Grade 5Matheasy
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 5.
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What Your Child Will Learn
- Solve multi-step arithmetic expressions by correctly applying the order of operations (PEMDAS/BODMAS) with parentheses, multiplication, division, addition, and subtraction
- Identify which operation to perform first in expressions containing two or more different operations
- Apply the correct sequence of operations to evaluate expressions with parentheses and mixed arithmetic operations
- Explain why the order of operations matters by demonstrating how different orders produce different answers
How to Use This Worksheet
- Step 1: Before starting, review the PEMDAS/BODMAS acronym with your student and post it visibly. Have them write it at the top of their worksheet as a reference guide.
- Step 2: For each problem, have your student identify ALL the operations present (addition, subtraction, multiplication, division, parentheses) and mark them with different colors or symbols.
- Step 3: Instruct your student to solve one operation at a time in the correct order, rewriting the expression after each step. For example, if the problem is 3 + 2 × 5, they should write: 3 + 2 × 5 → 3 + 10 → 13.
- Step 4: Check that parentheses are handled first by having your student rewrite expressions with parentheses solved before moving to other operations.
- Step 5: Review completed answers together, asking your student to explain the order they used for each problem and why they solved it that way.
Tips for Parents & Teachers
Use the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) or BODMAS to help students remember the correct sequence. Emphasize that multiplication and division have equal priority (work left to right), as do addition and subtraction.
Watch for the common mistake of solving from left to right without following order of operations. For example, students often calculate 2 + 3 × 4 as (2 + 3) × 4 = 20 instead of the correct 2 + (3 × 4) = 14. Have them circle or underline operations in the correct order before solving.
When problems include parentheses, encourage students to solve inside parentheses first, then work outward. Use physical grouping symbols or color-coding to help visualize which parts should be solved together.
Practice with real-world contexts like recipes or shopping scenarios to show why order matters: 'If you buy 2 items for $5 each plus 1 item for $3, that's (2 × 5) + 3, not 2 × (5 + 3).'
Frequently Asked Questions
Why do we need an order of operations? Can't we just solve problems from left to right?
If everyone solved math problems differently, we'd get different answers for the same problem! The order of operations is a set of rules that everyone follows so that 2 + 3 × 4 always equals 14, not 20. It's like a traffic rule—everyone driving on the same side of the road keeps us safe.
What's the difference between multiplication and division in order of operations? Do I always do multiplication first?
Multiplication and division have equal priority, so you do whichever one comes first when reading from left to right. The same is true for addition and subtraction. For example, in 10 ÷ 2 × 3, you divide first (10 ÷ 2 = 5) then multiply (5 × 3 = 15) because division appears first reading left to right.
Do parentheses always come first, even before exponents?
Yes! Parentheses are always solved first, before any other operations. If there are exponents inside the parentheses, you solve the exponents after handling what's in the parentheses but before doing operations outside them. For Grade 5, focus mainly on parentheses with basic operations like addition, subtraction, multiplication, and division.
My student keeps getting different answers than the answer key. What should we check?
Have your student show you each step of their work written out. Common issues include: (1) forgetting to do operations inside parentheses first, (2) solving from left to right instead of following order of operations, (3) doing all additions before multiplications, or (4) making a simple arithmetic error. Going through step-by-step will reveal where the mistake happened.
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