**01 Whole Numbers**

Mathematics is more than numbers

It is within most things we do

So much more than adding or algebra

And knowing one and one is two.

It’s about the study of patterns

And the relationships that they contain

A fabulous body of knowledge

That is humanity’s great gain.

Mathematics is more than numbers

And over sixty centuries old

A story of ideas and thinking

Imagination and passions bold.

To do it, you must know its language

Symbols, definitions, and rules

It’s also worth learning times tables

They are useful, everyday tools.

Mathematics is more than numbers

It is the universe’s code

Seen in flowers, atoms, and galaxies

A logical, mystical ode.

Believe in yourself, you can do it

Have the right mindset, oh be involved

Some of the problems are a challenge

But your worries can be resolved.

Believe in yourself, you can do it

Have the right mindset, oh be involved

Some of the problems are a challenge

But your worries can be resolved.

Mathematics is more than numbers

And it can set your mind aflame

So answer questions, find the patterns

And play the mathematics game!

##### © 2016 M Murphy & H Prochazka

**02 Fractions**

The Egyptians invented fractions

For other than whole number actions

Fraction confusion is everywhere

But these numbers need not cause despair.

To add or subtract them

You must have the bottoms the same

And with a bit of multiplying

That becomes an easy aim

Fractions are simply parts of the whole

Mastering them is an achievable goal.

So take a chance and tackle fractions

Try these additions and subtractions

Some simple procedures are the key

To work with fractions confidently.

To multiply these numbers

Times the tops and the bottoms too

To divide, flipping the divisor

Is the correct thing to do

And where mixed numbers are concerned

Into improper fractions, they must be turned.

But if you still can’t deal with fractions

Calculators can do these actions

So just relax and press a few keys

Use their built in fraction expertise.

Fractions are simply parts of the whole

Mastering them is an achievable goal

Fractions are simply parts of the whole

Mastering them is an achievable goal.

©2016 M Murphy & H Prochazka

**03 Decimals**

Infinity is a powerful concept

That has puzzled many a mind

Think of it as the opposite of zero

But know that it is undefined.

In the beginning zero was a marker

That merely held an empty space

Then the Hindus made it a proper number

And gave zero its own place.

This made possible a new number system

Created by thinkers in the East

And later adopted by Baghdad scholars

Zero’s value had increased.

Every whole number could now be written

With the use of only ten digits

In positions that determined their value

This clearly had benefits.

The decimal point was a smart addition

And the system was now complete

Meaning parts of whole numbers could be written

So innovative and so neat.

Fibonacci championed these numerals

And in Europe a fight broke out

Saracen symbols versus Latin letters

A paper and abacus bout.

The new number system won the long battle

A maths invention to astound

This discovery now used around the world

So simple, so simple, so simple, yet so profound.

©2016 M Murphy & H Prochazka

**04 Geometry**

Geometry is physical and practical.

Seen in nature and man-made formations

Peacock feathers and flags of all nations

In diamond crystals and rare orchid blooms

City skyscrapers and new crescent moons

The geometric is really wonderful

Multi-faceted and many-dimensional.

Geometry is conceptual and logical.

Euclid’s “Elements” brought him much fame

This was mathematics as a mind game

Training intellects throughout the ages

We can read it now on internet pages

The geometric is truly provable

Multi-faceted and many-dimensional.

Geometry is spiritual and magical.

Mystical shapes made with circles and lines

Underpin many symbolic designs

Meaningful archetypes that resonate

And which sacred geometers contemplate

The geometric is inspirational

Multi-faceted and many-dimensional.

Geometry is so playful and beautiful.

Have fun with Platonic polyhedra

Or make stellated icosahedra

Delight in drawing tessellating art

And let symmetrical shapes shift your heart

The geometric is so sensational

Multi-faceted and many-dimensional.

©2016 M Murphy & H Prochazka

**05 Negative numbers**

Mathematics caters for society’s needs

Negative numbers were one such invention

An idea formed by creative minds

That solved a problem but caused contention.

When multiplying and dividing

There is no need to fuss

Two opposites make a minus

Two negatives make a plus

When adding and subtracting

Make paired signs a single sign

Then it’s easy to work it out

By using a number line.

Education responds to society’s needs

Such as the space race that caused much concern

Then real life skills and problem solving

Became the new maths for students to learn.

There are four problem solving steps

The first one is to ask

The questions that will determine

What is required by the task

Then decide upon a method

And a plan of what to do

Use it to find the solution

Check your answer and review.

Mathematics teaches deductive thinking

And solving problems is more than routine

You can invent your own approaches

Or use methods you have already seen.

©2016 M Murphy & H Prochazka

**06 Algebra**

First done in Babylonia

Later by Persians in Arabia

Algebra is about communication

Very elegant and very precise

With its own rules and conventions

And letters that make it concise

It’s a smart mathematical device.

With the pronumerals we operate

And maths ideas we can translate

Now that we have gotten that straight

To algebra we can relate.

Now “2b plus b” equals “3b”

And “2c plus c” is the same as “3c”

But “2b plus c” is not “3bc”

For “2b plus c” stays as “2b plus c”

Hopefully, you might soon agree

That algebra can be so easy!

Ladies once thought it fashionable

Entertaining and quite respectable

For algebra is about clarifying

And describing various relations

It is thinking and abstracting

Not just mere manipulations

And it has wide-ranging applications.

With the pronumerals we operate

And new equations we can create

For thoughts we want to illuminate

Our algebra is really great.

Now “b plus c” equals “c plus b”

But “b minus c” is not “c minus b”

And “b times 3” equals “3 times b”

But “b over 3” is not “3 over b”

Hopefully, you will now agree

That algebra can be so easy!

©2016 M Murphy & H Prochazka

**07 Powers & Roots**

Pythagoras is known for a theorem

Matters of music and the soul

He founded a fraternity

In which women could enrol

They learned philosophy and science

In his progressive mystery school

Students were called “mathematikoi”

And mathematics became their tool.

Number properties were reckoned

By these mathematical Greeks

They wondered about their qualities

For they were number theorist geeks

The feminine numbers were even

The masculine, indivisible by two

While the cubic and triangular

Were geometrically true.

The universe they sought to explain

With whole numbers to show the way

But a radical discovery

A square root that caused dismay

For this number was irrational

Unable to be fractionalised

And to their utter embarrassment

A new number had materialised.

The Hellenic ideas developed

Into modern exponent modes

Such as scientific notation

And the base of binary codes

That are used in digital photos

Or in producing a digital tune

A techno-mathematical leap

From the days of that Greek commune

From the days of that Greek commune

Pythagoras

Pythagoras

Pythagoras….

©2016 M Murphy, H Prochazka & A Jacobson

**08 Measurement**

During the French Revolution

Many mathematicians combined

To work out a measurement solution

And the metre was defined

Many countries later agreed

Seventeen of them signed a deed.

It’s such a clever metric system

And it’s based on powers of ten

For measuring all things on earth

Mathematics has done it again.

With kilo-, mega-, giga-, tera-

The unit sizes increase

With deci-, centi-, milli-, micro-

The unit sizes decrease

For any measurements big or small

Twenty prefixes handle them all.

It’s such an elegant metric system

And it’s based on powers of ten

For measuring the universe

Mathematics has done it again.

A kilo of water occupies a litre

A tonne takes up a metre cubed

One gram occupies a millilitre

Or a centimetre cubed

And a hundred metre sided square

Has an area of one hectare.

It’s such a marvellous metric system

And it’s based on powers of ten

For measuring things everyday

Mathematics has done it again.

It’s such a marvellous metric system

And it’s based on powers of ten

For measuring things everyday

Mathematics has done it again

Mathematics has done it again.

©2016 M Murphy & H Prochazka

**09 Percentages & Ratios**

A number has three equivalent forms

Percentage, fraction, and decimal

Divide or multiply by a hundred

For changing forms is arithmetical.

Percentages are central to finance

And with them you can compare

Sports scores and numerous other things

By transforming figures to make them fair.

The rules are quite easy to understand

And here are three facts to have on hand

A tenth or point one equals 10%

A fifth or point two equals 20%

And a half or point five equals 50%

Yeah a half or point five equals 50%.

There are two types of percentage problems

A fact worth taking into account

Changing from one form to another

Or finding a percentage of an amount.

The rules are quite easy to understand

And here are more facts to have on hand

To double, increase by a 100%

To triple, increase by 200%

To make it zero, decrease by a 100%

To make it zero, decrease by a 100%.

Ratios can be related to fractions

And with ratios you can compare

Quantities which are of the same kind

By transforming figures to make them fair.

And ratios in certain proportions

Can be found in nature’s curving lines

Golden shapes and the sounds of music

In company logos and sacred designs.

The rules are quite easy to understand

And here are three facts to have on hand

A tenth or point one equals 10%

A fifth or point two equals 20%

And a half or point five equals 50%

Oh, a half or point five equals 50%.

*(Un dixième ou point un est égal dix pour cent*

* Un cinquième ou point deux est égal vingt pour cent*

* Et un demi ou point cinq est égal cinquante pour cent*

* Et un demi ou point cinq est égal cinquante pour cent.)*

©2016 M Murphy & H Prochazka

**10 Areas & Volumes**

Get a sense of the formulaic

Formulas can show you the way

Written in letters algebraic

They are useful for us today.

For a rectangle or a triangle

Or a parallelogram case

We can formulate the area

Using height and length of base

But take care and be aware

That rounded shapes rely

On a radius and the number pi.

And pi is

3 point 1-4-1-5-9

2-6-5-3-5-8-9

On and on, endlessly

On and on, to infinity.

Formulas use symbols to summarise

The method that you might pursue

There are formulas you should memorise

And knowing them will help you.

For a cuboid or a cylinder

Indeed for any prism case

We can formulate the volume

Using height and area of base

But take care and be aware

That rounded shapes rely

On a radius and the number pi.

And pi is

3 point 1-4-1-5-9

2-6-5-3-5-8-9

On and on, endlessly

On and on, to

3 point 1-4-1-5-9

2-6-5-3-5-8-9

7-9-3-2-3-8-4-6-2-6-4-3-3-8-3

On and on, endlessly

On and on, to infinity.

Today computers fuel the races

To discover even more pi places

While all we need are three or four

Computers keep finding millions more

Millions more

Millions more!

©2016 M Murphy & H Prochazka

**11 Equations**

Mathematicians love to think

And to explore the world of the mind

Searching for beauty, pure or applied

Hoping for something new to find

Pure logic is their artistry

And equations are their poetry.

These thinkers write many equations

It’s essential for what they do

They set them up

They look at them

Sometimes they even solve them too.

Others also play in this mind world

Exploring with their patterning sense

Solving puzzles using imagination

Reason and life experience

Mathematics can make you feel glad

There is much enjoyment to be had.

School students solve many equations

Because their teachers want them to

Sometimes they sit

And just wonder

Exactly what they need to do.

First master the basic equations

The inverse undoes what’s been done

Always do the same thing to both sides

With balance, solutions are won

Learn the skills to find the unknown

Automate them and make them your own.

But equations aren’t always the answer

It’s good to think each problem through

Analyse the task

Seek different ways

There could be another avenue!

©2016 M Murphy & H Prochazka

**12 Pythagoras & Trigonometry**

A theorem is a mathematical truth

Irrefutable, permanent, and grand

A logical argument built step by step

To create a proof that will always stand

Pythagoras’ Theorem is the best-known one

Simple, intriguing, and with a touch of fun.

When using this famous triangle result

The basic strategy that maths provides

Is to identify the hypotenuse

Then go ahead and square all three sides.

Trigonometry deals with triangles too

And has numerous applications

Describing waves and making maps

And astronomical calculations

The hypotenuse, opposite, and the adjacent

Define the sine, cosine, and the tangent.

When doing a trigonometric task

The basic strategy that maths provides

Is to identify the hypotenuse

Then make a fraction with two of the sides.

Now to decide how to solve a right triangle

This is how to tackle the problem

If working with just the three sides

Then go with the Pythagorean theorem

But if working with two sides and one angle

Then trigonometry will the task untangle.

When using this famous triangle result

The basic strategy that maths provides

Is to identify the hypotenuse

Then go ahead and square all three sides.

©2016 M Murphy & H Prochazka

**13 Graphs & Relationships**

With just two numbers, it is well known

Positions of points can be shown

Placed inside brackets

To make little packets

Descartes’ coordinate zone.

We can describe a position

With just an “x” and a “y”

On only these two letters

We can rely.

Two coordinates can condense

Patterns in a number sequence

Turning the numeric

To nice algebraic

With rules of precise eloquence.

We can describe a pattern

With just an “x” and a “y”

On only these two letters

We can rely.

For lines that are drawn on a plane

Two pronumerals do it again

Straight or parabolic

Even hyperbolic

Using equations that explain.

We can describe a line

With just an “x” and a “y”

On only these two letters

We can rely.

They are used for animations

Video games and simulations

Fractal mathematics

In vector graphics

And modelling applications.

©2016 M Murphy & H Prochazka

**14 Chance & Data**

Mathematics has practical concepts

Such as median, mode, and mean

Averages that can lead us

Through an overwhelming data scene.

For to deal with chance and to manage risks

We need to understand statistics

And the laws of probability

Then we can see through a statistics lie

Decoding the numbers and the details

To find the truth that they imply.

And mathematics is the foundation

Of most things we do and see

For so much of modern life

It is the secret, it holds the key.

Mathematics is always there for us

This branch of knowledge, so fabulous

Helping predict and determine trends

Explaining and showing us what is real

And guiding us to make good decisions

Based on what the figures reveal.

But it is much more than number crunching

Calculating is not the goal

It is about brain training

While satisfying heart and soul.

You might even have a subtle feeling

Of something that could be appealing

Maybe mathematics is divine

It is mysterious and so immense

With harmony, order, and symmetry

Resonating with some inner sense.

Mathematics is much more than numbers

Come walk this wonderful road

Of beauty, ideas, and logic

That is the universe’s code.

©2016 M Murphy & H Prochazka