Ross MackellUK-qualified primary teacher · 8 min read

It's −3°C outside and 5°C inside. What's the difference in temperature? A lot of children say 2. The answer is 8, and that question, in one form or another, turns up in the Year 6 SATs almost every year.

Negative numbers feel strange to children because everything they've learned so far says numbers start at zero. Then suddenly there are numbers smaller than nothing. The good news is that one simple picture, the number line, makes almost every negative number question easy.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll explain what negative numbers are, how to order them, how to add and subtract through zero, how to find the difference across zero, how they come up in SATs, the mistakes I see most often, and practice questions with answers.

What your child needs first

Negative numbers are built on two things:

• Confident counting forwards and backwards. Your child needs to count back from 10 to 0 without thinking, and count on and back in steps of 2, 5 and 10.
• Number bonds and subtraction facts. Lots of negative number questions come down to "how far is it to zero?" If your child knows that 7 − 3 = 4 instantly, the rest is easy. See number bonds to 10, 20 and 100 if this needs work.

In the national curriculum, children count backwards through zero to include negative numbers in Year 4. In Year 5 they interpret negative numbers in context and count forwards and backwards through zero. In Year 6 they use negative numbers in context and calculate intervals across zero.

What negative numbers are

Start with something your child has already seen: a thermometer. When it gets very cold, the temperature drops below zero. 1°C below zero is −1°C. 5°C below zero is −5°C.

Now draw a number line across a piece of paper, with zero in the middle:

Numbers to the right of zero are positive. Numbers to the left are negative. The rule your child needs to hold on to is simple:

We say −4 as "negative four". You'll also hear "minus four", which is fine, but "negative" helps children tell the difference between a negative number and the subtraction sign. Other real-life examples help too: lift buttons for floors underground (−1, −2), being overdrawn at the bank, or the depth of a diver below sea level.

Ordering negative numbers

This is where most children trip up first. They know 8 is bigger than 3, so they assume −8 is bigger than −3. But −8 is further from zero on the cold side. It's colder, so it's smaller.

Example 1: put these in order, smallest first: 4, −7, 0, −1, −12

1. Find the negative numbers first: −7, −1 and −12.
2. The one furthest left on the number line is the smallest. That's −12 (the coldest).
3. Then −7, then −1 (closest to zero, so the biggest negative).
4. Then 0, then the positive number 4.
5. The answer is −12, −7, −1, 0, 4.

If your child gets stuck, ask: "Which is colder, −12°C or −1°C?" Almost every child gets that right, and the colder temperature is the smaller number.

Adding and subtracting through zero

In primary school, adding and subtracting with negative numbers is all about moving along the number line. Adding means moving right. Subtracting means moving left. The clever bit is to stop at zero on the way.

Example 2: 3 − 7

1. Start at 3 and move 7 to the left.
2. Get to zero first: that uses 3 of the 7 jumps.
3. There are 4 jumps left. Carry on past zero: 4 more to the left.
4. You land on −4.

Example 3: −5 + 8

1. Start at −5 and move 8 to the right.
2. Get to zero first: that uses 5 of the 8 jumps.
3. There are 3 jumps left. Carry on past zero: 3 more to the right.
4. You land on 3.

Example 4: −6 − 4

1. Start at −6 and move 4 to the left.
2. You're already below zero, so just keep going: −7, −8, −9, −10.
3. You land on −10. It's like the temperature dropping further when it's already freezing.

Splitting at zero is the same idea as bridging through 10, which your child may know from partitioning. It turns one awkward jump into two easy ones.

You may have heard "two minuses make a plus". That rule is for things like 5 − (−3), which children don't usually meet until secondary school. In primary, stick to the number line.

Finding the difference across zero

This is the Year 6 skill that shows up most in SATs, usually with temperatures. The method is the same: split the jump at zero.

Example 5: what is the difference between −3°C and 5°C?

1. From −3 up to zero is a jump of 3.
2. From zero up to 5 is a jump of 5.
3. Add the two jumps: 3 + 5 = 8°C.

Example 6: the temperature is −2°C. It rises by 9 degrees. What is the new temperature?

1. Start at −2 and move 9 to the right.
2. 2 jumps get you to zero. That leaves 7 jumps.
3. 7 more from zero lands on 7°C.

A quick sketch of a thermometer or number line is the best habit your child can build here. In the SATs reasoning papers, children who draw it almost always get these right, and children who try it in their heads often subtract the digits (5 − 3 = 2) by mistake.

Negative numbers in SATs

Negative numbers mostly appear in the Year 6 SATs reasoning papers rather than the arithmetic paper. These are the question types to practise:

Tables of temperatures in different cities are a favourite. Your child might be asked which city was coldest, or how much warmer one city was than another. If you want an overview of the whole test, read the guide to the Year 6 SATs arithmetic paper.

5 common mistakes and how to fix them

Mistake 1: Thinking −8 is bigger than −3

Your child orders −3, −8, −1 as −1, −3, −8, smallest first.

The fix: use temperature. "Which is colder, −8°C or −3°C?" The colder one is smaller. Then point to them on the number line: further left means smaller.

Mistake 2: Subtracting the digits

Your child says the difference between −3 and 5 is 2.

The fix: draw the number line and split the jump at zero. 3 to get to zero, 5 more after. They can see the gap is 8, not 2.

Mistake 3: Counting the starting number

Your child works out 3 − 7 by counting "3, 2, 1, 0, −1, −2, −3" and lands on −3.

The fix: count the jumps, not the numbers. Put a finger on 3 and say "one" as you move to 2. Hopping along with a toy on a drawn number line helps a lot.

Mistake 4: Going the wrong way

Your child works out −5 + 8 and gets −13.

The fix: adding always moves right (warmer), subtracting always moves left (colder). Before they start, ask: "Will the answer be bigger or smaller than where we started?"

Mistake 5: Forgetting zero is a number

Your child counts from −2 to 3 as −2, −1, 1, 2, 3 and gets a difference of 4.

The fix: zero is a stop on the number line like any other. Write it in clearly, and use the split at zero method: 2 to zero, 3 more, difference of 5.

Practice questions

Same three steps I use for every skill: watch, copy, practise. Do the first one out loud yourself, then let your child have a go at a similar one before they try the rest on their own. Cover the last column and ask your child to fill in the gaps.

Bonus question: the temperature at midnight was −7°C. By midday it was 12°C. How many degrees did it rise? (Answer: 19 degrees, because 7 up to zero and 12 more.)

Ten minutes, a few times a week, is plenty. Only move on when they're getting three in a row right.

Frequently asked questions

What are negative numbers?

Negative numbers are numbers less than zero. They are written with a minus sign in front, like −3, which we say as "negative three". On a number line they sit to the left of zero, and you see them in real life on thermometers, in bank balances and on lift buttons for floors below ground.

What year do children learn negative numbers?

In England, children start counting backwards through zero into negative numbers in Year 4. In Year 5 they use negative numbers in context, such as temperature, and in Year 6 they calculate intervals across zero, for example the difference between −4°C and 6°C.

Is −5 bigger than −2?

No. −2 is bigger than −5. On a number line, numbers get bigger as you move right, and −2 is to the right of −5. Think of temperature: −2°C is warmer than −5°C.

How do you find the difference between a negative and a positive number?

Split the jump at zero. For the difference between −3 and 5, it is 3 from −3 up to zero, then 5 from zero up to 5. Add the two jumps together: 3 + 5 = 8.

How do you explain negative numbers to a child?

Use a thermometer or a lift. A thermometer shows temperatures below zero, and a lift has floors below the ground floor. Draw a number line with zero in the middle, and show that numbers to the left of zero get smaller the further away they are.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (number and place value, Years 4, 5 and 6)
• Standards and Testing Agency, Key stage 2 mathematics test framework
• Ross Mackell, Teacher's Perspective on YouTube