# Counting

Counting can seem to be a simple skill – we hear young children recite a string of words and assume they can count but it's from this point onwards that children actually begin to learn the 5 principles of counting.

## 1. One-to-one

### "I can count each object only once and say one number name for each object"

When children are first learning to count, it is easier for them to count physical objects that can be seen, touched and moved.

## 2. Stable order

### "When I count I say the numbers in order and this order always stays the same"

Children begin by saying the number names in order simply because they have remembered the words.  The order of these numbers will begin to develop meaning as children recognise why numbers names are said in this order.

## 3. Cardinal

### "When I count the objects in a group the last number I say is the total for the group"

This is a milestone in mathematical development; understanding that the process of counting is not just sound making or a game but actually has meaningful and useful purposes – related to finding out how many. It is something that a child must understand before they can begin to carry out addition by ‘counting on’

This in itself has 4 stages of development

1 Reciting the last number with no clear idea that it relates to quantity – probably because they think it is the response the adult expects.

2 Understanding that the last number relates to the quantity.

3 Understanding the progressive nature of counting - if they are stopped in the middle of a count they can say how many they have counted so far, and then carry on.

4 Understanding that the next number in a sequence represents a larger quantity.

## 4. Abstraction

### "I can count anything, even things that can’t be touched or seen"

Children begin to understand that they can also count non-physical things, such as sounds, movements and even imaginary objects.

## 5. Order irrelevance

### "It doesn’t matter which order I count the objects in, the total will be the same"

This may seem simple, but children that do not understand this may need to recount a group if the objects are moved.