Grade 4Mathhard
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 4.
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What Your Child Will Learn
- Apply the correct order of operations (PEMDAS/BODMAS) to solve multi-step arithmetic problems involving parentheses, multiplication, division, addition, and subtraction
- Evaluate expressions with mixed operations by identifying which operations to perform first and executing them in the proper sequence
- Distinguish between similar-looking problems that yield different answers when operations are performed in different orders, demonstrating understanding of why order matters
- Solve complex word problems that require translating written descriptions into mathematical expressions and then applying order of operations correctly
How to Use This Worksheet
- Step 1: Review the PEMDAS/BODMAS acronym with your student before starting. Write it clearly: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right). Have them keep this reference visible while working.
- Step 2: For each problem, have your student first identify and underline or circle all the operations present. Ask them to predict which operation will be done first based on the order of operations rules before any calculation begins.
- Step 3: Work through the first 2-3 problems together as guided practice. Have your student verbalize which operation they're doing at each step and why it comes before others. This builds metacognitive awareness of their own thinking process.
- Step 4: Have your student work through problems 4-7 independently while you observe. They should write out each step rather than doing calculations in their head, as this is a hard-difficulty worksheet that may have errors embedded that are caught through showing work.
- Step 5: Review the final 3 problems together, especially if your student made errors. Discuss what went wrong—was it a calculation mistake or a sequencing mistake? Use these as teaching moments to solidify understanding of when and why certain operations take priority.
Tips for Parents & Teachers
Students at this level often perform operations left-to-right without considering order of operations priorities. Emphasize that multiplication and division ALWAYS come before addition and subtraction, even if they appear later in the problem. Use color-coding to highlight which operations to do first—this visual aid helps students see the hierarchy clearly.
Watch for errors with parentheses: students may solve what's inside parentheses but then forget that result still needs to follow order of operations in the remaining problem. Practice by having students circle or box what's in parentheses, solve it, substitute the answer, and then continue with the remaining operations.
Many students struggle when a problem has both multiplication and division (or both addition and subtraction). Clarify that these pairs have equal priority, so you work LEFT to RIGHT. Use arrow diagrams showing the direction of operations to reinforce this sequencing strategy.
For hard-level problems with nested operations or multiple steps, encourage students to write out each step of their work. This reduces careless errors and makes it easier to identify where mistakes occurred during review.
Frequently Asked Questions
Why do multiplication and division come before addition and subtraction in order of operations?
Multiplication and division are considered 'stronger' operations because they represent groups and equal parts, which are more fundamental mathematical relationships than combining or separating amounts. Think of it this way: 2 + 3 × 4 doesn't mean 'add 2 and 3, then multiply by 4.' Instead, it means 'make 3 groups of 4, then add 2 to that total.' The multiplication creates the base quantity first. This is a mathematical convention that ensures everyone solves a problem the same way and gets the same answer.
What's the difference between a hard order of operations problem and an easy one for Grade 4?
Easy problems typically have 2-3 operations with clear grouping, like 5 + 3 × 2 where multiplication is obviously first. Hard problems at the G4 level include multiple sets of parentheses, several operations in sequence, operations of equal priority (like multiple multiplications or divisions), and larger numbers that require careful calculation. Hard problems might also present operations in an order that 'tricks' students into going left-to-right, like 12 ÷ 2 × 3, where division and multiplication have equal priority and must be done left to right.
My student keeps getting different answers when they solve the same problem twice. Why is this happening?
This likely indicates inconsistent application of order of operations rules. Your student may sometimes remember to do multiplication first, but other times revert to solving left-to-right. Have them use a consistent strategy: write each operation down, highlight which one has priority, solve it, write the new expression, and repeat. Creating a checklist or flowchart they can reference for each problem helps build automatic, consistent behavior. Also verify their basic multiplication and division facts are solid, as calculation errors compound in multi-step problems.
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