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Counting Principles

Counting Principles

These are the counting principles. Counting supports all mathematical understanding and should be included in every lesson. Number can include the counting of a collection of items e.g. three boxes; a measure e.g. length; a label e.g. the number 17 bus or the amount you have of something e.g. a cup of flour or half an hour.

 

Counting Stage

Details

Strategies/ equipment to support

The one-one principle.

 

Children can count objects one for one

Children say one number name to each object that is being counted.

Without this skill, children will not be able to understand how many objects are in a group (the cardinal value).

Encourage children to line up objects and to touch each one as they count, saying one number name per object. This will also help avoid children counting more quickly than they touch the object which again shows they have not grasped one-one correspondence.

Stable order principle

 

Children can count up and down in order i.e. 1, 2, 3, 4, 5 and not 1, 3, 2, 5, 4.

Children know the counting words and can recite them in the correct order.

 

Collaborative play with an adult or an older child helps them to develop stable order counting. Counting things out loud and making deliberate mistakes is very effective in helping children to learn the correct counting order.

The cardinal principle.

 

Children understand that the last number counted indicates how many things are in the set.

In order to grasp this principle, children need to understand the one-one and stable-order principle.

From a larger group, children select a given number and count them out. When asked ‘how many?’, children should be able to recall the final number they said. Children who have not now grasped this principle will recount the whole group again.

Subitising

 

Children can recognise a small number of objects or dots without counting them. Can be achieved for quantities up to approximately 5.

Dot patterns on dice, dominoes and playing cards. Small groups of randomly arranged shapes stuck on cards.

The abstraction principle

 

Children can count anything- visual, objects, hidden objects, sounds, movements (jumps) etc.

When starting to count, many children rely on touching the objects in order to count accurately. They can find it tricky to count things they cannot move, touch or see. Encourage abstraction on a daily basis by counting claps or clicks.

Conservation (of number)

 

Children understand that the number stays the same if none have been added or subtracted.

 

 

Place objects in a bag. Empty them out and encourage child to count how many there are. Place them back in the bag and give them a shake. Take them all back out of the bag. Do you need to count them again? Why?

The order-irrelevance principle

 

Understanding that the order we count a group of objects is irrelevant as there will still be the same number of objects.

Encourage children to count objects, left to right, right to left, top to bottom and bottom to top.

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