Grade 4Mathhard
Order of Operations
Order of Operations — Order of Operations worksheet for Grade 4.
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What Your Child Will Learn
- Apply the correct order of operations (PEMDAS/BODMAS) to solve multi-step arithmetic problems involving parentheses, multiplication, division, addition, and subtraction
- Distinguish between problems that require different sequences of operations and explain why the order matters when solving complex expressions
- Evaluate expressions with mixed operations by correctly prioritizing parentheses first, then multiplication and division from left to right, then addition and subtraction from left to right
- Solve challenging real-world word problems that require identifying the correct operation sequence and demonstrating mathematical reasoning in written or verbal explanations
How to Use This Worksheet
- Step 1: Before beginning, have your student write 'PEMDAS' or 'BODMAS' on a separate sheet and explain what each letter stands for. This priming activity activates prior knowledge and ensures they have the correct sequence in mind.
- Step 2: Work through the first problem together as a model. Verbally identify each operation in the expression, underline or circle parentheses first, and demonstrate solving step-by-step, narrating your thinking aloud (e.g., 'I see parentheses, so I do this part first. Now I see multiplication, so I do that next').
- Step 3: Have your student independently attempt problems 2-4, pausing after each to check their work. Ask them to identify which operation they did first and why, reinforcing the decision-making process rather than just the answer.
- Step 4: Problems 5-10 represent hard-difficulty challenges; provide these as independent practice or guided practice depending on your student's confidence. Encourage them to write out each step on paper rather than solving mentally, as this makes errors visible and easier to correct.
- Step 5: Upon completion, review any incorrect answers together by re-solving step-by-step. Have your student identify exactly where they made a mistake (e.g., 'I did addition before division') and explain what the correct order should have been.
Tips for Parents & Teachers
Emphasize the left-to-right rule for operations at the same level: When students encounter consecutive multiplication and division (or addition and subtraction), they must work from left to right, not automatically do all multiplication before division. This is a common Grade 4 misconception—practice problems like 12 ÷ 3 × 2 to reinforce this concept.
Use a physical or visual anchor chart showing PEMDAS with color-coded steps, and have students verbally state the correct order before solving each problem on the worksheet. This metacognitive practice builds automaticity and reduces careless errors on harder problems with multiple operations.
Address the parentheses trap: Students often ignore or misidentify what's inside parentheses on hard problems. Have them circle or box parenthetical expressions first, solve what's inside completely, then treat that result as a single number before moving to the next step.
Connect order of operations to real-world scenarios (e.g., 'If you buy 3 packages of pencils with 4 pencils each, then add 5 loose pencils, you calculate 3 × 4 + 5, not 3 × (4 + 5)'). This contextual understanding helps Grade 4 students see why order matters beyond just following rules.
Frequently Asked Questions
Why do my Grade 4 student do multiplication before division when they appear next to each other?
This is a very common misconception at the Grade 4 level. The order of operations says multiplication and division have equal priority and must be performed from left to right in the order they appear. For example, in 24 ÷ 3 × 2, you divide first (24 ÷ 3 = 8) then multiply (8 × 2 = 16), not multiply first. Reinforce this with multiple examples and have your student point to which operation comes first when reading left to right.
How do I help my student remember PEMDAS when they struggle with order of operations on hard problems?
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) is a helpful acronym, but Grade 4 students often memorize the letters without fully understanding the 'equal priority' relationships. Teach that multiplication and division are partners (do left to right), and addition and subtraction are partners (do left to right). Use color-coding or physical grouping to show these partnerships. Practice frequently with expressions that mix operations at the same priority level.
Should my student always solve the entire parenthetical expression before moving on?
Yes. Whatever is inside parentheses must be completely solved first, treating it as a single number. For example, in 2 × (3 + 4), you must calculate 3 + 4 = 7 first, giving you 2 × 7 = 14. On harder problems, parentheses might contain multiple operations, so ensure your student solves everything inside completely before using that result in the rest of the problem.
What's the difference between a Grade 4 'hard' order of operations problem and an easier one?
Easier Grade 4 problems typically have 2-3 operations in a simple sequence (e.g., 5 + 3 × 2). Hard problems include 4 or more operations, nested or multiple parentheses, consecutive operations at the same priority level (e.g., 12 ÷ 2 × 3), and require students to apply PEMDAS carefully across an entire multi-step expression. Hard problems demand greater attention to detail and more deliberate step-by-step work.
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