Grade 5Mathhard
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 5.
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What Your Child Will Learn
- Apply the PEMDAS/BODMAS rule correctly to solve multi-step expressions containing all four operations, parentheses, and exponents
- Evaluate expressions with nested parentheses and multiple levels of operations to determine the correct order of simplification
- Justify the sequence of steps used to solve complex order-of-operations problems and explain why alternative orderings would produce incorrect results
How to Use This Worksheet
- Step 1: Before solving, have your student identify all the operation types present in each problem (parentheses, exponents, multiplication, division, addition, subtraction) and write 'PEMDAS' on the side as a checklist to work through systematically.
- Step 2: For each problem, instruct your student to begin with parentheses and exponents first, working through nested parentheses from innermost to outermost. Have them rewrite the simplified version after each step so they can track their progress clearly.
- Step 3: Next, guide them to handle multiplication and division from left to right in the order they appear, reminding them these operations have equal priority. Have them underline these operations before completing them.
- Step 4: Finally, complete addition and subtraction from left to right, again emphasizing equal priority. Ask your student to explain aloud why they chose the order they did for each step.
- Step 5: Check answers by having your student re-solve the problem using a different colored pencil, or by working backward from the answer to verify the steps are correct.
Tips for Parents & Teachers
Many Grade 5 students struggle with nested parentheses—encourage them to work from the innermost parentheses outward, and physically circle or underline each set of parentheses with different colors to track which operations to complete first. A common mistake is performing operations left-to-right without considering parentheses, so explicitly model why (2+3)×4 ≠ 2+3×4.
When multiplication and division appear in the same expression, emphasize that they have equal priority and must be evaluated left-to-right in the order they appear—not 'always divide first.' Similarly for addition and subtraction. Use arrow diagrams to show the direction of left-to-right processing when operations have the same priority level.
Hard-difficulty problems often combine exponents with other operations. Help students understand that exponents are evaluated before multiplication and division. Practice identifying what number the exponent applies to (e.g., in 2+3², only the 3 is squared, not the 2+3) by having them rewrite expressions with expanded notation like 2+(3×3) to make the order explicit.
Frequently Asked Questions
Why does my child get different answers when solving the same problem multiple ways?
This usually indicates they are not following the order of operations consistently. For example, if they sometimes multiply before division (when division comes first from left to right), they'll get wrong answers. Emphasize that PEMDAS is not a suggestion—it's a mathematical rule everyone must follow so we all get the same answer. Have them use a step-by-step format where each operation appears on a new line, so you can identify exactly where the mistake occurred.
Should my Grade 5 student memorize PEMDAS, or is it okay to have a reference chart available?
By Grade 5, especially at a hard difficulty level, students should be moving toward internalizing the order rather than constantly referencing the acronym. However, having a visual reference chart available during initial practice is helpful. Gradually reduce reliance on it by having them write PEMDAS themselves at the top of their worksheet. The goal is automaticity by Grade 6, so repetition with these harder problems is essential.
What's the difference between 3² and 2×3, and why does it matter for order of operations?
3² means 3×3=9 (the exponent is evaluated first), while 2×3=6. In a complex expression like 2+3², the exponent applies only to the 3, not to the 2, so the answer is 2+9=11, not 5²=25. This is critical at the hard difficulty level—students must understand that exponents have high priority and apply only to the number they're attached to. Have them rewrite 3² as 3×3 until they feel confident with the notation.
How do I help my student avoid making careless mistakes with negative numbers in order-of-operations problems?
Negative numbers can complicate order of operations, especially in subtraction where students might confuse the operation with the sign. For example, in 10-2×3, they must multiply 2×3=6 first, then subtract: 10-6=4. Have them circle or box the negative sign and the number together as a unit, and separate it visually from the operation being performed. If negative numbers appear in these problems, consider that an additional layer of difficulty for your Grade 5 student.
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