Negative Numbers
Negative numbers are values less than zero, written with a minus sign in front, such as −3, −15, or −0.5. They appear to the left of zero on a number line and represent quantities below a reference point. In Year 5 of the UK National Curriculum, pupils learn to interpret negative numbers in context, such as temperatures below freezing or floors below ground level.
Why it matters
Negative numbers appear throughout daily life in Britain, from winter temperatures dropping to −8°C in Scotland to bank overdrafts showing −£25. Weather forecasts regularly display negative temperatures, whilst underground car parks use negative floor numbers like −2. In GCSE mathematics, negative numbers form the foundation for algebra, coordinate geometry, and advanced arithmetic operations. Financial contexts rely heavily on negatives — a business loss of £3,000 appears as −£3,000 in accounts. Sports also use negatives: golf scores below par are negative, and football goal differences can be −5. Scientific measurements frequently involve negatives, from altitudes below sea level to pH levels in chemistry. Mastering negative numbers at Year 5 level prepares pupils for complex mathematical concepts in secondary school, including solving equations with negative solutions and working with negative gradients in graphs.
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
Is -4 positive or negative?
Answer: negative
- Check for å minus sign → -4 has a minus sign — Look at the number -4. There IS a minus sign in front, which means it is negative — less than zero.
- Think of a number line → negative — On a number line, -4 is to the LEFT of zero (negative side). Positive = right of zero, negative = left of zero.
It was 4°C outside. The temperature dropped 6 degrees. What is the temperature now?
Answer: -2°C
- Start at 4°C and subtract 6 → 4 - 6 = -2 — We start at 4 and go down 6 degrees. First we drop to zero (4 degrees down), then we keep going 2 more degrees BELOW zero.
- The result is negative — below zero! → -2°C — The temperature is now -2°C. That's 2 degrees below freezing! When you subtract more than you start with, the answer goes negative — like going below ground level.
The temperature was -2°C and rose by 15 degrees. What is the temperature now?
Answer: 13°C
- Start at -2°C and add 15 → -2 + 15 — The temperature starts below zero at -2°C. 'Rose by 15 degrees' means it got warmer — we ADD 15. On a thermometer, the liquid goes UP.
- Calculate → 13°C — -2 + 15 = 13°C. We crossed zero and went above freezing!
Common mistakes
- Confusing the order of negative numbers: −8 is incorrectly thought to be greater than −3, when actually −3 > −8 because −3 is closer to zero on the number line.
- Adding negatives incorrectly: calculating 5 + (−3) = 8 instead of 2, treating the negative sign as a positive when combining numbers.
- Subtracting negative numbers wrongly: computing 7 − (−2) = 5 instead of 9, failing to recognise that subtracting a negative equals adding the positive equivalent.