A student claims that −8 > −2 because 8 is greater than 2. What is wrong with this reasoning?
AThe student is using the wrong inequality symbol
BThe student is applying whole-number magnitude thinking to negative numbers, which reverses the actual comparison
CThe student forgot that negative numbers cannot be compared with inequality symbols
DNothing — the student is actually correct
This is the most common misconception when comparing negative integers. On the number line, −2 is to the RIGHT of −8, which means −2 is greater. 'Greater' means 'further right on the number line,' not 'larger absolute value.' With negative numbers, the one closer to zero (smaller absolute value) is the greater number. Temperature is a good check: −2°F is warmer than −8°F, so −2 > −8.
Question 2 Multiple Choice
Which of the following correctly orders the set {−3, 4, −7, 0, −1} from least to greatest?
A4, 0, −1, −3, −7
B−7, −3, −1, 0, 4
C−1, −3, −7, 0, 4
D−7, −1, −3, 0, 4
Least to greatest means moving from left to right on the number line. Among negatives, the most negative (furthest left) comes first: −7 is furthest left, then −3, then −1. Zero is in the middle. Then positive numbers: 4. The key is that among negatives, the one with the largest absolute value is the LEAST. Option B (−7, −3, −1, 0, 4) is correct.
Question 3 True / False
On the number line, −5 is to the right of −9, so −5 > −9.
TTrue
FFalse
Answer: True
This is correct. The number line rule is simple and absolute: whichever number is further to the right is greater. −5 is closer to zero than −9, placing it to the right of −9. So −5 > −9, even though 5 < 9 in terms of absolute value. Using the number line as a visual anchor eliminates the confusion that comes from thinking about magnitude alone.
Question 4 True / False
Among negative integers, the one with the larger absolute value is the greater number.
TTrue
FFalse
Answer: False
This is the central misconception for negative number comparisons. Among negatives, larger absolute value means further from zero, which means further LEFT on the number line — which means LESS, not greater. −8 has a larger absolute value than −2, but −8 < −2. The correct rule: among negatives, the one with the SMALLER absolute value (closer to zero) is the greater number.
Question 5 Short Answer
Explain why −2 > −8, even though 2 < 8. Use the number line in your explanation.
Think about your answer, then reveal below.
Model answer: On the number line, −2 is closer to zero and sits to the RIGHT of −8. 'Greater' means 'further right,' not 'larger absolute value.' With negative numbers, being closer to zero means being less negative — which is higher on the scale. A useful analogy: −2°F is warmer (closer to freezing) than −8°F. The absolute values follow the opposite order of the numbers themselves when both are negative.
This question targets the core insight: the number line gives meaning to 'greater than' that the absolute-value intuition reverses for negative numbers. Students who can explain this in their own words genuinely understand the concept rather than having memorized a rule.