Primary Mathematics/Numbers

Numbers

This section is for students to read by themselves or with the help of a teacher or parent.

Natural Numbers

When we count apples or oranges or elephants, we are using natural numbers. Natural numbers are 1, 2, 3, and so on without end. There is no largest natural number; one can always get a larger natural number by adding 1 to the previous number.

Zero

Zero represents nothingness. Zero is less than every natural number. If we have zero apples or oranges or elephants, we simply do not have anything.

Teaching Numbers

This section is for teachers or home-schoolers. It is about teaching the basic concepts and conventions of numbers.

Developing a sound concept of number

Children typically learn about numbers at a very young age by learning the sequence of words, "one, two, three, four, five" etc. Usually, in chanting this in conjunction with pointing at a set of toys, or mounting a flight of steps for example. Typically, "mistakes" are made. Toys or steps are missed or counted twice, or a mistake is made in the chanted sequence. Very often, from these sorts of activities (and from informal matching activities), a child's concepts of numbers and counting emerge as their mistakes are corrected. However, here, at the very foundation of numerical concepts, children are often left to "put it all together" themselves, and some start off on a shaky foundation. Number concepts can be deliberately developed by suitable activities. The first one of these is object matching.

Matching Activities

As opposed to the typical counting activity children are first exposed to, matching sets of objects gives them a solid foundation for the concepts of numbers and numerical relationships. It is very important that matching should be a "physical" activity that children can relate to and build on.

Typical activities would be a toy's tea-party. With a set of (say) four toy characters, each toy has a place to sit. Each toy has a cup, maybe a saucer, a plate etc. Without even mentioning "four", we can talk with the child about "the right number" of cups, of plates etc. We can talk about "too many" or "not enough". Here, we are talking about number and important number relations without even mentioning which number we are talking about! Only after a lot of activities of this type should we talk about specific numbers and the idea of number in the abstract.

Number and Numerals

Teachers should print these numbers or show the children these numbers. Ideally, the numbers should be handled by the student. There are a number of ways to achieve this: cut out numerals from heavy card stock, shape them with clay together, purchase wooden numerals or give them sandpaper numerals to trace. Simultaneously, show the definitions of these numbers as containers or discrete quantities (using boxes and small balls, e.g., 1 ball, 2 balls, etc. Note that 0 means "no balls"). This should take some time to learn thoroughly (depending on the student).

0 1 2 3 4 5 6 7 8 9

Place Value

The Next step is to learn the place value of numbers.

As you are aware, the number after 9 is 10 (called ten). This number is represented by a new place, the tens, and each time the number in the second place value increases, represents a collection of ten units. After this comes the hundred place, followed by thousands. Even though numbers can be much bigger, we will not need to create larger numbers at this time.

To help visualization, you can represent 10 as a bag of 10 coins, and 100 as a box filled with 10 such bags.

Place Values in other number systems

Other number systems are not the same as the one we currently use. For example, the Maya Culture where there are not the ten symbols above but twenty symbols. Even though there are more symbols, the place value system still remains intact.

A common number system used with computers is the use of binary, which uses the two symbols 0 and 1.

Here is how the system will be created:

Binary	0	1	10	11	100	101	110	111	1000	...
Decimal	0	1	2	3	4	5	6	7	8	...

If one uses the symbols A and B, you can get:

Binary	A	B	BA	BB	BAA	BAB	BBA	BBB	BAAA	...
Decimal	0	1	2	3	4	5	6	7	8	...

Trinary, which uses three digits, is also possible:

Trinary	0	1	2	10	11	12	20	21	22	100	...
Decimal	0	1	2	3	4	5	6	7	8	9	...

These external websites may give you enough information to figure the place value idea of any number system.

1. ^ Numbers
2. ^ http://www.michielb.nl/maya/math.html