Number lines: how children use them from Year 1

What is a number line?

A number line is a line with numbers marked on it in order, equally spaced, usually getting bigger from left to right. It shows two things at once: the order of numbers and how far apart they are. That's why schools use it for counting, comparing, adding and subtracting.

In Year 1 the curriculum asks children to represent numbers on a number line and use words like "more than", "less than", "most" and "least". The guidance for teachers also wants children to picture a number line in their heads, and to draw their own with the numbers evenly spaced.

Number lines to 10, 20 and 100

Children start with a number line to 10, then to 20, and by Year 2 a number line to 100. In Year 3 the numbers go up to 1,000, and the line might be marked in steps of 10 or 100 instead of ones.

A number line doesn't have to start at 0. A line from 10 to 20, or from 300 to 400, works in the same way. Lines are also good for counting in steps: there's a number line in each of the times tables pages, showing the multiples as equal jumps.

Where is the dot on the number line?

To read a point on a marked number line, find the nearest labelled number and count from there, forwards or backwards. The guidance for teachers gives examples of the reasoning children should use on a 0 to 20 line:

• "5 is halfway between 0 and 10."
• "12 is 2 more than 10."
• "19 is one less than 20."

Working back from 20 to find 19 is quicker and more accurate than counting 19 marks from the start. On a 0 to 100 line it's the same: 79 is one less than 80.

Estimating on an unmarked number line

An unmarked number line has only its two ends labelled, with no marks in between. Children are asked to estimate where a number goes, or what number an arrow is pointing at. They don't need to be exact: the aim is a sensible guess based on the whole length of the line.

The guidance for teachers says the best start is to find the middle. On a 0 to 20 line the midpoint is 10, so "16 is about here, because it's just over halfway between 10 and 20." On a 0 to 100 line, 60 is just over halfway.

A common thing to watch for: children who mark 1, 2, 3 and so on from the left often run out of room and squash the bigger numbers together at the end. Marking the middle first fixes it.

Adding on a number line

To add on a number line, start at the first number and jump forwards by the second. For bigger numbers, children split the jump by place value: tens first, then ones. Here is 27 + 25, jumping 10, 10 and then 5:

Each jump is an easy step: 27 + 10 = 37, 37 + 10 = 47, 47 + 5 = 52. Splitting 25 into 10, 10 and 5 is partitioning, which has its own guide: partitioning numbers.

Children might also jump to the next ten first. For 47 + 5 they can jump 3 to reach 50, then 2 more, using their number bonds to 10.

Subtracting on a number line

To subtract, start at the first number and jump back. Here is 52 − 25, jumping back 10, 10 and 5:

Jumping back ends on 27, the number we started with in the adding example. That's the inverse at work: subtraction undoes addition, and children in Year 2 use it to check their answers.

Finding the difference by counting on

To find the difference between two numbers, you can count on from the smaller one to the bigger one and add up the jumps. For 54 − 38, start at 38, jump 2 to the next ten, 10 more to 50, then 4 to 54:

The jumps add up to 16, so 54 − 38 = 16. Questions that say "how many more", "how many fewer" or "what is the difference" in Year 2 are often easiest this way, because the two numbers are close together.

Fractions on a number line

The number line isn't only for whole numbers. In Year 2, children count in halves and quarters along a line: 1, 1 and a quarter, 1 and a half, 1 and three quarters, 2. In Year 3 they place fractions on the line as numbers in their own right, which helps them see that a half is bigger than a quarter.

Later: negative numbers and rounding

From Year 4, the number line carries on to the left of zero. Children count backwards through zero into negative numbers, and in Years 5 and 6 they use negative numbers for things like temperature. Here is 3 − 7 on a number line:

Also in Year 4, children round numbers to the nearest 10, 100 or 1,000. A number line makes the rule clear, because you can see which ten is nearer:

A step on the way to mental maths

Number lines are a tool for understanding, not a method to keep forever. The guidance for teachers says that by the end of Year 2, children should work out sums like 90 − 40 from facts they know (9 − 4 = 5, so 90 − 40 = 50), without sketching jumps. If your child draws a line for every sum, that's fine while they learn, and the aim is to picture it in their heads over time.

How to help at home

• Draw one together. A line on paper with 0 and 20 at the ends: ask where 10 goes, then 15, then 19.
• Use the ones around you. Rulers, tape measures, thermometers and the scale on a kitchen jug are all number lines.
• Count forwards and backwards from any number. "Start at 46 and count back 5" is the same skill as jumping back on a line.
• Ask how they got there. If your child adds 27 and 25, ask which jumps they made. There's often more than one good answer.
• Play "guess my number". Think of a number to 100 and answer only "bigger" or "smaller". Children start to picture the line to narrow it down.

The Year 1, Year 2 and Year 3 guides show where number lines fit with everything else in those years, and the guide to place value covers what each digit in a number is worth.

Practice questions

1. On a 0 to 20 number line, which number is halfway?
2. Start at 34 and jump forward 10, then 10, then 3. Where do you land?
3. Start at 61 and jump back 20. Where do you land?
4. What is the difference between 47 and 52?
5. What is 45 rounded to the nearest 10?

Answers

1. 10
2. 57
3. 41
4. 5
5. 50