Pre-Number Concepts 2

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The activities in the previous chapter help the child form an idea of numerical quantity.

Once an idea of quantity takes root, it can be developed & strengthened through a series of activities which can be developed by teachers.

Idea of One

All living beings have an idea of "One" since they are able to distinguish themselves from others. And also one object or a living being from another. They are able to see themselves as "separate" from others. It is obvious that animals also have this ability, from the fact that they can track a prey and catch it.

The idea of "one" is the starting point in understanding numbers.

One and Many

On seeing that things also exist as groups, the idea of "One and Many" evolves. Gradually, the "many" is seen as several kinds of "many" (one, two, few etc) and concepts about other numbers evolve.

One More/ One Less 

Putting one more in a collection increases it. Similarly taking one away from a collection reduces it. The idea of "one more" also leads to the idea that given any collection, we can always increase it. This in turn leads to the idea that there is always a number more than any given number.

This enables children to understand that numbers continue forever and there is no biggest number.

On the other hand the idea of "one less" always ultimately leads to a solution where there is "nothing" left in any collection. Later this leads to an understanding of zero as a number.

Order and relations of numbers 1 to 5

Through the idea of perceptual numbers, children can already identify & represent numbers 1 to 5.The idea of One More or One Less can be used to reinforce the relations between numbers 1 to 5.

Children can identify collections up to five items by sight.

Using the "one more" idea we can help them realize that One and "One More" leads to "two", a number. They already know "two" independently (as a perceptual number) and now they also know that it is "One more than One".

They realise that "one more" is an idea which connects One & Two. Similarly, the other relations - Three is one more than two, Four is one more than Three etc - can be discovered and reinforced.

The relations can also be established in "One less" activities - Four is one less than Five, Three is one less than Four etc.

They also realise that "One More" and "One Less" are related but opposite ideas.

Order in Numbers & Ordinality

Children realise that this ide of order applies to numbers beyond 5 also.

This relation leads to an understanding of the concept of order in numbers and the idea of ordinality of numbers.

That quantities can be arranged in an order and called first, second, third etc.

This in turn leads to an understanding of the concept underlying counting.

Numbers can be Compared

It also leads to the concept that ideas like "bigger/ smaller", "More/ Less" etc are applicable to numerical quantities also.

They also realise that the meaning of words like "bigger" has to be interpreted depending on the context.

That, in terms of bags of rice, it refers to "size" and in terms of toys it refers to "number".

Give/ Take/ Bring/ Discard 

While giving something to another, the quantity that we have reduces. At the same time, the quantity which the other person has, increases!

In contrast when we take, the quantity that we have increases and the "other" quantity reduces.

These experiences can be related to addition and subtraction at a later stage.

Give One Each 

One of the important life experiences is sharing. Giving one to each person is the basis of the idea of sharing equally.

The above activities enable children to see objects as part of various collections and understand the idea of sets. They can also lead to development of concepts related to sets. We will see them in detail in the next chapter.

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