11+ Negative Numbers: Ordering, Temperature and Practice
Learn to compare negative numbers, count across zero and find intervals, with a worked temperature table and eight explained questions.
A minus sign changes where a number sits. On a number line, −9 is to the left of −2, so −9 is smaller even though the digit 9 is larger than 2. Keep the sign attached to the number whenever you copy it into working.
These original questions support preparation for exams taken in 2027. They are not official school papers. Topic coverage and question formats vary: check your target school’s current information. Try the questions on paper before opening each answer.
Start with position, then movement
Zero is the reference point. Positive values lie to its right and negative values to its left. Moving right increases the value; moving left decreases it. A thermometer uses the same idea vertically: a higher reading is warmer, including when both readings are below zero.
For an ascending list, place the values from smallest to greatest: −12, −5, −1, 0, 6. The number nearest zero is not always the smallest. If all values are negative, the one furthest below zero is smallest. If the instruction says descending, reverse the direction of the completed list.
Worked example: a rise through zero
A reading begins at −7°C and rises by 12°C. Reaching zero uses 7 degrees of the rise. There are 5 degrees still to go, so the final reading is 5°C. The 12 describes a change; it is not the final temperature. Writing “start + change = finish” helps separate those quantities.
Worked example: the gap between two readings
A freezer reading changes from −14°C to −6°C. It has become warmer by 8°C, even though both readings remain negative. Count from −14 up to −6: eight one-degree intervals. You do not add 14 and 6 because the interval does not cross zero.
For the gap from −4°C to 9°C, the route does cross zero: 4 degrees to zero, then 9 more, giving 13°C. In this guide a gap means the non-negative distance between two values. A signed change also records the direction: a fall from 9°C to −4°C is a change of −13°C.
Read a table before doing arithmetic
| Time | Temperature |
|---|---|
| 06:00 | −8°C |
| 10:00 | −3°C |
| 14:00 | 4°C |
| 18:00 | 1°C |
The coldest reading is −8°C at 06:00. The rise between 06:00 and 14:00 is 12°C. The fall from 14:00 to 18:00 is 3°C. These are invented measurements for practice, not weather observations. Notice that the greatest reading and the greatest change are different questions.
Count intervals, not labels
From −2 to 2 there are four steps: −2 to −1, −1 to 0, 0 to 1 and 1 to 2. There are five printed whole-number labels, but only four gaps. This is the same distinction as counting fence posts versus spaces between them. On an unlabelled scale, establish the value of each interval before reading a point.
Eight original questions
1. Put −3, 5, −11, 0 and −1 in ascending order.
Show answer and explanation
−11, −3, −1, 0, 5
Increasing order means moving right along the number line, starting with the smallest signed value.
2. Which is greater, −8 or −5?
Show answer and explanation
−5
−5 is further right and closer to zero. Compare the signed numbers, not just their digits.
3. A temperature of −6°C rises by 11°C. What is the final reading?
Show answer and explanation
5°C
Six degrees of the rise reach zero. The remaining five degrees take it to 5°C.
4. A reading is 7°C, then falls by 15°C. What is it now?
Show answer and explanation
−8°C
A fall of 7 reaches zero; a further fall of 8 reaches −8°C.
5. How many degrees warmer is 3°C than −9°C?
Show answer and explanation
12°C
The interval is 9 degrees from −9 to zero plus 3 from zero to 3.
6. A lift is on floor −4. It goes up 9 floors, then down 3. Where does it finish? Assume each adjacent numbered floor is one floor apart and ground is 0.
Show answer and explanation
Floor 2
−4 + 9 = 5, then 5 − 3 = 2. The stated floor convention avoids an unnumbered-ground-floor ambiguity.
7. Complete the sequence: 8, 3, −2, ___, ___.
Show answer and explanation
−7, −12
Subtract 5 each time, retaining the minus sign after passing zero.
8. A temperature rises by 9°C and finishes at −2°C. What was the starting temperature?
Show answer and explanation
−11°C
Undo the rise: −2 − 9 = −11. Check forwards: −11 + 9 = −2.
Review a wrong answer
- If your answer is on the wrong side of zero, redraw the starting point and direction.
- If a difference is one too large, check whether you counted labels rather than gaps.
- If the arithmetic is correct but the answer does not fit, check whether the question asked for a change or an endpoint.
Use the same labelled steps in multi-step word problems, and practise expression rules in order of operations. The maths hub links the wider skills sequence.
Source context: Department for Education maths programme includes negative numbers and intervals across zero. This guide does not claim all schools test them in the same way. Questions and answers checked 24 October 2026.
Ready to practise?
Choose original practice and use the answer explanations to decide what to work on next. These are not official school papers.