Grade 6 Integers Test
Integers test for grade 6 students. Practice problems with instant feedback and explanations.
20 Questions
Understanding the Concept
Integers include all positive and negative whole numbers plus zero (..., -3, -2, -1, 0, 1, 2, 3, ...). Understanding integers is crucial for representing real-world situations like temperature, elevation, debt, and direction.
Key Integer Concepts
- 1Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
- 2Absolute value: distance from zero (|-5| = 5)
- 3Number line: negatives to the left, positives to the right
- 4Adding same signs: add and keep the sign
- 5Adding different signs: subtract and keep the sign of the larger absolute value
- 6Subtracting integers: change to adding the opposite
- 7Multiplying/dividing: same signs = positive, different signs = negative
- 8Opposite of a number: same distance from zero, other side (-3 and 3)
⚠️ Common Mistakes to Avoid
- •Thinking -5 is greater than -2 (it's less: farther from zero in negative direction)
- •Forgetting that subtracting a negative is adding: 5 - (-3) = 5 + 3 = 8
- •Wrong sign when multiplying two negatives (negative × negative = positive)
- •Confusing absolute value with the number itself
- •Miscounting on the number line when crossing zero
- •Thinking zero is positive (it's neither positive nor negative)
🌍 Real-World Applications
- •Temperature: above and below zero
- •Elevation: above and below sea level
- •Finance: deposits (positive) and withdrawals (negative)
- •Football: yards gained and lost
- •Time zones: hours ahead or behind GMT
- •Stock market: gains and losses
Sample Practice Problems
Q1: -5 + 8 = ?
Show Answer & Explanation
Answer: 3
Different signs: subtract (8-5=3), keep sign of larger absolute value (positive)
Q2: -3 + (-7) = ?
Show Answer & Explanation
Answer: -10
Same signs: add (3+7=10), keep the sign (negative) = -10
Q3: What is |-12|?
Show Answer & Explanation
Answer: 12
Absolute value is distance from zero: |-12| = 12
✨ Expert Study Tips
Use a number line to visualize operations
For adding: same signs add and keep, different signs subtract and take the bigger sign
KCC: Keep-Change-Change for subtraction (keep first, change minus to plus, change sign of second)
For multiplication: count the negatives — odd count = negative, even = positive
Absolute value is just distance — always positive
Practice with money: earning (+) and spending (-) scenarios
📚 Learning Tips for Grade 6
Build fluency with integer operations before tackling algebra
Use algebra tiles or drawings to understand variable expressions
Practice setting up ratios and proportions from word problems
Connect percentages to discounts, taxes, and tips
Graph relationships to visualize equations
Use double number lines and tape diagrams for ratio reasoning
Practice absolute value and ordering integers on a vertical number line
Calculate area and surface area of composite shapes for extra challenge
Your Learning Path
⬅️ Prerequisites
Master these concepts first:
- Whole number operations
- Number line
- Understanding of zero
➡️ Next Steps
After mastering this, explore:
- Rational numbers
- Coordinate plane
- Integer equations
- Absolute value
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