Grade 7Mathmedium
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 7.
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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 expressions with two or more operations by identifying which operations must be performed first and explaining the reasoning behind the order
- Solve real-world problems that require applying the order of operations to expressions with mixed operations and nested parentheses
- Recognize and correct common errors in order of operations, such as performing addition before multiplication or ignoring parentheses
How to Use This Worksheet
- Step 1: Before solving any problem, have students write down the acronym PEMDAS or BODMAS at the top of their workspace. This serves as a checklist they can reference for each problem on the worksheet.
- Step 2: For each problem, have students scan the expression and identify all operations present (parentheses, exponents, multiplication, division, addition, subtraction). Ask them to mark or circle each operation type in different colors to make the structure clearer.
- Step 3: Working step-by-step, have students solve one operation at a time in the correct order, writing out each intermediate result. For example, if solving 3 + 2 × 4, they should first write 3 + 8, then 11. This prevents jumping to answers and helps catch errors.
- Step 4: For problems with multiple levels of complexity, encourage students to rewrite the expression after completing each major step (especially after finishing all parentheses or exponents). This creates a clearer visual progression and reduces careless mistakes.
- Step 5: After completing all 10 problems, have students go back and verify 2-3 of their answers using a different method or by asking themselves, 'Does this answer make sense given the size of the numbers?' This builds self-checking habits.
Tips for Parents & Teachers
Many Grade 7 students struggle with the left-to-right rule for operations of equal priority (multiplication/division and addition/subtraction). Emphasize that when students encounter two operations of the same level, they must work left to right. For example, in 12 ÷ 3 × 2, they should divide first (4 × 2 = 8), not multiply first. Have students draw arrows showing the left-to-right direction to make this visual.
A common mistake is treating subtraction and division as if they follow special rules. Reinforce that subtraction is the opposite of addition and division is the opposite of multiplication, but they don't have priority—only position matters. Use color-coding or circling operations in order to help students track what they've already completed.
Students often forget to work through parentheses completely before moving to the next operation. If a problem has nested parentheses (parentheses within parentheses), work from the innermost set outward. Have students rewrite the expression after completing each parenthetical section to reduce confusion and track progress.
Exponents frequently trip up Grade 7 students because they're less familiar with this operation. Remind students that exponents come after parentheses but before multiplication and division. Have them practice identifying the base and exponent separately (e.g., in 2³, 2 is the base, 3 is the exponent) before calculating.
Frequently Asked Questions
Why do we need the order of operations? Can't we just solve from left to right?
The order of operations ensures that everyone gets the same answer when solving the same expression. Without it, different people might calculate 2 + 3 × 4 differently and get either 14 or 20. Mathematicians agreed on a standard order so that expressions would have one correct answer. This becomes especially important in science, engineering, and higher mathematics where precision matters.
My student keeps making mistakes with subtraction and division. Why are these operations tricky?
Subtraction and division are not commutative, meaning the order matters. With 10 - 3, you get 7, but with 3 - 10, you get -7. Students sometimes forget that they must work left to right when they encounter subtraction or division of equal priority. A helpful strategy is to rewrite subtraction as adding the opposite (10 - 3 = 10 + (-3)) so students remember the order matters.
What's the difference between PEMDAS and BODMAS, and which should my student use?
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) and BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) are the same system with different terminology based on region. PEMDAS is common in the United States, while BODMAS is used in the UK and other countries. Your Grade 7 student should use whichever acronym their school uses, as they're identical in practice. The key is remembering that multiplication and division have equal priority (work left to right), as do addition and subtraction.
How can I help my student avoid careless errors when there are many operations in one expression?
Encourage your student to write out every single step, no matter how small or obvious it seems. When solving 5 + 2 × 3 - 1, they should write: first 2 × 3 = 6, then 5 + 6 = 11, then 11 - 1 = 10. This slows them down in a helpful way and makes it easy to spot where an error occurred. Also have them circle or box the operation they're about to solve, so they stay focused on one step at a time.
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