Grade 6Mathmedium
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 6.
Download Free PDF
No signup required — instant download
mathorder-of-operationsG6medium
Worksheet Preview
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
- Distinguish between expressions that require different operation sequences and explain why performing operations in the wrong order produces incorrect results
- Evaluate expressions with mixed operations at the intermediate level, including those with exponents and nested parentheses, demonstrating mastery of operation priority rules
- Justify the steps taken when solving order-of-operations problems by identifying which rule was applied at each stage of the calculation
How to Use This Worksheet
- Step 1: Review the PEMDAS/BODMAS acronym with your student before beginning. Have them write it down and create a personal reference card listing what each letter means and noting that M/D and A/S are performed left to right, not grouped together.
- Step 2: Work through the first 2-3 problems together as a guided practice. For each problem, have your student verbally identify which operation should be performed first, second, and so on before writing any calculations. This builds metacognitive awareness of the process.
- Step 3: Have your student complete problems 4-7 independently while you observe. Encourage them to annotate their work by writing small numbers (1, 2, 3, etc.) above operations to show the order in which they will be performed. This creates an explicit visual record of their thinking.
- Step 4: Review the independent work together, discussing any problems where the order was applied incorrectly. Ask your student to explain which step they performed first and why, reinforcing the reasoning behind each operation.
- Step 5: Have your student complete the final problems (8-10) independently as a summative check. These should represent increasing complexity with nested parentheses or multiple exponents. Collect and review to assess mastery of order-of-operations at the intermediate level.
Tips for Parents & Teachers
Use the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) as a memory aid, but emphasize that multiplication and division have equal priority and are performed left to right—this prevents common errors where students always do multiplication before division. Similarly, addition and subtraction are equal priority and work left to right.
Address the frequent mistake of ignoring exponents entirely or misunderstanding their position in the order. Have students circle or highlight exponents first before solving, as many Grade 6 students are still developing comfort with exponent notation and often skip this step, leading to incorrect answers.
Watch for the error where students perform all additions before subtractions (or vice versa). Use color-coding or arrow diagrams to show that addition and subtraction must be evaluated from left to right in the order they appear, not grouped by operation type. For example, in 10 - 3 + 2, the correct approach is (10 - 3) + 2 = 9, not 10 - (3 + 2) = 5.
Create visual anchor charts showing worked examples of expressions that contain all five operation types, with each step clearly numbered and the operation being performed circled. Post these where students can reference them while working through the worksheet independently.
Frequently Asked Questions
Why do we need the order of operations? Can't we just solve equations however we want?
The order of operations is a universal agreement that mathematicians and scientists follow so that everyone gets the same answer when solving the same problem. Without it, different people might solve 2 + 3 × 4 and get different results (14 if they go left to right, or 14 if they multiply first—actually, the correct answer is 14 because multiplication comes before addition). This shared rule makes mathematics a universal language and ensures accuracy in science, engineering, and everyday problem-solving.
Why does multiplication come before addition if they're both important operations?
Multiplication is repeated addition. For example, 3 × 4 means 4 + 4 + 4 (adding 4 three times). Because multiplication is built from addition, it makes sense mathematically to perform multiplication first, and then add the results. This order reflects the mathematical structure of how these operations relate to each other.
When I see both multiplication and division in the same problem, which one do I do first?
Multiplication and division have equal priority in the order of operations, so you perform whichever one appears first when reading from left to right. For example, in 12 ÷ 3 × 2, you divide 12 by 3 first (getting 4), then multiply by 2 (getting 8). If the operations were reversed as 12 × 2 ÷ 3, you would multiply first, then divide. Always work left to right when operations have the same priority level.
What's the difference between parentheses and exponents in terms of which goes first?
Parentheses are always solved first in the order of operations because they group numbers together and tell you 'do this part before anything else.' Exponents come second. However, if you have exponents inside parentheses, like (2 + 3)², you must solve what's in the parentheses first (2 + 3 = 5), and then apply the exponent (5² = 25). So parentheses always take priority, even over exponents.
Related Worksheets
More Math Worksheets
Related Articles
How to Teach Fractions to Kids: A Parent's Complete Guide
Learn how to teach fractions to kids in grades 2–5 with proven strategies, visual models, and hands-on methods that build real understanding — not just memorized rules.
How to Teach Ratios and Proportions: A Middle School Parent's Guide
Learn how to teach ratios and proportions to middle schoolers with step-by-step strategies, real-world examples, and hands-on activities for grades 6–8.
How to Teach Geometry to Kids: Angles, Shapes, and Lines
A practical parent guide to teaching geometry from kindergarten through 8th grade — covering shapes, angles, lines, and symmetry with hands-on activities and free worksheets.
Get Free Worksheets in Your Inbox
Subscribe for new worksheets and homeschool tips. No spam, unsubscribe anytime.