# Number Lines

## What is a number line?

A number line is a straight, horizontal line with numbers placed evenly along it. Since it is not a ruler, the spaces between each number don’t need to be a specific distance apart.

Number lines are a great way to reinforce number order, count in multiples, compare numbers and order numbers. A number line is a pictorial representation of numbers which means it supports children to develop the skills to solve number problems pictorially.

When a number line is vertical not horizontal it is sometimes called a number ladder. ## What is a number line to 10?

A number line to 10 is a horizontal line with numbers to 10. Number lines to 10 normally start at 0, but some start with 1. Each number is shown in the right place on the number line, equally spaced apart.

Number lines to 10 help children understand the links between counted objects and number representation. Childen can practice ordering numbers to make their own number lines, working out missing numbers and solving problems involving finding one more and one less than a number.

## What is a number line to 20?

A number line to 20 is a series of numbers from 0 to 20 that are placed on a line. Each number is shown in the right place on the number line, equally spaced apart.

Number lines to 20 are great visual resources for learners. They show children number sequence and give them the opportunity to solve number problems that bridge 10. They can be used to highlight number patterns for example counting in 2s.

## What is a number line to 30?

A number line to 30 is a series of numbers from 0 to 30 that are placed on a line. Each number is shown in the right place on the number line, equally spaced apart.

Number lines to 30 show children number sequence and give them the opportunity to solve number problems involving larger numbers.

## What is a number line to 50?

A number line to 50 is a series of numbers from 0 to 50 that are placed on a line. Each number is shown in the right place on the number line, equally spaced apart.

Number lines to 50 show children number sequence and give them the opportunity to solve number problems involving place value. They can be used to highlight number patterns for example counting in 5s and 10s.

## What is a number line to 100?

A number line to 100 is a series of numbers from 0 to 100 that are placed on a line. Each number is shown in the right place on the number line, equally spaced apart.

Number lines to 100 show children number sequence and give them the opportunity to solve number problems involving place value. Number lines to 100 are sometimes arranged in a square grid called a hundred square, this helps children to spot patterns with the tens and ones digits.

## What is a counting in 2s number line?

A counting in 2s number line only includes even numbers. The numbers on the number line start at 0 and usually go up to 20.

Counting in 2s or ‘skip counting’ helps children to develop number fluency and number facts, which support them solving addition, subtraction, multiplication and division calculations.

## What is a counting in 5s number line?

A counting in 5s number line only includes numbers that are multiples of 5s. The numbers on the number line start at 0 and usually go up to 50.

Counting in 5s or ‘skip counting’ helps children to develop number fluency and number facts, which support them solving addition, subtraction, multiplication and division calculations.

## What is a counting in 10s number line?

A counting in 10s number line only includes numbers that are multiples of 10s. The numbers on the number line, or hundred square, start at 0 and usually go up to 100.

Counting in 10s or ‘skip counting’ helps children to develop number fluency and number facts, which support them solving addition, subtraction, multiplication and division calculations. As children become confident with counting in multiples of 10 and their understanding of place value, they can begin to use number lines to add and subtract 10 from any number.

## What is a negative number line?

A negative number line shows numbers that are less than 0.

## What is a negative and positive number line?

A negative and positive number line shows numbers that are less than and more than 0.

## Blank number line

A blank number line is a straight line without numbers. Some blank number lines have tabs on them. Blank number lines enable children to draw out any number problem by using the line and their knowledge of numbers to create their own number line. Blank number lines allow children to easily show jumps of any size, for example if adding 12 to a number they could first show the jump of 10 and then the jump of two.

## How do you solve a problem with a number line?

Number lines support children’s problem-solving by helping them move from using concrete methods e.g. counting objects to pictorial methods. Number lines show numbers in sequence which allows children to manipulate the numbers and show their workings without having to hold lots of numbers or steps in their heads.

Number line addition involves ‘jumping’ along a number line to add two or more numbers together. Children are encouraged to find the largest number in the addition number sentence and circle it on the number line. The other numbers in the number sentence tell them how many jumps they need to go along the number line. The number sentence 2+5= could be solved by circling the number 5, then jumping along the number line twice. Children should be encouraged to check they are jumping the right away along the number line, this can be done by getting them to think about what the number sentence is asking them to do. If it is an addition number sentence the answer will be a bigger number than the starting number. Encouraging children to think about what they need to do and why will help them when number lines are not laid out in the way they are expecting.

## Number line subtraction

Number line subtraction involves ‘jumping’ along a number line to subtract two or more numbers from each other. Children should be taught both to solve subtraction number sentence by taking away and by finding the difference.

When subtracting children are encouraged to find the first number in the subtraction number sentence and circle it on the number line. The other numbers in the number sentence tell them how many jumps they need to go along the number line. The number sentence 12-7= could be solved by circling the number 12, then jumping along the number line 7 times. Children should be encouraged to check they are jumping the right away along the number line, this can be done by getting them to think about what the number sentence is asking them to do. If it is an subtraction number sentence the answer will be a smaller number than the starting number. Encouraging children to think about what they need to do and why will help them when number lines are not laid out in the way they are expecting.

When solving a subtraction number sentence by finding the difference children should circle both numbers on the number line and work out the difference between them. This method allows children to count up rather than count backwards. The number sentence 12-7= could be solved by circling the number 12 and 7, then jumping along the number from 7 to 12.

## Missing numbers on a number line

Missing numbers out on a number line is a great way to develop children’s problem-solving skills.

## Fractions on a number line

Fractions on a number line help children understand what can be a tricky concept to grasp. Fraction number lines can show fractions with the same denominator, or fractions with a mixture of denominators. These number lines can start out as a point of reference for children, as children become familiar with the order of fractions they can complete missing number fraction number lines, or use the number line to solve fraction problems.

## Tenths on a number line

Tenths on a number line help children understand the sequence of these fractions. These number lines can start out as a point of reference for children, as children become familiar with the order of fractions they can complete missing number fraction number lines, or use the number line to solve decimal problems.

## Decimals on a number line

Decimals on a number line help children understand the sequence of these numbers, and what happens when there are multiple numbers after the decimal point. These number lines can start out as a point of reference for children, as children become familiar with the order and structure of decimal numbers they can complete missing number decimal number lines, or use the number line to decimal solve problems.

## Number line division

Division on a number line can be shown by plotting the multiples of the divisor starting from 0 up to the dividend. The divisor is the number of groups and the dividend is the number being divided. The number of jumps or groups on the number line needed to reach the dividend is the answer. To solve 20 ÷ 5 on a number line we can circle 20 (the dividend) on the number line. Then we jump in groups of 5 (the divisor) from 0 up to 20. 4 jumps are needed so the answer to 20 ÷ 5 is 4.