Number Sense: Order Irrelevance Principle

Developing Number Sense: Principles of Counting

All concepts of number sense need to be actively taught. Stable order principle is one of the beginning concepts of counting that children learn! Although children are usually unaware of their learning of this concept it is an important skill to be taught. 

Teaching students explicitly about order irrelevance helps develop their fluency with numbers

Order Irrelevance Principle

This principle applies to counting a set of objects. It does not matter which object you start with when you begin to count and that the total remains the same.

For example:
If I have three toy animals (a bird, dog and cat) I can start counting with the dog the first time I count the set and the next time I can start with the cat and I will always end up with the same number of three!

This seems like a simple concept to understand but if you ask kids tell you how many objects there are in a set by counting in a different order often they have to count the objects over and over again. 

When children are developing this skill they will count each object each time they are asked how many are in the set. If they don't understand the concept they might count the same object several times without realizing it. This understanding is very closely tied to the concept of cardinality which I will discuss in another upcoming blog post.

Children will demonstrate their complete understanding of this concept when they automatically know the answer without counting. "I know it is three because I counted it before and it hasn't changed!"


Simply have children count objects in their every day environment in a variety of different ways that are meaningful the them. Constant exposure to counting helps develop this skill as well as making a game out of it by "mixing up" objects in a set to see if the numbers change.

I have also used the following activity to assess students understanding. It uses a fun situation of a frog hopping over a pond on lily pads. Students are asked if they can get the frog to "hop" across and then show a new way. Students who always repeat the same pattern have not developed the concept of order irrelevance yet.

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