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Numbers Curriculum

A List of Lessons in the Numbers Curriculum

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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.

numbers examples

A History of Numbers

numbers_ishango_bone 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.

numbers roman numerals 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.

numbers hindu arabic numerals

The Curriculum

The lessons are grouped into mini-curriculum to help you organise your learning. A brief description is given for each mini-curriculum. Click the MORE button to learn more.

Types of Numbers

numbers 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.

Types of Whole Numbers
The Number curriculum deals with whole numbers.
There are different types of whole numbers, depending on whether you include 0 and the negative numbers.
numbers types of whole numbers

Natural Numbers
A natural number is a whole number from 1 upwards. It is a counting number.
numbers natural number

Whole Numbers
The whole numbers are the numbers 0, 1, 2, 3...
numbers whole number

Integers
An integer is a whole number that may be positive, negative, or zero.
numbers integer

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the types of whole numbers
natural numbers
whole numbers
integers

Positive and Negative Numbers

numbers positive and negative

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.

Positive Numbers
A positive number is a number greater than zero.
numbers positive

Negative Numbers
A negative number is a number less than zero.
numbers negative

Arithmetic with Negative Numbers
Take extra care when doing arithmetic with negative numbers. Two negatives make a positive.

1 − −1 = 1 + 1 = 2
1 − × −1 = 1

Absolute Value
The absolute value of a number is the non-negative value of a number without regard to its sign. It is denoted by || either side of the number.
numbers absolute value

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positive numbers
negative numbers
arithmetic with negative numbers
absolute value

Even and Odd Numbers

numbers even and odd

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.

Even Numbers
An even number is a whole number that can be divided exactly by 2.
numbers even

Odd Numbers
An odd number is a whole number that cannot be divided exactly by 2.
numbers odd

Arithmetic with Even and Odd Numbers
Arithmetic with even and odd numbers follow predictable patterns.

even + even = even
even + odd = odd

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even numbers
odd numbers
arithmetic with even and odd numbers

Prime Numbers

numbers prime and composite

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.

Prime Numbers
A prime number is a number that can be divided by only itself and 1.
numbers prime

Composite Numbers
A composite number is a number that can be divided exactly by at least one number that is not itself or 1.
This means a composite number is any number (other that 1) that is not a prime number.
numbers composite

Fundamental Theorem of Arithmetic
The fundamental theorem of arithmetic states that any number is either a prime number or can be found by multiplying prime numbers together.
This means that any composite number can be written as a product of primes.
numbers fundamental theorem of arithmetic

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prime numbers
composite numbers
the fundamental theorem of arithmetic

Square Numbers and the Square Root

numbers square

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.

Square Numbers
A square number is a number that results from a number being multiplied by itself.
numbers square number

Square Root
The square root of a number, when multiplied by itself, gives that number. It is denoted by writing a √ symbol in front of a number.
The square root is the opposite of finding the square of a number.
numbers square root

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square numbers
square roots

The Number Line

numbers about 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.

Number Line
A number line is a line where every point corresponds to a number..
numbers number line

Add on a Number Line
A number line can be used to add numbers.
numbers number line add

Subtract on a Number Line
A number line can be used to subtract numbers.
numbers number line subtract

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the number line
how to add on a number line
how to subtract on a number line

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This page was written by Stephen Clarke.

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