# Reason about the location of numbers to 20 within the linear number system (1)

## Description

Pupils should be introduced to the number line as a representation of the order and relative size of numbers.

Pupils should:

• begin to develop the ability to mentally visualise a number line, with consecutive whole numbers equally spaced along it
• draw number lines, with consecutive whole numbers equally spaced along them
• identify or place numbers up to 20 on marked and unmarked number lines

Pupils should also be able to estimate the value or position of numbers on unmarked number lines, using appropriate proportional reasoning, rather than counting on from a start point or back from an end point.

Pupils should learn to estimate the value/position of a number relative to both ends of the number line, beginning with a 0 to 10 number line, then moving on to 0 to 20 and 10 to 20 number lines.

When pupils are asked to mark all numbers on, for example, an unmarked 0 to 10 number line, they typically start at 1 and run out of space as they approach 10, and so bunch the larger numbers together.

Pupils should learn to look at the full length of the number line and mark on the midpoint first. They should be able to reason about the location of numbers relative to both ends, and the midpoint, of a number line, for example, “16 is about here because it is just over halfway between 10 and 20.”