One representation, which has often been underused in the past, is the humble number line. Some of our popular podcast episodes have explored how these wonderfully simple representations, which are too often reduced to mere calculating tools, can be used in different ways to support children to explore and reason with numbers. In this feature, we focus on a podcast episode with the NCETM’s Director for Primary, Debbie Morgan, which explored using number lines in KS1.

In the podcast episode, Debbie suggested five different ways teachers might use number lines to reason about the location of numbers within the linear number system.

1. Finding the midpoint on a blank number line

Our first number line is a straight line with zero at one end and ten at the other. Could your pupils place the numbers one to nine on the straight line? It is likely numbers will be crowded together at either end of the line because the children have yet to develop the spatial reasoning skills needed. Asking pupils to find the midpoint (before asking them to place all the numbers) allows us to draw the children’s attention to the fact that numbers are evenly spaced and to reinforce the concept of five as a midpoint.

A number line, or strip of paper folded in half, can be used to give children the opportunity to find the midpoint. Children can also create lines of different lengths on the playground with chalk or skipping ropes, and practise placing the class teddy on the midpoint. This activity provides a great opportunity to develop classroom talk and spatial language, such as ‘in the middle’ and ‘equally spaced’.

2. Reasoning with a completed zero to ten number line

You could start this activity by revisiting the idea of the midpoint and ask children how they know what the midpoint is, providing a further opportunity for children to practise spatial language. However, the beauty of this number line is the opportunities it provides to fully explore the linear nature of the number system and to reason about the location of numbers within it.

One way to start this exploration is through games of true or false using the inequality symbols; for example, seven is greater than eight. Can the children prove their answer using the number line? Another game that could be played is Guess My Number. Can children use clues about a number’s location on the number line to find the number? These games bring the children back to the spatial language of ‘greater than’ and ‘less than’. They are asked to justify their answers, whilst their attention is also drawn to where these numbers fit on the number line.

3. Placing numbers on a blank number line

Returning to the activity we started with, asking children to place the numbers onto the line allows us to revisit the concept of the midpoint and builds on our last activity. Children should have a better sense of being able to place the numbers evenly, but the main teaching point here is that they should be able to reason where their numbers sit in relation to each other. 

You may ask them to compare their number line with a friend’s number line, which provides an opportunity to ask which is better and why. Whose numbers are more evenly spaced? Have they correctly found the midpoint? At this stage, teachers can assess whether children are placing their number between or on the intervals.

4. Using a number line as a measuring tool

This time we adjust the blank number line slightly by adding measures. Measure operates within our linear number system so a ruler is, in essence, a number line. Armed with their 10cm number line strip, can the children find objects shorter than 10cm or longer than 10cm? 

By reminding children to line up their strip of paper so that 0cm lies at one end of the object, we are developing accuracy, which children will need when they start using a ruler. Can children find the midpoint? We can move on by asking them to find objects longer than 5cm or shorter than 10cm. We may even start to estimate and reason about where numbers fit in the linear system by asking where 7cm might be. Can children reason that it is between 5cm and 10cm? Where would they place it? 

5. Comparing values on two completed number lines—zero to twenty

Comparing number lines encourages children to notice what is the same and what is different about numbers zero to 10 and numbers 10 to 20. With the number lines placed one on top of each other and lined up, ask children what they notice. Draw children’s attention to the fact that where we have 1, on the next number line we have 10 and 1, which we call 11. Where we have 2, on the next number line we have 10 and 2, which we call 12 and so on. This enables children to see the relationship between the numbers that come after 10 and the numbers that come before 10 and the pattern of the number system. 

The children can discuss what is the same and what is different about the midpoints of both number lines. Will the midpoint always feature a five? By introducing a new number line, placed underneath, with the numbers zero to 20 placed at either end, children will identify that our midpoint is now 10. 

This activity enables children to explore ‘10 and a bit’ numbers—the tricky teen numbers—and how they fit into the linear number system. This can be a ‘wow’ moment for children, as they start to make those connections, recognise those patterns, and begin to understand how they repeat into infinity.