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 correct order of operations (PEMDAS/BODMAS) to solve multi-step expressions containing parentheses, exponents, multiplication, division, addition, and subtraction
- Evaluate complex expressions with mixed operations and nested parentheses by identifying which operations to perform first and justifying their reasoning
- Solve real-world word problems that require applying order of operations to multi-step calculations involving all four arithmetic operations and exponents
How to Use This Worksheet
- Step 1: Before beginning, have your student write out the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) on a separate sheet as a reference guide they can consult throughout the worksheet.
- Step 2: For each problem, instruct your student to underline or circle parentheses and exponents first, then work through those operations step-by-step before moving to multiplication and division.
- Step 3: As students work through each expression, have them write down the intermediate steps on scratch paper rather than trying to calculate everything mentally. This reduces computational errors and makes their thinking visible.
- Step 4: After completing each problem, ask your student to explain aloud which operation they performed first and why. This verbal reinforcement strengthens their understanding of the order rule.
- Step 5: Review incorrect answers together by walking backward through the expression, asking 'Which operation should we have done at this step?' to help your student identify where their order-of-operations logic broke down.
Tips for Parents & Teachers
Many 5th graders struggle with the left-to-right rule for multiplication and division (and addition and subtraction). Emphasize that these operations have equal priority, so students must work strictly left-to-right when they appear consecutively. For example, in 24 ÷ 6 × 2, students should divide first (24 ÷ 6 = 4) then multiply (4 × 2 = 8), not multiply first.
Students often forget to evaluate exponents before other operations. Create a visual reminder showing that exponents come early in PEMDAS—right after Parentheses. Work through examples like 2 + 3² where students must calculate 3² = 9 first, then add 2, resulting in 11 (not 25).
For this hard-difficulty worksheet, watch for students who solve expressions correctly but cannot explain their steps. Require them to write which operation they're performing at each stage and why it comes first. This metacognitive approach helps prevent careless errors on subsequent problems.
Frequently Asked Questions
Why do we need the order of operations? Can't we just solve expressions left-to-right?
The order of operations exists so that everyone solves expressions the same way and gets the same answer. If we all just went left-to-right, 2 + 3 × 4 would equal 20 for some people (2 + 3 = 5, then 5 × 4 = 20) and 14 for others (3 × 4 = 12, then 2 + 12 = 14). Mathematicians agreed on PEMDAS to ensure all calculations are correct and consistent.
How should my child handle expressions with multiple sets of parentheses or parentheses inside parentheses?
Encourage your student to work from the innermost parentheses outward. For example, in 5 × (2 + (3 + 1)), they should first solve the innermost (3 + 1) = 4, which gives 5 × (2 + 4), then solve (2 + 4) = 6, and finally calculate 5 × 6 = 30. Breaking nested parentheses into smaller steps prevents confusion.
When multiplication and division appear in the same expression, which one do I do first?
Multiplication and division have equal priority in the order of operations, so you perform whichever appears first when reading left-to-right. In 20 ÷ 4 × 2, you divide first (20 ÷ 4 = 5) then multiply (5 × 2 = 10). But in 20 × 4 ÷ 2, you multiply first (20 × 4 = 80) then divide (80 ÷ 2 = 40). This same rule applies to addition and subtraction.
My student solved 2 + 3 × 4 and got 20 instead of 14. What's the error?
Your student likely added 2 + 3 first (getting 5), then multiplied by 4 (getting 20). Remind them that multiplication must happen before addition. The correct order is: first 3 × 4 = 12, then 2 + 12 = 14. Have them write PEMDAS above the expression and circle the multiplication before touching the addition.
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