Your son comes home with a question: what is 5 minus 8? And why do two minuses make a plus? This article gives you all the tools to explain — in clear language, without panic.
Your child comes home from school with a puzzled look: "Mum, minus and minus can't make a plus — it doesn't make sense." And you, who have not touched this material since your own school days, are urgently trying to remember exactly what the teacher said. If that sounds familiar — you are not alone. Integers and negative numbers are one of the topics that create the most confusion among pupils in Years 6-8, so we have prepared this guide for you: a complete explanation, in parents' language.
Why minus at all? An explanation through everyday life
Children understand numbers through things they can see and feel. The most common mistake parents make is trying to explain minus abstractly ("a number smaller than zero"). Instead, it is better to start from life:
- Temperature — in the Scottish Highlands in January the temperature can drop to −5 °C. That is not "zero minus five" — it is simply colder than zero.
- Land below sea level — parts of the Fens in East Anglia lie at around −3 metres, below sea level. The minus says we are below the reference point.
- A lift — floor −2 in a car park is below the ground floor. The building carries on downwards, exactly as the numbers carry on to the left.
- A bank account — if you spent £200 and the account only had £150 in it, you go overdrawn: −£50. "You're in the red" — that is a real minus in real life.
The central idea: minus is a direction, not just a subtraction operation. When you teach the child to think of negative numbers as a direction (down, left, colder, owed), everything starts to make sense.
The number line — the most important tool
The number line is the road map of the world of integers. Draw a horizontal line with your child, mark zero in the middle, and line up positive numbers to the right and negative numbers to the left:
⟵ −5 −4 −3 −2 −1 0 1 2 3 4 5 ⟶
Three rules that must be learnt on the line:
- Right = bigger. −1 is bigger than −3, because −1 is to the right of it.
- Left = smaller. −5 is smaller than −2, even though 5 is bigger than 2.
- The distance from zero matters — that will be the absolute value later on.
A practical tip: print a number line and pin it up over the homework desk. When your child comes with a question, show them on the line first — before touching the calculation.
Adding a negative number — heading left
When you add a negative number, you move left along the line. This goes against intuition: children are used to adding = bigger. But:
- 3 + (−5) = 3 − 5 = −2. Start at 3, move 5 steps left, arrive at −2.
- −4 + (−3) = −7. Two debts combine into a bigger debt.
- It was 3 °C in Aviemore, then the temperature fell by 5 degrees: 3 + (−5) = −2 °C. A real experience.
The simple parents' explanation: adding a minus is really subtracting. 3 + (−5) is the same as 3 − 5. You can teach the child to rewrite the expression before solving it.
Subtracting a negative number — two minuses that turn right
This is where the big confusion arrives. When you subtract a negative number, you move right — as though you had added:
- 5 − (−3) = 5 + 3 = 8
- −2 − (−6) = −2 + 6 = 4
- You were £50 overdrawn (−50), and someone let you off a debt of £30 (−30): −50 − (−30) = −50 + 30 = −20. You are still overdrawn, but by less.
Multiplying and dividing: the sign rules — the classic confusion
When multiplying or dividing integers, the child needs to know two rules: "same signs give plus, different signs give minus." The following table helps to remember them:
| Expression | The signs | The result | Example |
|---|---|---|---|
| positive × positive | ( + ) × ( + ) | positive (+) | 3 × 4 = 12 |
| positive × negative | ( + ) × ( − ) | negative (−) | 3 × (−4) = −12 |
| negative × positive | ( − ) × ( + ) | negative (−) | (−3) × 4 = −12 |
| negative × negative | ( − ) × ( − ) | positive (+) | (−3) × (−4) = 12 |
The example that helps remember negative × negative = positive: if "doing bad" (−) to your enemy (−) is "doing good" (+) for yourself — two negatives produce a positive result. It is not science, but it sticks.
Important: the sign rules apply to division too. (−12) ÷ (−3) = 4, and −12 ÷ 3 = −4.
Absolute value — the distance from zero
The absolute value is simply the distance of a number from zero, with no direction. It is written with vertical bars: |−7| = 7 and |7| = 7.
The Fenland example: Holme Fen sits at about −3 metres. Its absolute value is |−3| = 3 metres — the distance from sea level, ignoring the direction (down). Comparison questions love absolute value: which is further from zero — −7 or 5? |−7| = 7 and |5| = 5, so −7 is further away.
A common mistake: children think |−7| = −7. Explain: the absolute value is always positive or zero — never negative. (Absolute value is not on the GCSE syllabus, but the idea of 'distance from zero' is exactly what helps children order negative numbers correctly.)
Seven common mistakes — and tips that help you remember
After checking hundreds of exercises solved by children, these are the mistakes that come up again and again:
- Mistake 1 — confusing size with value: children think −8 is bigger than −3 because 8 is bigger than 3. Remind them: on the line, right = bigger.
- Mistake 2 — forgetting the brackets: 5 − −3 and 5 − (−3) are the same thing, but children do not see it straight away. Always add brackets.
- Mistake 3 — adding two minuses in a subtraction: −4 − 3 ≠ −1. Subtracting a positive adds distance to the left: −4 − 3 = −7.
- Mistake 4 — a negative absolute value: |−5| cannot be −5. Absolute value is always positive.
- Mistake 5 — forgetting the sign rule in multiplication: (−2) × (−3) = 6, not −6.
- Memory tip 1 — the colour method: write positive numbers in blue and negative numbers in red. The colour helps instant recognition.
- Memory tip 2 — hops on the line: when solving any addition or subtraction, physically hop with a finger along the printed line before writing an answer.
The golden rule for parents: do not say 'it's simple'. For a child meeting negative numbers for the first time, it really is not simple. Say 'let's look at the line together' — and that changes everything.
In summary: how to help your child at home
Integers are a topic that takes time. Explaining once is not enough — you need to practise with real-life examples, keep a number line to hand, and be patient with the confusion. Here is a simple plan for a week:
- Monday: explain minus through real-life examples (temperature, a lift, a bank account).
- Tuesday: draw a number line together and practise ordering numbers.
- Wednesday: practise adding and subtracting with the line — with a finger, not in the head.
- Thursday: learn the sign rules for multiplication with the table.
- Friday: absolute value — distances and the below-sea-level examples.
- Saturday: solve 10 mixed exercises — and celebrate every correct answer.
Daily practice of 10-15 minutes with immediate feedback is far more effective than one long study session a week. MathsUK offers personalised practice — the child solves, gets a hint when stuck, and progresses at their own pace.
Frequently asked questions
At what age do children start learning negative numbers in England?
In the National Curriculum, negative numbers first appear in Year 4 (counting backwards through zero) and Year 5 (ordering and temperature). Year 6 introduces calculating across zero, and Year 7 extends this to all four operations with negative numbers. From Year 8 they are combined into algebraic expressions.
Why do children get so confused by minus?
Up to Year 5 children are used to numbers only going right (getting bigger). Minus breaks that rule. In addition, the minus sign has three different meanings: a subtraction operation (8 − 3), a negative sign (−5), and negation (−(−5)). That is a lot for the brain.
How do you explain to a child why minus times minus equals plus?
The best intuitive explanation is through patterns. 3 × 3 = 9, 3 × 2 = 6, 3 × 1 = 3, 3 × 0 = 0 — each time 3 less. So 3 × (−1) = −3, 3 × (−2) = −6. Now (−3) × (−1): the pattern (−3) × 3 = −9, (−3) × 2 = −6, (−3) × 1 = −3, (−3) × 0 = 0 — each time 3 more. So (−3) × (−1) = 3.
What is absolute value and why does it matter?
The absolute value is the distance of a number from zero on the number line, with no direction. |−7| = 7 and |7| = 7. It matters because many practical problems are about distances rather than directions — how many degrees cold, how many metres deep.
How does the number line help with adding and subtracting?
When you add a positive number, you move right. When you add a negative number (or subtract a positive), you move left. When you subtract a negative number, you move right. The line turns an abstract rule into a visible physical action.
Is there an easy way to remember the sign rules for multiplication?
Yes: same signs = plus, different signs = minus. Another trick: count how many minuses there are in the product. An even number of minuses = a positive answer. An odd number = a negative answer.
What is the difference between −3 and −(3)?
There is no difference. −3 and −(3) are the same number: minus three. The brackets are used for clarity in expressions like 5 − (−3), so it is clear that the second minus belongs to the number and not to the operation.
How long does it take to master integers?
Most children need 3-6 weeks of regular practice (15 minutes a day) to feel comfortable. The topic includes several sub-skills — value, adding, subtracting, multiplying, dividing, absolute value — so it takes relatively long to sink in.
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