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§ Neg Numbers

Negative Numbers

§ Neg Numbers

Negative Numbers

CCSS.6.NS3 min read

Negative numbers represent values below zero and appear everywhere from basement floors to bank overdrafts. CCSS 6.NS requires students to understand that negative numbers extend the number line leftward from zero, creating a complete system for describing real-world quantities like temperature drops and debt.

§ 01

Why it matters

Negative numbers model countless real situations students encounter daily. Bank accounts show negative balances when overdrawn by $25. Weather reports display temperatures like -8°F during winter storms. Elevators descend to basement level -3 in shopping malls. Sports statistics track golf scores 4 strokes under par as -4. Stock prices fall $12 below their opening value. Without understanding negatives, students cannot interpret these common scenarios or solve problems involving debt, temperature changes, elevation differences, or any situation where quantities decrease below a starting reference point of zero.

§ 02

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.

§ 03

Worked examples

Beginner§ 01

The elevator is at floor -2. Is that above or below the ground floor (floor 0)?

Answer: below

  1. The ground floor is floor 0 → Ground = 0, elevator = -2 — Floor 0 is ground level. Floors above ground are positive (1, 2, 3...). Floors below ground (basements) are negative (-1, -2, -3...).
  2. Floor -2 has a minus sign → Floor -2 is below ground — The elevator is 2 floors BELOW the ground. Negative floor numbers mean underground — like a basement or parking garage.
Easy§ 02

Which is greater: -3 or 7?

Answer: 7

  1. Compare a negative and a positive number → -3 < 7 — ANY positive number is always greater than ANY negative number. Think of it this way: positive means you HAVE something, negative means you OWE something. Having 7 is always better than owing 3!
  2. State the answer → 7 — 7 is greater than -3. On a number line, 7 is to the RIGHT of -3, and right means bigger.
Medium§ 03

The temperature was -3°C and rose by 14 degrees. What is the temperature now?

Answer: 11°C

  1. Start at -3°C and add 14 → -3 + 14 — The temperature starts below zero at -3°C. 'Rose by 14 degrees' means it got warmer — we ADD 14. On a thermometer, the liquid goes UP.
  2. Calculate → 11°C — -3 + 14 = 11°C. We crossed zero and went above freezing!
§ 04

Common mistakes

  • Students think -5 is greater than -2 because 5 > 2, writing -5 > -2 instead of -5 < -2
  • When adding a negative like 7 + (-3), students write 7 + (-3) = 4 instead of recognizing it equals 7 - 3 = 4
  • Students confuse subtracting a negative, writing 6 - (-4) = 2 instead of 6 - (-4) = 6 + 4 = 10
  • Students place negative numbers incorrectly on number lines, putting -3 to the right of -1 instead of to the left
§ 05

Frequently asked questions

Why do two negatives make a positive when multiplying?
Think of multiplication as repeated groups. (-3) × (-2) means 'the opposite of 3 groups of -2.' Since 3 groups of -2 equals -6, the opposite is +6. This rule ensures mathematical consistency and models real situations like reversing a debt.
How do I teach students to compare negative numbers?
Use a number line or thermometer. Numbers farther left (or lower) are smaller. -10°F is colder than -5°F, so -10 < -5. Practice with temperature, elevation, and money examples where 'more negative' means 'worse off' in real life.
What's the difference between a minus sign and a negative sign?
Context determines meaning. In 5 - 3, the minus indicates subtraction. In -3, it indicates a negative number. In 5 + (-3), parentheses clarify we're adding the negative number -3. Students need practice distinguishing these uses.
How do I help students remember rules for adding and subtracting negatives?
Teach 'adding a negative equals subtracting' and 'subtracting a negative equals adding.' Use mnemonics like 'same signs add, different signs subtract' for addition, or number line movements: right for positive, left for negative operations.
When do students typically struggle most with negative numbers?
The biggest hurdle is subtracting negatives like 4 - (-7). Students often get -3 instead of 11. They also struggle ordering negatives, thinking -15 > -8 because 15 > 8. Temperature and debt analogies help overcome these conceptual barriers.
§ 06

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