Negative Numbers for Kids: Number Lines, Temperature and Easy Rules
Negative numbers are numbers less than zero, such as −1, −5 or −20. Children already meet them in everyday life, from freezing temperatures to the basement buttons in a lift (elevator). Start with those real examples and a number line, and negative numbers quickly make sense. Adding and subtracting them follows a few clear rules that are easy to picture.
Where children see negative numbers
- Temperature: −3 °C is three degrees below freezing.
- Buildings: floors below the ground are often labelled −1 and −2.
- Below sea level: a diver 10 metres under the surface is at −10 metres.
- Money: owing money can be shown as a negative balance.
- Sport: golf scores below par, or goal difference in a league table.
Step 1: Extend the number line
Draw a number line with 0 in the middle. Positive numbers go to the right, and negative numbers go to the left, like a mirror:
… −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5 …
Ask questions such as “what is one less than 0?” and count backwards together through zero: 3, 2, 1, 0, −1, −2, −3. The key idea is that numbers get smaller as you move left, even when the digit looks bigger. So −8 is less than −3, because it is further left. Our Number Line game is a great way to get used to placing numbers on a line.
Step 2: Use a thermometer
A thermometer is a number line standing up. It makes questions about change feel natural:
- It is 3 °C and the temperature drops 5 degrees. Count down 5: it is now −2 °C.
- It is −4 °C in the morning and warms up by 7 degrees. Count up 7: it is now 3 °C.
- One city is −6 °C and another is 4 °C. The difference is 10 degrees: 6 degrees up to zero, then 4 more.
Splitting a jump at zero, as in the last example, is a really useful strategy for finding differences.
Step 3: Add and subtract positive numbers
On the number line, adding moves right and subtracting moves left:
- −3 + 5: start at −3, move 5 right. The answer is 2.
- 2 − 6: start at 2, move 6 left. The answer is −4.
- −1 − 4: start at −1, move 4 left. The answer is −5.
Step 4: Adding a negative number
Adding a negative number is the same as subtracting. Think of money: if you are given a bill for 3, you are 3 worse off.
- 5 + (−3) is the same as 5 − 3 = 2.
- −2 + (−4) is the same as −2 − 4 = −6.
Step 5: Subtracting a negative number
This is the one that surprises children: subtracting a negative is the same as adding. Two ways to show why:
Follow the pattern. Write a list and let your child continue it:
- 4 − 2 = 2
- 4 − 1 = 3
- 4 − 0 = 4
- 4 − (−1) = 5
- 4 − (−2) = 6
- 4 − (−3) = 7
Each time we take away one less, the answer goes up by one, so the pattern carries on past zero.
The hot air balloon. Imagine a balloon with sandbags (negative) and bags of hot air (positive). Taking away a sandbag makes the balloon go up. Taking away a negative has the same effect as adding a positive.
- 4 − (−3) = 4 + 3 = 7
- −5 − (−2) = −5 + 2 = −3
The rules at a glance
| Calculation | What to do | Example |
|---|---|---|
| Add a positive | Move right | −3 + 5 = 2 |
| Subtract a positive | Move left | 2 − 6 = −4 |
| Add a negative | Same as subtracting: move left | 5 + (−3) = 2 |
| Subtract a negative | Same as adding: move right | 4 − (−3) = 7 |
Common mistakes
- Thinking −8 is bigger than −3. Go back to the number line or thermometer: −8 °C is colder.
- Overusing “two minuses make a plus”. It only applies when you subtract a negative number, as in 4 − (−3). In −3 − 2 there is only one subtraction, and the answer is −5.
- Miscounting across zero. From −2 to 3 is 5 steps, not 6. Count the jumps, not the numbers.
- Losing the minus sign. Encourage brackets around negative numbers, such as 5 + (−3), so the sign stays visible.
Later on: multiplying and dividing
In secondary school, children learn that a positive times a negative is negative (−3 × 4 = −12) and a negative times a negative is positive (−3 × −4 = 12). Division follows the same sign rules. There's no need to rush this; a secure feel for the number line comes first.
When do children learn negative numbers?
Children often count back through zero and read negative temperatures around Primary 4 to Primary 5, and calculate with negative numbers around Primary 6 and into secondary school. Algebra relies heavily on them, so time on the number line now pays off later. The Algebra game is a good next step when your child is ready.
Frequently asked questions
How do you explain negative numbers to a child?
Use a number line that goes past zero to the left and a thermometer showing temperatures below freezing. Negative numbers are numbers less than zero, and they get smaller as you move left.
Is −8 bigger or smaller than −3?
−8 is smaller than −3 because it is further left on the number line. A temperature of −8 °C is colder than −3 °C.
What happens when you subtract a negative number?
Subtracting a negative is the same as adding. For example, 4 − (−3) = 4 + 3 = 7. The pattern 4 − 1 = 3, 4 − 0 = 4, 4 − (−1) = 5 shows why.
Do two negatives always make a positive?
No. Subtracting a negative or multiplying two negatives gives a positive result, but −3 − 2 = −5 and −2 + (−4) = −6 are both negative.