Grade 6Mathhard
Integer Operations
Integer Operations — Integers worksheet for Grade 6.
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What Your Child Will Learn
- Solve multi-step integer operations involving addition, subtraction, multiplication, and division with both positive and negative numbers
- Apply the order of operations (PEMDAS) correctly when evaluating expressions containing integers and multiple operation types
- Interpret and solve real-world problems that require combining integers, such as temperature changes, account balances, and elevation changes
- Demonstrate understanding of integer properties, including the commutative and associative properties, when simplifying complex expressions
How to Use This Worksheet
- Step 1: Before starting, review the integer operation rules (addition, subtraction, multiplication, and division of positive and negative numbers). Have your student create a reference chart with examples for each operation type to reference while working.
- Step 2: Read each problem carefully and have your student identify which operations are present. For harder problems with multiple operations, ask them to underline or circle each operation and number to organize their thinking before computing.
- Step 3: For each problem, explicitly state the order of operations needed. Have your student write 'PEMDAS' at the top of each problem and number the steps they'll take before computing any answers.
- Step 4: After solving each problem, have your student check their work by substituting the answer back into the original expression or by solving using an alternative method to verify the result is reasonable.
- Step 5: Upon completion, review any incorrect answers together. Focus on identifying where the error occurred (sign error, wrong operation order, or computational mistake) so your student can recognize and prevent the same type of error on future problems.
Tips for Parents & Teachers
Many 6th graders struggle with negative × negative = positive. Use concrete examples like: 'If you remove 3 debts of $5 each, that's a gain of $15' or use number lines with direction and magnitude to make this concept concrete rather than purely abstract.
Watch for sign errors in multi-step problems. Have students circle the operation sign and the number's sign separately (e.g., in '5 + (-3)', circle the plus sign and the negative sign on 3 as two different things). This prevents confusing the operation with the number's sign.
Encourage students to rewrite subtraction of negative numbers as addition of the opposite. For example, '8 - (-5)' becomes '8 + 5'. This reduces careless errors with double negatives and makes the problem clearer to solve.
For hard-level problems with multiple operations, require students to show every step and identify which operation they're doing first. This prevents jumping steps and catching errors before they compound through the problem.
Frequently Asked Questions
Why do we need to learn integer operations if we can use a calculator?
While calculators are useful tools, understanding integer operations builds number sense and mathematical reasoning. These operations form the foundation for algebra, which requires understanding how positive and negative numbers work together. Additionally, understanding the 'why' behind operations helps students catch calculator errors and apply math to real-world situations where they need to interpret results, not just get an answer.
My child keeps making mistakes with negative numbers. Is this normal at Grade 6?
Yes, this is very normal. Negative numbers are abstract and don't match students' real-world experience of quantities. The best approach is to connect negatives to familiar contexts: temperatures below zero, owing money (debt), or moving backward on a number line. Practice with these concrete contexts before moving to abstract operations, and allow extra time for this to 'click.'
How should I handle problems with multiple operations involving negative numbers?
Break the problem into smaller chunks. Have your student first identify the order of operations (PEMDAS), then solve one operation at a time, writing out the intermediate result as a new problem. For example, with '-5 + 3 × (-2)', first solve 3 × (-2) = -6, then rewrite as '-5 + (-6)' and solve that step. This prevents overwhelming your student and makes errors easier to locate.
What's the most common mistake students make on hard integer operation worksheets?
The most common mistake is not carefully distinguishing between the operation sign and the number's sign. For example, students might read '5 - (-3)' as '5 minus negative 3' and get confused about how to proceed. Teaching students to say 'five minus the opposite of three' or rewriting it as 'five plus three' helps them process it correctly and avoid sign errors.
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