# Primary mathematics/Numbers
## Introducing Numbers

Numbers should be introduced as early as possible, as young students need to understand that numbers represent values. Both teachers and guardians should engage children in activities that connect numbers to real-life objects, allowing them to count and explore numbers through physical examples. Psychologically, this approach helps students recognize the practical applications of numbers in daily life. However, the formal concept of numbers should not be skipped; it should be taught alongside these practical activities to provide a well-rounded understanding.

## Developing a sound concept of numbers

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 concept of numbers and counting emerges 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 a firm foundation for the concept of number 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.

## Numbers 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
Children should be alerted to the use of numbers in a variety of contexts, prices, measurements of various types (eg. length, weight, volume), the speedometer in a car, labels on products, road signs, dates and time.
At this early stage of numeracy it is also helpful to introduce the idea of the relative size of numbers by asking what comes before or after, or what is a larger or smaller number. For example, a guessing game: the teacher thinks of a number between 1 and 10, the children try to guess the number. After each guess the teacher indicates whether the number is smaller or larger.
Other skills include learning to count to 20 or higher, and counting backwards.

## Place Value

The Next step is to learn the place value of numbers.
It is probably true that if you are reading this page you know that after 9 comes 10 (and you usually call it ten) but this would not be true if you would belong to another culture.
Take for example the Maya Culture where there are not the ten symbols above but twenty symbols.
Imagine that instead of using 10 symbols one uses only 2 symbols. For example 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 | ... |
Or if one uses the symbols A and B one gets:
| Binary | A | B | BA | BB | BAA | BAB | BBA | BBB | BAAA | ... |
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ... |
This may give you enough information to figure the place value idea of any number system.
For example what if you used 3 symbols instead of 2 (say 0,1,2).
| Trinary | 0 | 1 | 2 | 10 | 11 | 12 | 20 | 21 | 22 | 100 | ... |
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... |
If you're into computers, the HEXADECIMAL (Base 16) or Hex for short, number system will be of interest to you. This system uses 4 binary digits at a time to represent numbers from 0 to 15 (decimal).
This allows for a more convenient way to express numbers the way computers think - that we can understand. So now we need 16 symbols instead of 2, 3, or 10. So we use 0123456789ABCDEF.
| Binary | 0 | 1 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 | 10000 | ... |
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | ... |
| Hex | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | ... |