Grade 4Mathmedium
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 containing addition, subtraction, multiplication, and division
- Identify which operation to perform first in expressions with mixed operations and explain why parentheses change the order of calculation
- Solve 10 progressively complex problems that require following the sequence: Parentheses, Exponents, Multiplication/Division (left to right), then Addition/Subtraction (left to right)
- Demonstrate understanding that multiplication and division have equal priority and must be solved from left to right, as do addition and subtraction
How to Use This Worksheet
- Step 1: Review the order of operations together before starting. Write PEMDAS on paper and define each letter with a simple example (e.g., P = solve what's in parentheses first). Do one warm-up problem together as a model, such as 5 + 2 × 3, showing how you identify multiplication first, then addition.
- Step 2: Have your student read the first problem aloud and circle or underline any parentheses. If parentheses exist, solve that part first and rewrite the problem. If no parentheses, move to the next step.
- Step 3: Scan the remaining expression from left to right for multiplication and division. Mark these operations with a number (1st, 2nd) to show the order. Solve them in sequence from left to right.
- Step 4: After all multiplication and division are complete, scan from left to right for addition and subtraction. Mark these and solve left to right. Remind your student that even though we say 'addition before subtraction,' we actually solve whichever comes first when reading left to right.
- Step 5: Review the 10 completed problems together. For any incorrect answers, rework that specific problem step-by-step, identifying where the mistake occurred (often skipped parentheses or wrong operation priority). Have your student explain what they'll do differently on similar problems next time.
Tips for Parents & Teachers
Use the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BODMAS as a memorable anchor, but emphasize that M and D are equal priority (solve left to right), as are A and S. Many fourth graders incorrectly think multiplication always comes before division—clarify this misconception by working through examples like 12 ÷ 2 × 3, showing it equals 18, not 2.
Have your student verbally walk through each step before writing the answer. For example, with 3 + 4 × 2, ask: 'Which operation do we do first?' (multiplication) 'Why?' (it comes before addition in our order) 'So what is 4 × 2?' (8) 'Now what's 3 + 8?' (11). This narration builds procedural fluency and catches mistakes early.
Watch for the parentheses trap: Students often ignore parentheses or miscalculate what's inside them. When you see parentheses, draw a box around them and solve that first, completely, before moving to other operations. Practice with simple examples like (2 + 3) × 4 versus 2 + 3 × 4 side-by-side to show how parentheses change the answer.
For medium-difficulty problems on this worksheet, expect expressions with 3-4 operations. Break these into chunks: identify parentheses first, then scan left to right for multiplication/division, then left to right for addition/subtraction. Using pencil marks or arrows to number the order of operations helps visual learners stay organized.
Frequently Asked Questions
Why do we even need an order of operations? Can't we just solve problems left to right?
Great question! Without a standard order, different people would get different answers to the same problem, which would be confusing. Mathematicians agreed on rules so everyone gets the same correct answer. For example, 3 + 4 × 2: if we go left to right, we'd get 7 × 2 = 14. But using order of operations, we do multiplication first: 4 × 2 = 8, then 3 + 8 = 11. Only one answer is correct, and order of operations tells us which one!
My child keeps getting multiplication and division mixed up in priority. How do I help?
Multiplication and division are actually equal in priority—they're 'partners' in the order of operations. The key is solving whichever comes FIRST when you read left to right. Try this: 12 ÷ 2 × 3. Reading left to right, division comes first, so: 12 ÷ 2 = 6, then 6 × 3 = 18. Use practice problems where division appears before multiplication to show they don't always follow the same pattern. A visual chart showing left-to-right arrows can help reinforce this.
What's the difference between the acronyms PEMDAS and BODMAS? Which should I teach?
Both acronyms teach the same order of operations. PEMDAS (used in the U.S.) stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. BODMAS (used in other countries) stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. The only real difference is naming (parentheses vs. brackets, exponents vs. orders). For Grade 4, either works fine, though PEMDAS is more common in U.S. classrooms. Pick one and stick with it so your student doesn't get confused.
There are no parentheses in some of these problems. Do I still need to follow order of operations?
Absolutely yes! Order of operations applies to ALL math problems, whether parentheses are present or not. Parentheses just make it more obvious where to start. Even in simple-looking problems like 10 - 2 + 3, order of operations matters (you add and subtract left to right: 10 - 2 = 8, then 8 + 3 = 11). The rules don't disappear just because parentheses aren't there—they're always working in the background.
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