The Number Line

The number line can lead to a deeper understanding of numbers and the number system itself. Refer to Chapter 23.04 "Number Line 2".

The number line is mostly represented, to start with, as a discrete representation of whole numbers and used as a tool for counting, comparing, addition & subtraction operations with them.

It is essentially a model representing the "measurement metaphor". Students should be encouraged to think of it as a “continuous” line. The idea of a continuous number line should be revisited as and when new types of numbers are invented.

The number line which extends “forever” in both directions beautifully captures the idea of “real umbers”. Ultimately the number line becomes the “real number line”.

It also becomes the x-axis of the two-dimensional cartesian plane.

This in turn facilitates the idea of representing imaginary & complex numbers!

Students need to understand three aspects of a number line,

1.	As a representation for the number system

a.	We start with marking the whole numbers from 0 onwards

b.	Then we add negative numbers to the line

c.	Then fractions

d.	Then irrationals

e.	Finally reaching real numbers

2.	As a pedagogical tool for

a.	Ordering and positioning of natural numbers & later fractions, decimals. Integers and eventually all real numbers

b.	Forward/ Backward & skip counting

c.	Developing numeracy skills

d.	Calculation strategies got addition & subtraction

3.	As an aid in thinking 

a.	While using the number line for counting, children are actually counting the spaces and not the numbers written at intervals

b.	Identifying wholes when they mark fractions on the number line

c.	Of the real number system as an integrated one.

The Empty Number Line

Empty Number Line is just a line without any markings. Children should be able to mark the points and use the lines for addition or subtraction.

See https://www.k-5mathteachingresources.com/empty-number-line.html