# Primary mathematics/Numbers

## Contents

# Teaching Number

This page is for teachers or home-schoolers. It is about teaching the basic concepts and conventions of simple number.

## Developing a sound concept of number

Children typically learn about numbers at a very young age by learning the sequence of words, "one, two, threee, 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 number and counting emerges as their mistakes are corrected. However, here, at the very foundation of numerical concepts, the child is 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 childen 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.

## Number and Numerals

Teachers should print these numbers or show the children these numbers. Also, show the definitions of these numbers (using counters, eg. 1 apple, 2 apples, etc. Note that 0 means "no apples") This should take some time to learn thoroughly (depends 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.

It is probably true that if you are reading this page you know that after 9 come 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 | ... | |||||

Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ... |