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 4th Class to 5th Class, and calculate with negative numbers around 6th Class 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.