KS3

Negative Numbers

A parent's guide to negative numbers — what they are, how schools teach them, and how to help.

What Your Child Is Learning

Negative numbers are numbers below zero. Your child is learning that the number line doesn't stop at zero — it keeps going to the left. Think of a thermometer: on a cold day, the temperature drops below zero to \(-1\), \(-2\), \(-3\) and so on. The minus sign in front means "below zero."

This is a big shift in thinking. Up until now, your child has mostly worked with counting numbers — 1, 2, 3 and so on. Now they have to understand that \(-3\) is a real, usable number, and that it sits to the left of zero on the number line. The further left you go, the smaller the number.

They'll learn to add, subtract, multiply and divide with negative numbers. The key rules they need are: adding a negative is the same as subtracting, and subtracting a negative is the same as adding. Schools use the number line heavily to make this visual and concrete.

-5 -4 -3 -2 -1 0 1 2 3 4 5

How Schools Teach It Now

Schools use the number line as the primary tool. Your child will physically (or mentally) "walk" along the number line to solve problems. Here's how they'd work through \(-3 + 5\):

Start at \(-3\) on the number line. Find negative three — that's three steps to the left of zero.
You're adding 5, so move 5 places to the right. Adding a positive number means moving right. Subtracting a positive number means moving left.
Count the jumps: \(-3 \rightarrow -2 \rightarrow -1 \rightarrow 0 \rightarrow 1 \rightarrow 2\). You land on 2.
So \(-3 + 5 = 2\). You crossed through zero, which is perfectly normal.

The two key rules your child will learn:

Adding a negative is the same as subtracting: \(4 + (-3) = 4 - 3 = 1\)
Subtracting a negative is the same as adding: \(4 - (-3) = 4 + 3 = 7\)

Schools sometimes use the phrase "two negatives make a positive", but it only applies in two places: when two minus signs sit next to each other (like \(- (-3)\)), and when two negative numbers are multiplied or divided (like \((-2) \times (-3) = 6\)). This does not mean \(-3 + (-5) = 8\). Context matters.

Common Mistakes to Watch For

Adding magnitudes instead of cancelling. If your child writes \(-3 + 5 = -8\), they've added the numbers together and kept the minus sign. Remind them to use the number line: start at \(-3\), move right 5 steps.
Thinking \(-3\) is bigger than \(-1\). "3 is bigger than 1, so \(-3\) must be bigger." Use the thermometer: \(-3°\)C is colder (and therefore smaller) than \(-1°\)C. Further left on the number line means smaller.
Confusing "two negatives make a positive." This rule applies when the signs are directly next to each other, like \(5 - (-2) = 7\), and when multiplying or dividing two negatives, like \((-2) \times (-3) = 6\). It does not mean \(-3 + (-4) = 7\). That's \(-3 - 4 = -7\).
Forgetting to count through zero. When subtracting across zero, children sometimes skip it. Counting on fingers or tapping the number line helps: \(2 - 5\) goes \(2 \rightarrow 1 \rightarrow 0 \rightarrow -1 \rightarrow -2 \rightarrow -3\).

Try It Together

The Problem

Start at 4. Subtract 7. Where do you end up?

Step 1: Start at 4 on the number line.

Step 2: Subtracting means moving left. Move 7 places to the left.

Step 3: Count the jumps: \(4 \rightarrow 3 \rightarrow 2 \rightarrow 1 \rightarrow 0 \rightarrow -1 \rightarrow -2 \rightarrow -3\)

Answer: \(4 - 7 = -3\)

You crossed through zero — that's fine. The number line keeps going.

Try another one together: start at \(-2\), add 6. Where do you end up? (Answer: 4.)

Let Them Practise

This free game lets your child practise moving along the number line with negative numbers.

Play Negative Number Line on MaffsGames →

MaffsGames needs no account and no sign-up; what it records while your child plays is set out on the privacy page.

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