitrary rules.
Frequently Asked Questions
Why do we need an order of operations? Can't we just solve math problems from left to right?
Great question! Without a standard order of operations, the same expression could have different answers depending on who solved it. For example, 2 + 3 × 4 could equal 20 (if we go left to right) or 14 (if we multiply first). Mathematicians agreed on one order so everyone gets the same answer. Order of operations ensures consistency and allows us to communicate mathematical ideas clearly.
My child keeps doing addition before multiplication, even though multiplication should come first. How can I help them remember?
This is extremely common at the Grade 5 level! Try using a memory trick: write 'MD' and 'AS' on separate index cards to emphasize that Multiplication and Division are partners (done left-to-right together), and Addition and Subtraction are partners (done left-to-right together). Have them say 'MD comes before AS' several times. Also, practice expressions where multiplication comes after addition in the problem (like 5 + 2 × 3) to break the pattern of doing operations in the order they appear.
Does multiplication always come before division, or division before multiplication?
Neither! Multiplication and division have equal priority. You perform whichever comes first when reading the expression from left to right. For example, in 12 ÷ 3 × 2, you divide first (getting 4) then multiply by 2 (getting 8). But in 12 × 3 ÷ 2, you multiply first (getting 36) then divide by 2 (getting 18). The position matters, not a fixed ranking.
What if an expression has parentheses within parentheses, like 2 × (5 + (3 + 1))?
Start with the innermost parentheses first. In this example, solve 3 + 1 = 4 first. Then use that answer in the next set of parentheses: 5 + 4 = 9. Finally, multiply by 2 to get 18. Grade 5 worksheets typically have simpler nesting, but this principle applies: always work from the inside out with parentheses.
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