# Numbers and Arithmetic (Mathematics Curriculum)

# Numbers

## What Are Numbers?

Numbers are used to count. They are the first thing we learn in mathematics.

Numbers are represented by symbols called numerals: 1, 2, 3, 4, 5...

### Dictionary Definition

The Oxford English Dictionary defines a number as "an abstract entity representing a quantity, used to express how many things are being referred to, or how much there is of some thing."

Here are some examples of numbers.

## A History of Numbers

The earliest record of numbers are marks carved into bone and other objects, like this Ishango stick shown on the left.

These would have been very useful as an accounting tool. The trouble is, you need to make as many marks as there are objects to count.

The next breakthrough would have been using symbols (called numerals) to represent numbers.

Roman numerals were used in Europe.

The number **0** was introduced by the Indian mathematician Brahmagupta in 628AD.

Another innovation made in India was the use of place value. The same numeral in a different place can mean a new number: 10 and 100 are different numbers although they make use of the same numerals.

The Hindu numerals were brought, via the Arabs, into the West, where they were adopted. Our modern day numerals are descended from Hindu-Arabic numerals.

## Types of Numbers

There are different types of numbers: whole, positive and negative, odd and even, and many more.

In this mini-curriculum, you will learn about the types of numbers.

## Positive and Negative Numbers

Numbers can be positive and negative.

In this mini-curriculum, you will learn about positive and negative numbers and how to do arithmetic with negative numbers.

## Even and Odd Numbers

Numbers can be even and odd, depending on whether they can be divided by 2.

In this mini-curriculum, you will learn about even and odd numbers.

## Prime Numbers

Numbers are prime numbers if they can only be divided by 1 and themselves.

Otherwise they are composite numbers.

In this mini-curriculum, you will learn about prime and composite numbers.

## Square Numbers and the Square Root

Square numbers are the the result of multiplying a number by itself.

A square root is the number, which when multiplied itself, creates a square number.

In this mini-curriculum, you will learn about square numbers and square roots.

## The Number Line

A number line is a line where numbers are written in order, evenly spaced.

Number lines help us add and subtract numbers.

In this mini-curriculum, you will learn about number lines and how to use them.