Negative Numbers on a Number Line, Explained Simply

For the first few years of school, the answer to "what is 3 take away 5?" is "you can't". Then negative numbers arrive and suddenly you can. That is a big change, and a number line is the clearest way to show it: the line does not stop at zero, it carries on in the other direction.

What are negative numbers?

Negative numbers are numbers below zero. They are written with a minus sign in front: −1, −2, −3 and so on, read as "negative one" or "minus one". Numbers above zero are positive. Zero is neither. Children already know negative numbers from real life, even if they have not met the name:

• Temperature: −4 °C is four degrees below freezing.
• Lifts and car parks: floor −1 is one level below the ground floor.
• Height: a diver at −10 m is ten metres below the surface of the sea.
• Money: a balance of −£5 means you owe five pounds.

Where do negative numbers go on a number line?

To the left of zero, each one the same distance apart as the positive numbers. −1 is one step left of zero, −2 is two steps left, and so on. The negative side is a mirror image of the positive side. On the interactive number line you can drag the line past zero and see the negative zone appear, or tap −1 and −10 to step back through zero.

Which is bigger, −5 or −2?

−2 is bigger. The rule for the whole number line is simple: numbers get bigger to the right and smaller to the left. −5 is further left than −2, so it is smaller. Children get this wrong because 5 is bigger than 2 and they carry that over. Temperature fixes it quickly: −5 °C is colder than −2 °C, so −5 is the lower number. In order from smallest to biggest: −5, −2, 0, 3, 7.

How do you add and subtract through zero?

Use the number line as a path. Adding moves right, subtracting moves left.

1. 3 − 5: start at 3 and move 5 left. Three steps reach 0, two more reach −2. So 3 − 5 = −2.
2. −4 + 6: start at −4 and move 6 right. Four steps reach 0, two more reach 2. So −4 + 6 = 2.
3. −2 − 3: start at −2 and move 3 left. You land on −5.

Stopping at zero on the way, as in the first two examples, is the same "bridging" children use to cross ten in addition and subtraction. It breaks one awkward jump into two easy ones.

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

Count the distance in two parts: from the negative number up to zero, then from zero to the positive number. The difference between −3 °C and 5 °C is 3 + 5 = 8 degrees. This is the Year 6 skill of working out intervals across zero, and it is easiest when a child can see both numbers on the same line.

What mistakes do children make with negative numbers?

• Thinking −8 is more than −3: because 8 is more than 3. Go back to "further left is smaller".
• Swapping the numbers: working out 3 − 5 as 5 − 3 and writing 2. The order matters in subtraction.
• Counting zero twice, or missing it: from 2 back to −2 is 4 steps, not 3 or 5. Count the jumps, not the numbers.
• Mixing up the two jobs of the − sign: in 6 − 2 it means "subtract"; in −2 it means "negative". Reading −2 as "negative two" helps.

How can you practise negative numbers at home?

• Look at a weather app in winter and ask which city is coldest, and by how many degrees.
• Draw a number line from −10 to 10 in chalk outside and walk the sums.
• Play a game with a dice and a counter that starts at 0: odd rolls move left, even rolls move right.
• Use the number line to check answers, zooming out to count in tens below zero.

The same number line shows how the positive side is built from equal jumps. See skip counting on a number line for how those jumps become the times tables, and the number line view of the multiplication visualiser to try it. For decimals between the whole numbers, fractions, decimals and percentages covers where they sit, and there are printable worksheets for extra subtraction practice.