Negative Numbers
Teaching negative numbers often triggers confusion when students see -3 > -7 and wonder how that's possible. CCSS.6.NS and KP.MAT.6 standards require sixth graders to master these concepts, yet many students struggle with the counterintuitive nature of negative comparisons.
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Why it matters
Negative numbers appear constantly in real-world contexts that students encounter daily. Weather forecasts show temperatures like -15°C, bank statements display overdrafts as -$250, and elevators indicate basement levels as -3. In sports, golf scores below par use negatives (-4 means 4 under par), while football shows yardage losses as negative gains. Students need to understand that -20°F is much colder than -5°F, and that a debt of $500 is worse than a debt of $50. These concepts become critical in algebra, where students manipulate expressions like 3x + (-2) = 7, and in coordinate geometry when plotting points like (-4, 6). Without solid negative number foundations, students struggle with integer operations that form the backbone of higher mathematics.
How to solve negative numbers
Negative Numbers
- Negative numbers are less than zero, written with a minus sign (−3).
- On a number line: negatives are to the left of zero.
- Adding a negative = subtracting: 5 + (−3) = 5 − 3 = 2.
- Subtracting a negative = adding: 5 − (−3) = 5 + 3 = 8.
Example: −4 + 7 = 3. −3 − 2 = −5. −2 × −3 = 6.
Worked examples
Which is warmer: -4°C or -1°C?
Answer: -1°C
- Think of a thermometer → -4°C and -1°C are both below zero — Both temperatures are negative (below zero). On a thermometer, the higher the liquid goes, the warmer it is. Among negative numbers, the one CLOSER to zero is warmer.
- Compare: which is closer to zero? → -1°C is closer to zero than -4°C — -1 is closer to zero (only 1 away), while -4 is further from zero (4 away). So -1°C is warmer. It might seem backwards, but -1 > -4 because -1 is less negative!
Order from least to greatest: 12, 16, -1, 13
Answer: -1, 12, 13, 16
- Separate negative and positive numbers → Negatives: -1 | Positives: 12, 13, 16 — Negative numbers are ALWAYS less than positive numbers. Among negatives, the one furthest from zero is the smallest (most negative). Think of a thermometer: -20 is colder than -5.
- Order negatives first (most negative to least), then positives → -1, 12, 13, 16 — Start with the most negative, go up to zero, then continue to the most positive. The correct order is: -1, 12, 13, 16.
What is 5 + (-13)?
Answer: -8
- Understand what adding a negative means → 5 + (-13) = 5 - 13 — Adding a negative number is the SAME as subtracting. Think of it like this: if someone 'gives' you a debt of $13.00, you actually LOSE $13.00. So + (-13) = - 13.
- Calculate: 5 - 13 → -8 — 5 - 13 = -8. The result is negative because we subtracted more than we had.
Common mistakes
- ✗Students often think -8 > -3 because 8 > 3, writing -8 as the larger number instead of recognizing that -3 > -8
- ✗When calculating 5 - 8, students frequently write 3 instead of -3, forgetting that subtracting more than you have creates a negative result
- ✗Students confuse subtracting a negative with adding, writing 7 - (-4) = 3 instead of 7 - (-4) = 11
- ✗During ordering exercises, students place negatives after positives, writing 12, 15, -3, -7 instead of -7, -3, 12, 15
Practice on your own
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