Negative numbers — for parents
Negative numbers are one of those "aha" moments in primary maths. For five years children have been told "you can't subtract a bigger number from a smaller one". Now suddenly, you can — and the answer lives on the other side of zero. This conceptual jump trips up almost every child the first few times.
What your child should master
- The idea that negative numbers are smaller than zero — a real part of the number line.
- Reading and writing −5, −12, etc., with the minus sign at the front.
- Reading a thermometer or number line that goes below zero.
- Comparing two integers with `<` and `>`, including the surprising "−2 > −7".
- Counting back through zero: e.g. 4 − 9 = −5.
- A first feel for temperature changes and depth — using negative numbers in real-life situations.
Common confusions
"−9 is bigger than −5"
The single biggest stumbling block. The child reads "9 > 5" and assumes the minus signs don't matter.
Help: switch to the number-line picture. −9 sits further left than −5, so −9 is smaller. Also useful: phrase it in terms of money or temperature. "Would you rather owe £5 or £9?" Most children prefer to owe less. So −5 > −9.Stopping at zero when subtracting
"4 − 9 is 4 − 4 = 0, and the other 5 just disappears."
Help: act out the number-line walk. From 4, count back: 3, 2, 1, 0. You're not done — there are 5 more steps to take. Each one goes into the negatives. Final spot: −5.Treating "−" as subtraction everywhere
"The minus sign is subtraction." Sometimes it is (5 − 3) — but at the front of a number it's a sign, not an operation. The number −3 is one number, not "minus 3" the operation.
Help: read it out loud as "negative three" rather than "minus three" for a few weeks. The two are the same number — but "negative three" doesn't sound like an operation.Getting confused by "below zero" sizes
"−1000 is a huge number." Tempting if you focus on the 1000. But on the number line, −1000 sits very far to the left of zero — so it's a very small number.
Help: insist on the number-line picture for every comparison until it sticks.Activities at home
Thermometer watching
Check the outdoor temperature every morning and evening for a week. Record it. Calculate the rise or fall between any two readings. If you live somewhere that gets below zero, this is gold.
Lift floors
If you live in a building with a basement, ask your child about the floor numbers. "Floor −1 is below ground. To get from floor 3 to floor −2, how many floors do you go down?" Answer: 5.
Money game
Give your child a pretend wallet and run a make-believe shop. Let the balance go below zero a few times. "You have £10, you bought a £15 toy — you're £5 in the red. Your balance is −£5."
Number-line race
Draw a number line from −10 to +10 on paper. Take turns rolling a die. Even number → move right; odd → move left. First to reach +10 wins. Children will accidentally pass through zero into the negatives often.
"Where am I?"
Read out a coordinate-style game: "I'm at +3. I take 8 steps left. Where am I?" Quick mental practice.
Why this matters
Negative numbers are the first time mathematics goes beyond "what's countable in real life". You can't have −3 apples — but you can have −£3 in the bank, −3 °C outside, or −3 floors below ground. It's the start of the slow march into abstraction that secondary mathematics is built on.
Once the negative-number idea clicks, the rest of mathematics (algebra, equations, graphs) all assume it. Get it right at Year 5 and the future is easier.