Grade 6Mathhard
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 6.
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What Your Child Will Learn
- Apply the correct sequence of operations (PEMDAS/BODMAS) to solve multi-step expressions containing parentheses, exponents, multiplication, division, addition, and subtraction
- Evaluate complex expressions with multiple levels of grouping symbols and determine the correct order in which operations should be performed
- Solve challenging order-of-operations problems that involve mixed operations with decimals, fractions, or whole numbers to build computational fluency and accuracy
How to Use This Worksheet
- Step 1: Review the PEMDAS/BODMAS acronym together (Parentheses, Exponents, Multiplication/Division from left to right, Addition/Subtraction from left to right) before attempting the worksheet. Have your student write this on a reference card they can use while working.
- Step 2: Work through the first problem together as a model. Circle or highlight the operation that should be performed first, complete that step, rewrite the simplified expression, then repeat. This demonstrates the systematic approach needed for hard-level problems.
- Step 3: Have your student complete problems 1-3 independently, checking each answer before moving forward. If errors occur, have them retrace their steps using the numbered annotation method to identify where the mistake happened.
- Step 4: For problems 4-7 (mid-worksheet), encourage self-checking by asking the student to explain aloud which operation comes first and why before performing it. This metacognitive step prevents careless errors.
- Step 5: Problems 8-10 represent the most challenging expressions. Have your student work these slowly, writing out each intermediate step on separate lines rather than trying to simplify in a single line. Review answers together and discuss alternative approaches if different results are obtained.
Tips for Parents & Teachers
Emphasize that students must work left-to-right for operations at the same level of priority (multiplication/division and addition/subtraction). A common mistake is assuming multiplication always comes before division or addition before subtraction—reinforce that they have equal priority and must be handled in the order they appear.
Have students physically annotate their work by numbering each step above the expression (1st, 2nd, 3rd, etc.). This slows them down, prevents rushing, and creates a visible checklist that makes it easier to catch mistakes. For hard-level problems with nested parentheses, this is essential.
Watch for students who forget to simplify inside parentheses completely before moving outward. In expressions like 2 × (3 + 4 ÷ 2), they may calculate 3 + 4 first and ignore the division. Remind them that within parentheses, order of operations still applies.
Frequently Asked Questions
My sixth grader solved the same problem two different ways and got two different answers. How can I explain why there's only one correct answer?
This is a great teachable moment! Order of operations exists precisely because without a standardized sequence, mathematicians would get different answers. Have your student show you both methods step-by-step. Identify where they diverged and explain that one path doesn't follow the PEMDAS/BODMAS rules. Emphasize that math has a universal agreement about which operation to do when, and that's what makes math reliable and consistent worldwide.
Why do multiplication and division have the same priority, and addition and subtraction have the same priority? This confuses my student.
Great question! Multiplication is repeated addition, and division is the inverse of multiplication—they're fundamentally related operations. Similarly, subtraction is the inverse of addition. Because they're so closely connected, mathematicians grouped them at the same priority level and said 'do whichever one appears first, from left to right.' This prevents arbitrary choices and keeps answers consistent. You can use concrete examples: 12 ÷ 2 × 3 must be done left-to-right (6 × 3 = 18), not as 12 ÷ 6 = 2, to show why order matters.
My student keeps making mistakes with expressions that have nested parentheses (parentheses inside parentheses). How can I help?
Nested parentheses require working from the innermost pair outward. Have your student use different colored pencils or brackets to mark each layer: innermost parentheses in one color, next layer in another color, etc. This visual strategy makes it clear which operation to tackle first. Practice with simpler nested examples like 5 × (2 + (3 + 1)) before returning to harder multi-operation problems with nesting.
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