Teach Number Mandala with Cyclic Addition Mathematics

8/20/2019 Teach Number Mandala with Cyclic Addition Mathematics

1/245

By Jeff Parker

13

2

6

4

5

5

15

10

30

20

25

4

12

8

24

16

20

6

18

12

36

24

30

3

9

6

18

12

15

2

6

4

12

8

10

7

21

14

42

28

35


2/245

Teach Number Mandala

with Cyclic Addition Mathematics

© Copyright 2015 Jeff Parker


3/245

Contents

Introduction … 5Create Number Mandala… 9

Sphere #7 Teach Number Mandala… 11

Problems with Current-Day Number

Solutions using Cyclic Addition Mathematics

Cyclic Addition as a Complete Number System

Cyclic Addition ToolKit

Cyclic Addition Laws on 5 Steps and Cylinder

A Teacher’s Study of the Sphere’s #1 to #6

The Role of Circle with Number Mandala

Advantages and Improvements to plain ‘ol Number

Teaching, Learning and Curriculum for Cyclic Addition Mathematics

A pretend story of Cyclic Addition and Current-Day Number Teach Sphere #1 to Sphere #6

Sphere #1 The Book of Wheels… 61

Wheels Reference Page with Common Multiple 1 to 7

Rational Number

Pure Circular Fractions

Exponentials

Match Whole Number to Pure Circular FractionsWheels

Sphere #2 The Wheels within the Wheel … 96Object Count

Mini-Wheels onto NumberGridsJourney from Current-Day Base 10 Number to Cyclic Addition Number

721

14

42

28

35

1

3

2

6

4

5 69207

138

414

276

345


4/245

Contents cont…

Sphere #3 The Creation of a Whole Number… 112

Cyclic Addition 5 StepsStep 1: Counting

Step 2: Place Value

Step 3: Move Tens

Step 4: Remainder

Step 5: 7×Multiple

How Circle completes Whole Number

Sphere #4 The Count Sequence… 165

The Role of Count Sequence with Cylinder

Count Spacing with Wheel and Cycle

Remainder Pattern with Count Cycle and Cylinder Fibonacci Number together with Cyclic Addition

Cylinder with Common Multiple 7

Sphere #5 The Cylinder… 183

Shape, Structure and Design…

Cylinder with Common Multiple 1, 49 and 343

Patterns with Remainder and Cylinder

Cylinder Hierarchy and Tier Unity

Sphere #6 Patterns with Number, Circle and Common Multiple… 206

A Beginning for Number 1 to 7Completion with Units 9

Hexagon PatternsMisinterpreting Number 533 and proving Number true

Reference Page with Common Multiple, Wheel and Tier

Practical Tiers 1, 2, 3 and 4 with 1 Cycle on the Cylinder for

Common Multiple 2, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21 and 23

7

21

14

42

28

35

13

2

6

4

569

207

138

414

276

345


5/245

5

Introduction of ‘Teach Number Mandala with Cyclic Addition’

What is a Mandala ? Mandala is a Sanskrit word meaning “Circle” and is a spiritual and ritual

symbol, in Eastern Religion, representing the Universe. Following mystical and spiritual

traditions, Mandalas are used to focus attention and as a spiritual guidance tool, and to create

a sacred space and as an aid to meditation.

Today, Mandalas have become more common describing Circular diagrams, charts or

geometric Patterns that represent the cosmos metaphysically or symbolically.

There are many Mandala pictures or images on the internet. Showing the beauty and harmony

with varied types of Circular Patterns. Children’s colouring in books could be filled with

Mandalas showing infinite possibilities for the Circle.

Circle can be of many forms. Both natural and personmade. Like flowers, a water droplet into

a pond, a tree trunk, hexagonal crystals, a candle flame, a soap bubble and the equator around

the Earth. In the material realm Circle is often found. Like a car or bicycle tyre, a bowl, a

plate, a CD or DVD, an electrical globe or chandelier or lampshade with cone, a button, a fan,

most power plugs, a cap or hat, a cup with cylinder and sphere, a coaster, a compass, a bottle

lid, a bangle, a clock or analogue watch face, a pen or texta with cylinder again, a volume

control and relevant to this book is the Cyclic Addition mathematical ‘Cylinder’.

This book delves into a universe of Circular Number, thus the title “The Number Mandala”.

Showing natural Laws and Patterns that last forever no matter where you are in the cosmos.

Practically speaking, coming down to earth, there are significant discoveries of Number

shared in the following pages. Proving the home of our 1400 year old Number is with Circle.All types of Number – Whole or Natural, Rational, Exponential, Fibonacci all show their best

and original form with Circle. Number within Circle allows exploration into all mysteries and

patterns possible. There by firing up a child’s or young adult’s creative awe and wonder, to

follow the paths of ancients, and to show a genuine curiosity for such a subject as Number.

Cyclic Addition is the Mathematical pathway and framework used to communicate the

Number Mandala. Cyclic Addition has 5 books on Google Play. Each of these show a unique

facet of Number. As this book is a ‘complete’ work on Number it draws upon all of these 5

books. Let’s brief each of these books.

The first book “Wheels” discovered around 2002 shows Circles of 6 Numbers. Each Wheelhas a hierarchy of Tiers. Each Wheel belongs to a Common Multiple. These Wheels connect

to Exponentials and Rational Number with Mathematics. The Wheel is the foundation of

Cyclic Addition Number. All Mathematics stems from the Wheel’s Number and Circle.

The second book “A New Invention: Cyclic Addition Mathematics that repairs and perfects

An old Invention: Number” presents a reference book of Cyclic Addition. The Mathematics

of Cyclic Addition is called the 5 Steps –

Step 1: Counting

Step 2: Place Value

Step 3: Move Tens to Units

Step 4: Remainder Step 5: 7×Multiple.


6/245

6

All of which act with the Wheel. To place a framework of Mathematical nature around these

5 Steps the ToolKit was invented as well. There are 7 facets of the ToolKit – Wheel,

Sequence, Operation +× ̶ ÷, Pattern, Circle, Common Multiple and Cylinder. All of these act

in part or whole with the Wheel to perform each Mathematical Step.

This book “A New Invention: Cyclic Addition” was made in 2012–2013. Showing the nutsand bolts of the Mathematics to master Cyclic Addition. There are early mapping techniques

to navigate with Wheels of the hierarchy. This mapping began the tireless search for order

and form of Number. Constantly striving to find beauty, perfection and natural Law from

Number and with Number. Also the influence and Maths from Rational Number. These are

termed Pure Circular Fractions. Pure as only 1 number creates the whole fraction and

Circular because all of the generated sequences are a perfect Circle of Number.

A New Invention gives a place to 4 types of Number – Whole, Rational, Exponential and

Fibonacci. These 4 types are woven together with Mathematics. As the high order of this new

invention: Cyclic Addition commands an overall authority with Number by its unity and

perfection of all 4 types. The exploration into Whole Number serves Mathematics of theother types of Number.

Right in the middle of Cyclic Addition 5 Steps there was the need to stop and search for other

Mathematics surrounding the Count Sequence. These were eventually called ‘A Collection of

Emphasis’. An example is how the Count Sequence serves the next higher Tier 7×Multiple.

This was the beginning of the modern Tool termed ‘Cylinder’. Without this preparation in A

New Invention: Cyclic Addition perfect Number from the Cylinder may well have been

overlooked. There are subtle vibrations of perfect Mathematics that crop up and one is

required to fit them into the big picture. Such is the ‘completeness’ of Cyclic Addition.

The Third Book “A Prophetic Design for Number from Cyclic Addition Mathematics” is a

contrast between the ‘current-day’ Number and Cyclic Addition Number. There are 12 topics

in the book that show dangers in the current-day use of Number. The book looks at the basic

fundamental Base 10 Place Value System in use. The whole system relies on fragile beliefs of

Number that have persisted over centuries. These beliefs are questioned with Mathematics

rather than lengthy discourses of argument and meaningless debate.

There is a brief look at the current-day teaching of the Mathematics Number Strand for

Primary years. This at first may seem irrelevant, however to forge a new Number System

from scratch requires a detailed examination of current-day techniques used to prop up the

existing System.

Cyclic Addition answers in this book most of the big questions that determine how Number is

translated into the school or workplace. For example ‘Is Number merely 10 symbols smashed

together side by side to form Number ?’ big questions, right at the very heart of how we

interpret Number. This book A Prophetic Design as the title says is the way forward for

Number to remain with mathematical qualities. The future of mathematical Number requires

all of the Mathematics of Cyclic Addition Number.

The Fourth book “The Complete Mathematics of the Cyclic Addition Cylinder” looks solely

at the completely numerical ‘Cylinder’. This book was also the first year of the ToolKit:

‘Cylinder’. From its numerical perfection and mathematical Mandala the Cylinder was madethis year, 2015, into a small 67 page book in its own right. Showing how to map any Count


7/245

7

Sequence spiralling around the Cylinder. Perfecting the Common Multiple and Tier by

concentrating energy of one Common Multiple and one Tier on one Cylinder at a time. The

Patterns show how the Cylinder submits all Counts to the next Tier 7×Multiple.

The Cylinder is an amazing feat of mathematical engineering. Bringing together all the

Mathematics of Cyclic Addition 5 Steps into a glorious spiralled array of Number. Thismeshing of Counts all the way down the Cylinder makes for a strong Reference Tool that can

be used anytime. Proving all possible Patterns and Mathematics for a Common Multiple.

The Pattern Making with Number on a Cylinder is without equal. Literally this is the pinnacle

of Mathematics with Whole Number. Nothing else can stand side by side and offer the unity

and perfection and teaching of Whole Number amongst all Number.

Mathematical Laws guide and steer a direction amongst a sea of Number, aid navigation with

the ToolKit and the Cyclic Addition 5 Steps, invite exploration of Patterns freely without any

barrier. To benefit those who climb higher to see further with practical Number. This

pathway of Laws prevents getting lost or drifting aimlessly around the Cylinder.

The Fifth Book “Cylinder PDF’s” is found on Google Play Books and on the CD-Rom in a

user friendly form. All possible and perfect Cylinders for the first 5 Tiers of the Cyclic

Addition Hierarchy are presented. This is to allow an infinite exploration into the Cyclic

Addition Cylinder. There is no limit to the Cyclic Addition Hierarchy. One can even create

your own Cylinder for higher Tiers.

Thus we return to this book “The Number Mandala with Cyclic Addition”. The major

emphasis is ‘The Circle’ and its complete encompassing nature with Whole Number. The

Number Mandala begins with the Cyclic Addition Wheel. From where Cyclic Addition

began. Proving all Number evolves from Circle.

This book is the first study of Number and Circle. Consequently the mathematician strives for

order, form, creation, perfection, and harmony with previous works of Cyclic Addition. Like

the recent Cylinder book broke new ground with Mathematics of Cyclic Addition, so too the

Number Mandala binds the Circle with Number forever.

In amongst the perfection of Number and Circle forming this text ‘The Number Mandala’ is

the great and momentous task of improving the original invention of ‘Number’. The first 5

text iterated above show this and this text brings to light all Cyclic Addition knowledge

within a view of the limitless Circle.

Here are some of these improvements to plain ‘ol historical Number.

Strengthen Place Value positions of a Number.

Strengthen sequence of Numerals forming a Number.

Unify Operations +× ̶ ÷ with Number.

Bring together an ordered collection of Number on a Cylinder for Mathematics.

Unify knowledge of a Common Multiple and Hierarchy with this Cylinder of Number.

Discover infinite Pattern making and Order to Whole Number, Rational Number, Exponential

Number and Fibonacci Number.

Bring Number together with the geometry of Circle and Spiral.

Improve the original invention whilst maintaining existing order of Whole Number.Lay a Mathematical foundation to broaden the strand of Number in school/college.


8/245

8

The Number Mandala is a Mathematical picture of Cyclic Addition. Each Sphere #1 to #7 is

with a collection of illustrations. These are labelled as “Sphere #1A” where the #1 is the

Sphere chapter and the A to Z is the ordered page by page collection of diagrams.

This book is a little experimental. Where the three previous books of “A New Invention”, “A

Prophetic Design” and “The Complete Mathematics of the Cyclic Addition Cylinder” weretargeted to show an aspect of Cyclic Addition. This book “The Number Mandala” asks the

mathematician to recreate their world of Whole Number, Rational Number, Exponential

Number and Fibonacci Number. This journey searches for a path of discovery and

exploration into Number Mandala.

There are many pages of illustrations thrown in to create a ‘Whole’ aspect of Cyclic

Addition, possibly unseen by the approach of the above three text. The author this time, in the

Number Mandala, puts English second to the Mathematics. Allowing the Teacher, Student or

interested budding mathematician, to discover for themselves how perfect and awesome these

Natural Laws to Number are.

Often the illustrations prove the Circle and Cyclic Addition Mathematics as being simple yet

all encompassing. Finally Laws on how Number works amongst all Number has a benchmark

of “the Number Mandala” and the CD-Rom with other texts and practicals.

All along the journey one might question: Why have this Cyclic Addition discovery now

rather than several hundred years ago ? Is not it easier to incorporate Mathematics of

centuries ago into a curriculum for school to teach ? This puzzle of purity and perfection is

left to the reader of “the Number Mandala”.

This is the first work of Mathematics proving Number and Circle are one. Thus the author

asks all to create along with this text. All new all fascinating Mathematics aimed at

expressing all inter-relationships of any Number with all Number. Thus each participant in

this Cyclic Addition Mathematics can do anything with these Natural Numerical Laws !

A Quote from Carl Friedrich Gauss:

“Mathematics is the queen of the sciences and number theory is the queen of mathematics.”

A quote from the author:“To bring Number and Circle together with Mathematics is like two facets shining light uponeach other”

A little History of our Hindu-Arabic Number

Leonardo of Pisa, commonly known as Fibonacci, wrote ‘Liber Abaci’ in 1202. This book

was to be a milestone and a reference point for our modern day Hindu-Arabic Numerals.

From this point onward, and a battle over the next 300 years+, the ten numerals (0, 1, 2, 3, 4,

5, 6, 7, 8, 9) and the way Fibonacci wrote about them were to be received by the Commercial

and Schooling World of the Day. There ease of use, efficiency and mathematical perfection,

over particularly the Roman Numerals and worded numerals, was to win the day, eventually,

across the known world right through to the Renaissance Era. Many Schools trained students

in the Italy of the Day using Leonardo’s mathematics. There were over a thousand books

written like his book over the next 300 years+. Thus this is marked as a historical moment for

our modern day Number. An ounce of history and man’s reaction to change, illumes lightupon problems of the day, to enable us to receive a kilogram of future.


9/245

9

Create Number Mandala

Let’s consider the Number Mandala on multiple spheres of Cyclic Addition Mathematics. No

matter the direction of viewpoint onto a sphere a Circle is always seen.

The first sphere is the book of Wheels which covers all Common Multiples. Showing theCircular nature of the whole Reference Page. Circular Pure Circular Fraction 69 Sequence,

Circular Exponentials and corresponding Circular Wheels. Also Rational Number and how to

link Whole Number with Pure Circular Fractions. The two are inextricably joined together

with equality numeral by numeral. And the small relevance of other Remainder Sequences.

The second sphere is the wheels within the Wheel. By chopping up the Wheel ‘1 3 2 6 4 5’

into 60 mini-wheels we receive the simple basics of Cyclic Addition. There is even an early

learning Object Count preserving the Circle, Sequence, Object and Number with Count.

Progressing to a standard NumberGrid for each Common Multiple focuses learning. A simple

believable pathway to join Base 10 Number to Cyclic Addition Number. Thus forming the

Cyclic Addition Wheel from ‘current-day’ Number.

The third sphere is the creation of a Whole Number from the 6 Number Wheel and the Cyclic

Addition 5 Steps. All 5 Steps: Count, Place Value, Move Tens, Remainder and 7×Multiple

utilise the Circle of the Wheel. This is the heart of Cyclic Addition presenting each Number

to a higher Order of the same Common Multiple. Each Step, in sequence, applies a

Mathematical Order to a Count. Yielding a place, position and Order for all Whole Number.

Each of the 5 Steps improve ones knowledge of Place Value positions on a Number. Each of

the 5 Steps is with Circle. Each of the 5 Steps is with Sequence of Number and Numeral.

Each Count has a Remainder to link it to the next higher Tier Order. Learning these 5 Steps,with practise, one acquires perfect Whole Number. Many illustrations detail these 5 Steps.

The fourth sphere is the Count Sequence. The previous Sphere generates a continuous Count

Sequence. This Count Sequence increments by the Circling Wheel. The next Sphere joins the

Mathematics of all possible Count Sequence with a Wheel together. Thus this Sphere

emphasises the relevance of the single Count Sequence. Each Sequence is roughly 1 to 7

Cycles long. Each Cycle is a complete Circle around the Wheel. To navigate with Whole

Number is to steer along the Count Sequence to discover Whole Number and a Common

Multiple. The Fibonacci Sequence of Number connects to Pure Circular Fractions. This

ancient Sequence shows its relevance to Whole Number Cyclic Addition Mathematics.

The fifth sphere is the Cylinder . Each Cylinder is Circular by its mathematical shape. All

Counts belonging to a Wheel, for Tier 1 Cylinders, are presented on one Circular Cylinder.

All Count Sequences Spiral down and around the Circular Cylinder. Forming Complete

knowledge about the Common Multiple. There are Circular Patterns of Remainder that bind

the Spiral Count Sequences all the way down the Cylinder. These Circular or Ring Patterns

equal the 6 Number Wheel. Thus the Circle of the Cylinder submits all Counts in return to the

Counting Wheel.

Amongst all Counts on a Cylinder are end of Cycle 7×Multiple. These are always found

united together on the same Ring or Circle of the Cylinder. This shows the nexus of actual

Counts on the Cylinder with the next higher Tier Wheel. The Cylinder(s) orchestrated by thehigher Tier Wheel show these 7×Multiple from the lower Tier Wheel with higher Order.


10/245

10

The Cylinder has a Hierarchy that follows the Wheel Common Multiple. The lower Tier

connects to the next higher Tier with all Counts via the 7×Multiple. All 7×Multiple are

shown upon the higher Tier Cylinder. Tier 2 and above have 4 Cylinders to present a Tier 2

and above Wheel. All Cylinders of the hierarchy share the same Common Multiple. Each

successive Tier put the lower Tier to a higher Order. Across all 4 Cylinders for a certain

Common Multiple there are Circular Patterns of equality that link all 4 Cylinders together.

The sixth Sphere is Patterns with Whole Number . Beginning with perfecting Place Values by

Completion of a Number with a Common Multiple units 9. This improves ones Place Value

position movement within a Whole Number. A great and simple resource. This Sphere

follows the previous Cylinder Pattern and looks at entirely a Common Multiple and Count

Pattern. Each Common Multiple illustration, generously sampled from the 69 Common

Multiples present how to navigate and search for Patterns within a Whole Number. There is a

mystical, strange and yet to be explored way of reading a Common Multiple ̶ this Sphere

starts that exploration.

This Sphere shows the Wheel and corresponding Cylinder present Circular Patternscompletely. Every mathematical action forming a Pattern with the Wheel and the Cylinder is

proved to be Circular. Thus mastering Cyclic Addition Mathematics one must see the Circle

and Number as One Whole.

The seventh Sphere is Teaching and Learning Cyclic Addition. This is split into 3 stages.

The first stage is Current-Day Base 10 Place Value Number. What it is and how it works

today. Looking at Whole Number and a snapshot of its problems and weaknesses. The

Design and how its taught. The role the Zero plays in Base 10 Number. Place Value Names.

Older style arithmetic. Lack of Order, Law and Form. Using Number as 10 symbols rather

than scaled Whole Number.

The second stage is Cyclic Addition as a Complete Number System. Presented as a collection

of solutions to the inadequacies of Current Day Base 10 Place Value Number. Incorporating

the previous chapters Sphere #1 to Sphere #6 to solve these problems. Sub-Topics include

Properties of a Number System. Major Cyclic Addition Laws in brief. Operations +× ̶ ÷ and

order. Scale of Number from a Cylinder. The role of Circle within Number Mandala.

Patterns, multiples and factors with Whole Number. Creativity and purpose with Cyclic

Addition. Uniting Rational, Whole and Exponential Numbers. Advantages and improvements

to plain ‘ol Number.

The third stage is a Method and Sequence to Teach and Learn Cyclic Addition Mathematics.

How Cyclic Addition can sit alongside of the existing ‘Current-Day’ Number. How the two

can coexist. Teaching the components of Cyclic Addition with interactive tools. Teaching the

5 Steps in Sphere #3. Teaching Common Multiple and higher Tiers. Teaching the wow and

fun with the mathematical Cylinder. A Top helicopter View to simplify Cyclic Addition.

The seventh Sphere is taught at the beginning of this book, rather than the end. The main

reason is so Teachers are able to question and search for there own answers to ‘deciding how

to Teach Number ?’ The Number Mandala is new to many, thus one requires proof, scientific

proof, that this work of Number Mandala with its knowledge, wisdom and practical

application is eventually included in a School Curriculum.


11/245

11

Sphere #7 Teach Number Mandala

The seventh Sphere is Teaching and Learning Cyclic Addition. This is split into 3 stages.

The first stage is Current-Day Base 10 Place Value Number. What it is and how it works

today. Looking at Whole Number and a snapshot of its pr oblems and weaknesses. TheDesign and how its taught. The role the Zero plays in Base 10 Number. Place Value Names.

Older style arithmetic. Lack of Order, Law and Form. Using Number as 10 symbols rather

than scaled Whole Number.

Current-Day Base 10 Place Value Number

Number is formed from 10 universal Numerals. These were established hundreds of years

ago. These numerals (1, 2, 3, 4, 5, 6, 7, 8, 9, 0) are put into an order and sequence to make a

Number. This Sequence joins numeral running together forming a Number, usually read and

written from left to right. For example a three digit Number using just ‘1’, ‘2’ and ‘3’ once

presents ‘123’, ‘132’, ‘213’, ‘231’, ‘312’, and ‘321’. Six different 3 digit Numbers in any

order, all still make a Number.

Each of these 6 numbers using a 1, 2 and 3 numerals form a unique Number. This uniqueness

is from each Number’s Place Value positions within a Number. For example Place Value

Notation says 123=100+20+3= (1×102 )+(2×101 )+(3×100 )=123 each numeral has a base 10

assignment. These powers or exponentials of 10n × numeral in that space signify the value of

the numeral. All the numerals are in essence, applying simple Addition to each numeral×10n ,

join to form the Number 123. In fact Current-Day Number can be taught in this fashion for

any Number.

These successive numerals, from right to left, increasing in powers of 10 have simple Names.

100 =1 units, 101 =10 Tens, 102 =100 Hundreds, 103 =1000 Thousands, 104 =10000 TenThousands and so on right up to gigantic Number of 10100 =1 with a hundred zeros called a

Googol. Normally these Names are grouped into 103n or three zeros.

From Sphere #2F the Top Table shows four rows. If one picks at most 1 number from each

row one can form the base 10 structure of a Number. For example 1+20+300+4000=4,321.

Any 4 digit or 4 numeral Number from 1 to 9,999 can be formed. Taught up to year 4+.

This Table shows all possible Base 10 Number needed to form any 4 digit Number. Step back

and just notice the dominance of the Zero in the Table. There is a burdensome and heavy

reliance on the Zero to communicate a 4 digit Number.

Number, at school, is taught with groupings for small 1, 2 and 3 digit Number. These

groupings put units from a choice of 1 to 9 or 0 in a column, then longs or Tens from a choice

of 10 to 90 in a column and then flats or grids 10×10 Hundreds from a choice of 100 to 900

or omitting the column all together. This pictorial relationship of cubes, longs and flats or

other diagrammatic forms of 1’s, 10’s and 100’s establish an early learning form of any three

digit or 3 numeral Number.

Is it fair to say that there is a concentration of teaching effort on what is a (3 digit) Number

rather than Mathematics to connect all the (3 digit) Number. So learning becomes a statement

of singular Picture, Word and Numerals to form a Number. Addition is taught later rather

than with two Number forming a third Number.


12/245

12

Number is taught to grasp these numerals from 1 to 9 and then trading (carrying) 10 of a

numeral for 1 of the next numeral left. This barter system of trading (carrying) is essentially

the real glue that sticks all the numerals together. Before our base 10 example above.

Number is taught with a count to 100. Utilizing a 10×10 grid for just about any mathematical Number is a standard we live by. Counting by 1’s from left to right along the Grid reaching

the next Ten and starting from the next row at 11 progressing by 1’s to 20 and the next row

from 21 to 30 and so on. In fact there is a dominant Pattern of +1 across the Grid and +10

down the Grid. Many other Patterns rely on this Grid for example teaching Step Counting by

1’s, 2’s, 5’s and 10’s.

If one teaches a Number, like our example numerals 1, 2 and 3 above how does the child or

teacher differentiate between the 6 possible Numbers. By Picture and cubes, longs and flats

other than that one requires Mathematics. And the 100 Grid is too small.

If one teaches 4 digit Number like our table in Sphere #2F one reverts back to 1 to 9 with theapplicable number of Zeros. Thus Counting from 1 to 10 is performed over and over for each

numeral from right (units) to left (tens, hundreds and thousands). This develops a scale or

magnitude of Number from 1 to 10 ×10n where n is from 0 to 3, from units to thousands.

Little else is gained by repeatedly performing Number creation from the Base 10 Table.

Thus Mathematics is required to transcend this Base 10 reliance and begin association of

Number with Number using our familiar Operations +× ̶ ÷. Number as taught with Cyclic

Addition heavily relies on the Operations +× ̶ ÷ in Order and following simple Laws.

Number, later, is brought together with Addition and Multiplication. In fact Number

Sentences are formed to enable the Operations +× ̶ ÷ to be fully understood rather than their

effect upon Number. For example Repeated Addition 3+3+3+3=12 or 4 lots of 3 or the

‘equation’ 4×3=12. The relationship between Addition and Subtraction is brought together.

For example 4+3=7, 3+4=7, 7 ̶ 4=3, 7 ̶ 3=4 from one number sentence others are formed.

Simple Number Multiplication is introduced with qualities of the 0 and 1 upon the Operations

+× ̶ ÷. 5×1=1×5=5, 4+1=1+4=5, 5×0=0×5=0, 4+0=0+4=4 and so on to inculcate the

intricacies of Number, numeral and Operations. This, later, becomes commutative and

associative Laws which may take preference over Number, Pattern and Operations +× ̶ ÷ .

Cyclic Addition quickly establishes simple diagrammatic Number and continuous Pattern and

Operation to allows speedy mastery for small 1 to 3 digit Number.

The Whole Number journey right through Years 1 to 7 uses Base 10 Place Value Number as

a fall-back to misunderstanding or misinterpretation of a Number. The Addition Algorithms

of the trading (carrying) 10 units for 1 ten continues and remains the basis for Adult Number.

If Number is too large to manually calculate on paper, the Calculator takes over the labour

and mathematics of Adding two numbers together. After all that investment in Primary Years

with Base 10 Place value Number one is encouraged to replace most of there numerical skills

with an automated approach to the Calculator.

Very rarely, surprisingly, Counting Number (or Whole Number) is shown against adescription of Counting something. Varying in magnitude, some hundreds, some thousands


13/245

13

and even some millions, showing children a sense of real world proportion and scale with

Counting Number.

Number is hammered against itself with terminology and symbol rather than Number with

Pattern and creativity. For example ascending and descending choices. Also greater than and

less than comparisons. These tug of war exercises with Number prevail right up to 5, 6 and 7numeral Number or up to millions.

Number Sequences are shown with 3 numbers with a Pattern followed by 3 blanks to fill in.

Only a 6 number sentence in all. These sequences concentrate on shifting a numeral in a

place value up or down by 1, 2 or 5. So a complex 6 digit number might increase by 5 tens

and the pattern follows. Again asking a child to unravel their learning from the 100 Grid

taught years ago to follow Number up or down, which way is of no concern. Cyclic Addition

can be considered the perfect way to investigate and learn about Patterns with just Number.

Rounding off of other Numerals to zeros. For example Round to the nearest million, ten

thousand, hundred and so on. This abbreviation of mathematical Number allows for faster communication of Number. For example 3 579 246 = 3.6 million (3 600 000). Note all the

effort of operational mathematics with Number is partially destroyed for Zero base 10

representation of a Whole Number. We conclude that the mathematics to reach that 7 digit

Number is questionably unable to be supported by ‘Current-Day Base 10 Place Value

Number’. Having to reach for a mathematical tool that destroys the effort of creating the

Number in the first place. Cyclic Addition makes no use or rounding as any length Number,

with practise, is made perfect.

Exponentials of 10 are mixed with Number Sequences to move a decimal point from left to

right making a bigger and bigger Number. Base 10 exponentiation is the primary tool to

interrelate numeral forming number.

A History and introduction to other Number Systems. Like Roman Numerals, Binary Base 2

System, Counting in Chinese, Codes and even Ancient Egyptian. These number systems

show just how easy it is to perform speedy Operations + × ÷ even by hand. And how the

side by side numerals forming a Number is very compact and efficient even for large

Number. Allowing us to use Number for a myriad of things. History showed for hundreds of

years a reluctance and resistance to fully celebrating our 10 Hindu-Arabic Numerals.

The foundation of the Hindu-Arabic Number system is based on Place Value. The way it’s

taught is basically repetition of Base 10 numeral aside numeral mathematics. There is very

little evidence, up until now, to show that Whole Number can be simply given to just Number and Mathematics. Although large Number like phone number, credit card number and

product codes are used solely with just numerals. Mathematics with these numbers is thrown

out the window and replaced with 10 logical symbols.

The Current Day Mathematics thus shows little else to rely on gluing the Numerals of a

Number. Thus our Adult Number, our Teaching Number and our communicating Number is

stuck in this norm. Cyclic Addition: A New Invention asks “to repair and perfect, preserve

and protect our Old Invention: Number”. A title of a previous Cyclic Addition text.

Thus there are no illustrations on Current Day Base 10 Place Value Number. Any modern

Australian Mathematics Text Book or Workbook for Primary and Secondary Years showhow Number is taught and learnt.


14/245

14

Searching for parallel teaching between Number Mandala and Current Day Base 10 Place

Value Number is left to the third stage of this Chapter. Be especially vigilant in your search

for how Current Day Number expresses Pattern with Number, Laws of Number, and a

Wholeness to Number. Search far and wide for an overall repetition of teaching that ‘seems

to’ constantly destroy previous work to create new work. This skill in teaching a subject

whole to interconnect all topics perfectly is a masterful Curriculum. The Number Mandala is just a small, significant and mandatory component of Mathematics.

The second stage is Cyclic Addition as a Complete Number System. Presented as a collection

of solutions to the inadequacies of Current Day Base 10 Place Value Number. Incorporating

the previous chapters Sphere #1 to Sphere #6 to solve these problems. Sub-Topics include

Properties of a Number System. The Cyclic Addition ToolKit. Major Cyclic Addition Laws

in brief. Operations +× ̶ ÷ and order. Scale of Number from a Cylinder. The role of Circle

within Number Mandala. Patterns, multiples and factors with Whole Number. Creativity and

purpose with Cyclic Addition. Uniting Rational, Whole and Exponential Numbers.

Advantages and improvements to plain ‘ol Number.

The Solution: Cyclic Addition as a Complete Number System

What are the properties of a Complete Number System with Cyclic Addition ? Cyclic

Addition preserves all existing qualities of our Current Day Base 10 Place Value Number.

Although Cyclic Addition may not use 1,234=1000+200+30+4= (1×103)+ (2×102)+ (3×101)+

(4×100)=1,234 the base 10 Zero in the same way, one can still navigate learning from the

‘Current Day’ Number to Cyclic Addition (Place Value) Number by applying existing

teaching methods. Cyclic Addition uses the exact same 10 numerals (1, 2, 3, 4, 5, 6, 7, 8, 9,

0) as does ‘Current-Day’. Cyclic Addition also perfectly preserves Operations +× ̶ ÷. Again

Cyclic Addition has Laws and a Sequence to follow with Operations +× ̶ ÷ however this can

be accomplished with ‘Current Day’ teaching methods. Current Day trading (or carrying) 10

ones for 1 ten is shown in many ways with Cyclic Addition. Current Day word names for a

Number are still applied to Cyclic Addition Number, there is again a transition of

Mathematics with Number that supersedes Current Day weaknesses. Cyclic Addition also

perfectly preserves Rational Number, Decimal Number, Exponential Number and Fibonacci

Number. Again Cyclic Addition applies Law and Order that may appear new, however

existing teaching methods can achieve a result of Numerical mastery with Cyclic Addition

Mathematics. Current Day Number and its Numerals are universal and eternal, Cyclic

Addition must preserve this universality and must work perfectly for all time. There is no

solution without these conditions placed upon a new Cyclic Addition Number System

A great parallel of Cyclic Addition with Current Day Number is how to start teaching

Number of Objects or a Count of Objects. Most have real life experience teaching children

how to Count from a plethora of ‘Current-Day’ text book examples. Cyclic Addition starts

with a very simple Object Count with Circle, Cycle, Sequence, (6) Numbers, groups of

Objects, and progressing to Counting multiple groups of Objects with Circular Addition. This

prepares the child to receive qualities of beginner Cyclic Addition at a very early age.

A simple Brief on the Cyclic Addition ToolKit

Cyclic Addition, as it is new, uses a simple ToolKit of 7 Tools to steer the Teaching of

Number. The ToolKit comprises of (WPOSCCC) Wheel, Pattern, Operation +× ̶ ÷,

Sequence, Circle, Common Multiple and Cylinder. Let’s look at each of the 7 Tools.


15/245

15

When a Teacher or student investigates Whole Number with Cyclic Addition invariably the

start is with the Cyclic Addition ToolKit Wheel. Every Wheel is completely Circular and

conforms to the Sequence formula of ‘Common Multiple’×‘1 3 2 6 4 5’×7(n-1) where the

Common Multiple is a single selection from integers 1 to 69 and n=Tier of the Hierarchy.

Normally one starts by forming a Count Sequence with the Common Multiple 1 Wheel

‘1 3 2 6 4 5’. When working with a Wheel the Common Multiple is stable and continuous,until one completes a Wheel and moves onto another Wheel. This second Wheel might be a

higher Tier than the first or a completely new Common Multiple.

The 6 number Circular Wheel is used to construct and build Cyclic Addition Mathematics.

There are 5 Steps to Cyclic Addition, discussed further on, these are Counting, Place Value,

Move Tens, Remainder and 7×Multiple. The Wheel interacts mathematically and uniquely

with each of these 5 Steps. These 5 Steps and their corresponding mathematical Laws to

make practical the Cyclic Addition are found in this chapter.

The Numerical and geometrical ToolKit Patterns formed by the Wheel are second to none.

Cyclic Addition leads Mathematics with Pattern making and Number. Basically there areseveral types of Patterns. The Count Sequence formed with the Wheel has Patterns of the

Common Multiple, Remainder Patterns and presentation Patterns of the 7×Multiple. Each

Count within a Count Sequence has Place Value Patterns and with larger Number, 3 to 8

digit, the Sequence of numerals within a Number also presents Patterns. A Wheel, from the

first Tier, can combine all possible Count Sequences to form a Cylinder of Number, unique to

that Wheel. This Cylinder shape and managing Number on the Cylinder requires mastery of

the Wheel, Circle, Spiral and Line all geometrical features of the Cylinder. The Cylinder, as

presented in a whole Sphere of this book, is completely full of numerous Patterns. Some of

these Patterns are Circular, some form a diamond, some have a special symmetry, other form

part of the Cyclic Addition Count Sequences that run in Spirals all the way from top to the

bottom of the Cylinder. The language of a Common Multiple consistently given to a Cylinder

also has Pattern. This is the pinnacle of Pattern Making with Whole Number.

The ToolKit Operations +× ̶ ÷ play a consistent and stable role with the mathematics of

Whole Number. Operation × is with one Wheel presenting all multiples of a certain Common

Multiple onto one or four Cylinders. Operation + is with the Cyclic Addition Step Counting.

As one Counts only Addition around the Wheel is used. Operation ̶ is with the Cyclic

Addition Step Remainder. Using the universal formula of ‘Count ̶ Remainder = 7×Multiple’.

Operation ÷ is with positions of Place Values around the Wheel. The Place Values are a Step

in Cyclic Addition. Thus all the Operations are formed from the 5 Steps of Cyclic Addition.

Note importantly the previous Count, the Wheel Count and the next Count all share the sameCommon Multiple and are all produced with Addition, thus Operations +× are together. The

examination of Patterns on a Cylinder is with equality and all Operations +× ̶ ÷.

The ToolKit Sequence has at least three forms. The first is the Cyclic Addition Step:

Counting used to construct a Count Sequence. This Sequence forms a Spiral of Counts on the

Cylinder belonging to the same Wheel. The second is the Sequence of numerals forming a

Count Number. Usually read from left to right, although conversely Operations + ̶ are

performed from right to left. The third is a Sequence of Counts forming a 6 number Ring

around the Cylinder. This Sequence connects Count Sequences together. And most

importantly a Sequence of action with the Cyclic Addition 5 Steps. Again these 5 Steps are

performed on a Count in Sequence. The first Counting, the second Place Value, the thirdMove Tens, the fourth Remainder and the fifth 7×Multiple.


16/245

16

The ToolKit Circle and its portrayal in Number Mandala emphasises that all Whole Number

is created by, for and with the Circle. The Wheel and all the Mathematics of 5 Steps of Cyclic

Addition are performed with the Circle. Counting is in a direction of clockwise or anti-

clockwise around the fixed Wheel. The Wheel remains stationary and the Mathematics

Circles around it. Place Value applies mini-Wheels within the Wheel, to build each Place

Value position, typically units, tens and hundreds. Each Place Value Set, in each position, is asimple 1 to 5 numbers from the Wheel, again only Circular numbers from the Wheel. Move

Tens to Units moves Place Values outside the Units to the Units via a rotation of a Place

Value around the Wheel. Move Tens is always in a clockwise direction following the

movement of reading a Number from left to right. Remainder uses Circular Patterns from the

Wheel, every Wheel, to calculate a final Remainder. The Mathematics of all steps prior to

Remainder are put to use calculating a Remainder. The 7×Multiple is confirmed by its

presence on the next higher Tier Wheel.

The Circle in this Number Mandala plays a perfect role with all Spheres of Cyclic Addition

Mathematics. Rational Number and their Pure Circular Fractions are always completely

Circular. Exponential Number is connected seamlessly with Pure Circular Fractions to givethem a special role in connecting the Wheel to the ‘Common Multiple’×7(n-1) . Even

Fibonacci Number also connects to Pure Circular Fractions. All Wheels no matter the Tier of

Common Multiple are always Circular. A way to begin Cyclic Addition is with mini-Wheels

onto NumberGrids being perfectly Circular. The Count Sequence from the Wheel becomes a

Spiral around the Cylinder. Navigating with Number around the Cylinder requires Circle,

Spiral and Vertical. Patterns with Number across multiple Cylinders show equality of Circle.

The ToolKit Common Multiple is given to every Wheel and every Cylinder that is

constructed with a single Wheel. This stability and constancy of the Common Multiple,

throughout Number and Pattern exploration, allows perfect knowledge to be gleaned.

Common Multiple unites Number for the whole Cylinder or Tier of Cylinders. The Common

Multiple can be simply a number from 1 to 69 and the Tier n. Or ‘Common Multiple’×7(n-1)

for example Common Multiple 2 for Tiers 1, 2, 3, 4 and 5 are exactly the same as Common

Multiple 2, 14, 98, 686 and 4802. This terminology is used throughout Number Mandala.

The Common Multiple may have a Pattern of numeral Sequence that proves the Common

Multiple and possibly higher Tiers. The Common Multiple may have a Pattern at the end of

Cycle to declare the 7×Multiple. The Common Multiple for higher Tiers shows numerals

within a Number that put the lower Tier to a higher Place, Position and Order amongst all

Cyclic Addition Mathematics. Thus when one reaches for a Cylinder and Wheel to perform

Cyclic Addition upon it one invariably is choosing a Common Multiple and Tier.

The Common Multiple 1 and its higher Tiers 7, 49, 343, 2401… are used more

predominantly than others for a couple of reasons. These Common Multiples act as a

benchmark to reference against other Common Multiples. The Common Multiple 1 and

higher Tiers aid the confirmation of a Tier n. This reference tool helps guide the

mathematician to familiar territory when starting a new Common Multiple. Thus it is

recommended to begin with a very strong and familiar Common Multiple 1 and Tier n. This

concentration of energy upon the 1’s is strongly connected to the dominance of the 1’s from

our early learning as children Counting by 1’s. In the long run every Count on a Cylinder

shows ‘Common Multiple’×‘Other Multiple’=‘Count’ once the role of the other multiple is

discovered the reliance on the 1’s dissipates.


17/245

17

The ToolKit Cylinder is a Cylinder covered in Number. Ordered by 6 Spirals in a clockwise

rotation and 6 Spirals in an anti-clockwise rotation. Thus forming 12 Count Sequences or

Spirals in any Tier 1 Common Multiple. One usually reads a Cylinder with the Spiral as a

guiding direction to interpret all the Cylinder’s Pattern and Knowledge of the Common

Multiple. The Wheel is highly connected with the Cylinder. In fact each Ring or Circle of 6

Numbers sliced through the Cylinder has a Remainder of exactly the whole Wheel. This featmakes for perfect Patterns shown in the Sphere Cylinder. This cross meshing of Count

Sequences binds and ropes the Counts into the strongest form of Whole Number known to

mankind. Higher Tiers, Tier 3 and above, have 4 complete Cylinders for every Common

Multiple. There is perfect cross Cylinder Mathematics that interweaves Rings of all 6 Counts

on one to other Cylinders. All this numerical Patterning is with the fact that every Cycle of 6

Counts on a Cylinder is perfectly unique.

The Cylinder, for Tier 2 and above, although it appears to be created from just 1 Wheel is

actually made from all the lower Tiers. Tier 3 Wheel and matching 4 Cylinders are made

from Tier 1 Counting connecting to Tier 2 without Remainder, followed by Tier 2 Counting

connecting to Tier 3 without Remainder and then continuing onto the Cylinder. So basicallyhigher Tier Cylinders use lower Tier Counting to generate more complete Count Sequences

or Spirals. In fact a Tier 3 and above Common Multiple set of 4 Cylinders have exactly 6 of

the same Count followed by a unique Count around the Wheel. All intermeshed Spirals to

presents the perfection and Pattern of the Common Multiple with Cyclic Addition

Mathematics.

When ever there is a problem or confusion with Cyclic Addition, bring the ToolKit into

action and promote Order and Law over chaos. Bringing truth to Whole Number has

ramifications across all strands of Mathematics and many other Subjects. The ToolKit is

simple and can universally be applied to Cyclic Addition and Number Mandala.

Cyclic Addition Laws and the 5 Steps

The Laws book pdf on the CD-Rom was created about 6 years ago. To permanently record all

the accumulated Cyclic Addition actions in one consolidated work of Mathematical Laws for

Number. This provided an avenue to communicate with English the works of Cyclic

Addition. However to teach Cyclic Addition from a text required the last two pdf text ‘A

New Invention’ and ‘A Prophetic Design’. These two pdf text together with the practical

Cylinder and this text show a readiness to be incorporated into a Mathematics Curriculum.

These Laws thus are a guide and formation of Cyclic Addition Mathematics, rather than the

be all end all as the previous Laws book attempted to be. Those wanting to fathom the originsof the Laws are welcome to the older pdfs on the CD-Rom.

The Structure of these Laws include (1) Cyclic Addition 5 Steps and (2) the Cyclic Addition

Cylinder. So that the foundation, and established wisdom of the 5 Steps remains perfect and

true to Law amongst all Cyclic Addition Mathematics.

Laws Step 1: Counting

The word ‘Counting’ is a continuous incrementing Addition from Number around the Wheel.

The Wheel is a 6 number Circular Sequence.

The Wheel is always in the form of ‘Common Multiple’×‘1 3 2 6 4 5’×7 (n-1) . n=Tier number.

A Cycle of Counting is a 6 Number Count Sequence. Usually finishing at an end of Cycle.A Number with Cyclic Addition has arithmetical qualities with Operations +× ̶ ÷.


18/245

18

A Number has place value positions describing each numeral from right to left.

A Wheel has a certain ‘Common Multiple’ from 1 to 69. All Wheel members contribute to

the study of a Common Multiple.

A complete Count with a single Common Multiple forms a Cyclic Addition ‘Cylinder’.

A Count Sequence of any Cycle of 6 numbers is unique to the Wheel and Cyclic Addition.

Counting with a Tier 1 Wheel presents all other multiples to the length of the Count wherethe ‘Common Multiple’×‘Other Multiple’=Count. This is with all 5 Steps of Cyclic Addition.

At any moment during a Count a ‘Pattern’ can be formed. Patterns include the Count

Sequence itself, 6 Remainders each Cycle, a Common Multiple, or 7×Multiple formed from 2

Cylinder Counts.

Cyclic Addition is not here to question an established 1400 year old invention of Number,

rather to perfect Number with Cyclic Addition Mathematics.

All 12 Tier 1 Count Sequences for a Common Multiple are generated by the Wheel. There

are 6 Clockwise and 6 anti-clockwise Count Sequences. This is shown best by the Cylinder.

All Counts from 1 Wheel share the same Common Multiple. This perfects Patterns.

An end of Cycle of Counts is in most cases with a 7×Multiple=Count, without Remainder.

A Count Number has its place, position and Order amongst all Counts by its position on aCylinder or Tier of Cylinders.

The Student of Cyclic Addition may review any Cylinder Count Sequence. Recommending

the review of an entire Spiral of Counts is performed at one duration of time. Aiding memory.

The Circle and Sequence of a Wheel are preserved by any of the 5 Steps of Cyclic Addition.

The 7 Cycle Count limit on the Cylinder is a guide to allow all Counts to be performed with

equal eye without prejudice or preference. All Counts require a go to receive the whole

Cylinder.

A Count can be with multiple Tiers. Begin at a lower Tier and connect the Count without

Remainder to the next higher Tier. Then apply Cyclic Addition with the higher Tier to all 5

Steps. Move to a higher Tier Wheel and all Cyclic Addition Mathematics acts upon this

higher Tier Wheel.

One can begin Cyclic Addition with Circular Addition using mini-wheels. These 30 mini-

wheels are created from the original Wheel ‘1 3 2 6 4 5’. Then grouped into like common

multiple. All of these mini-wheels train the beginner Counter with Circle, Cycle, Sequence,

Common Multiple all with Whole Number. See 2 recent pdf books on the CD-Rom.

Counting brings forth Mathematics of magnitude, scale, ratio, proportion, quantity and

estimation, exactness and preciseness.

Counting is the beginning of exploring other strands of Mathematics.

Laws Step 2: Place Value

Place Value builds a Set for each place value position in a Whole Number Count. This Set ismade from Circular Mathematics of the Counting Wheel.

A Place Value Set is 1 to 5 numbers counting clockwise with a mini-wheel. A mini-wheel is a

partial 1 to 5 number Sequence from a 6 number Wheel. A Place Value Set can begin at any

number around a mini-wheel and finish at any number. See Workbook pdf Chapter

‘Advanced Place Value’ on the CD-Rom.

A Place Value Set matches its total with the units of a Count. Then what remains is given to

another Place Value Set in the tens. Then, if the Count is high enough, a hundreds Place

Value Set. All Place Value Sets mesh with Addition to equal the Count.

There are only 30 mini-wheels to any Cyclic Addition 6 number Wheel. Any of these 30

mini-wheels can be used to create a Place Value Set.

There is only a potential 270 clockwise Place Value Sets possible for any 1 Wheel.


19/245

19

These laws provide a foundation to act creatively with any Wheel in this Step 2. All the while

this Step reinforces and preserves the Circle and Sequence of the Wheel.

Note illustrations and tables of Place Value Sets and how they’re derived in pdf book ‘Laws

within a Number Universe’ on the CD-Rom.

There are about 3× as many Place Value Sets between 10× to 20×‘Common Multiple’

compared with 1× to 9× ‘Common Multiple’. So connecting any possible Place Value Set toa Count is a Science and Art form. This choice leads to actively participating with the Wheel

members in a creative and Circular way. A brilliant way to build a Count.

Place Value Sets can and often do overlap into higher place value positions. For example

Count 525 with Wheel ‘7 21 14 42 28 35’ can use two Sets ’21 14 42 28’=105 in units and

‘7 21 14’=42 in tens. Note the overlap of 105 into tens and hundreds, and the overlap of 42

into hundreds.

Creating a Place Value Set can be viewed as Circular Addition with just 1 to 5 numbers.

Traditional Names for place value positions like units, tens and hundreds are completely

preserved. Merely applying Cyclic Addition Mathematics to Number.

The Place Value Step selects Wheel members that Add to the Count. This action joins the

numerals forming a Number with Mathematics. A highly sought after goal accomplished bysimple Wheel Mathematics.

A Place Value Set with Common Multiple 1 Wheel ‘1 3 2 6 4 5’, like the Sets adding to 11

above, prepare one to act, with exactly the same Wheel member locations, with another

Common Multiple. For example any of the 17 possible Place Value Sets to make 11, can be

then used to make 22=11×2 with Common Multiple 2, and 33=11×3 with Common Multiple

3 and so on.

This awesome flexibility to choose a Set is then available to any Wheel and any Tier.

Laws Step 3: Move Tens

The Move Tens Step makes use of Traditional Names for place value positions units, tens and

hundreds. As these are familiar to all and ideal to involve them with this Step.

The tens Place Values are matched to the Wheel and then rotated one number clockwise and

literally placed in the units position.

The hundreds Place Values and matched to the Wheel and rotated two number clockwise and

placed in the units position. Higher Place Values rotate around the Wheel clockwise one

number for each place value position left of units.

This acknowledges each Place Value’s position within a Count with Wheel Mathematics.

As all Wheels are in the form of ‘Common Multiple’×‘1 3 2 6 4 5’×7(n-1) this rotation

Mathematics of Step 3 Move Tens works universally.

The Cyclic Addition Step 3: Move Tens can be combined with Step 4: Remainder, performed

at the same time. The simplest and most accurate method is mathematically encouraged.See Workbook pdf for ‘Remainder’ examples showing a template for this Step 3.

The Sphere #3M and #3N illustrates the Math of this Step.

The Mathematics of this Step 3: Move Tens shows yet further application of the Wheel’s

Circle and Sequence.

The Wheel Sequence is actually the Remainder Sequence of 7×’Common Multiple’. Maths

with the 6 number Remainder Sequence can be viewed as the Step 3:Move Tens function.

Laws Step 4: Remainder

The Cyclic Addition Step 4: Remainder searches for 1 member of the Wheel that shows the

difference between the Count and the nearest 7×Multiple.

This follows the universal formula of ‘Count ̶ Remainder = 7×Multiple’. At the end of Cyclethere is no Remainder, thus the Count = 7×Multiple. See Cylinder.


20/245

20

By matching Place Values to the Wheel and applying Patterns or Remainder Laws to the

Wheel one receives the single number Remainder, again from the Wheel.

A Place Value Set in the Tens having 1 Remainder can be combined with a Place Value Set

in the Units having another Remainder. Merely apply Step 3: Move Tens after the Remainder

for both has been found. Leaving two Remainders in the Units for simple final Remainder

calculation.The Remainder Laws that apply to all Cyclic Addition Wheels are such.

Two Number Place Values condensing down to a single Remainder.

Consider the space around a 6 number Wheel.

Two of the same number yields a single Remainder found two numbers clockwise.

Two numbers next to each other yields a single Remainder found 3 numbers clockwise.

Two numbers two apart yields a single Remainder found in the middle of both.

Two number three apart, or opposite sides of the Wheel, yields no Remainder as they add to a

7×Multiple.

Three Number Place Values. 3 examples only.

Three of the same number yields a single Remainder found the next number clockwise.

Three numbers in Sequence yields a single Remainder found the next number in rotationclockwise.

Three numbers all spaced 2 apart yields no Remainder as they add to a 7×Multiple.

Practise making other Remainder Patterns with the simplest Wheel ‘1 3 2 6 4 5’.

With more Place Values in a position, search for Patterns that eliminate 7’s. The Laws pdf

has a complete Table of 270 possible Place Value Set and their corresponding Remainder.

This Table Patterns the Set in groups of 6 and in Sequence around the Wheel.

The searching for a Remainder can also be accomplished with Addition of the Place Value

Set and finding the Remainder from the nearest 7×Multiple. The Table above has this

Addition with Pattern and Remainder.

The Workbook pdf has a Chapter Remainder to practically apply many Place Value Sets with

a range of Common Multiples. Try Addition of the Set to form the Remainder as well.

The Step 4: Remainder mathematically acts upon the Wheel to preserve Circle and Sequence.

In a Cycle of 6 Counts, there are 6 unique Remainders. The end of Cycle, typically has a

7×Multiple=Count, with no Remainder. The other 5 Remainders have a Pattern. This Pattern

applies to most Cylinders and Cyclic Addition. It is important to master this Circular Pattern.

This Pattern of 5 Remainders and a 7×Multiple each Cycle of Counts remains the same for

the length of the one Spiral Count on a Cylinder.

Again this Pattern of Remainders, once mastered, prevents errors of double Counting a

Number on the Wheel, missing out a Count member of the Wheel, incorrect Place Value Sets

to Add to the Count, faulty application of the Move Tens Step. So the Pattern of Remainders

each Cycle protects the Count and consequent 7×Multiple. This is to perfect Cyclic AdditionMathematics.

When applying Cyclic Addition to a Whole Number, any Whole Number, search effectively

for that Remainder and Whole Number takes on the role given by the Hierarchy and

Common Multiple.

Remainder Mathematics on the Cylinder is left to the next Topic in this Chapter.

A Remainder has a position around the Wheel ‘Common Multiple’×’1 3 2 6 4 5’. Use the

location around the Wheel as one of ‘1 3 2 6 4 5’. Then apply Mathematics of that number to

the Count. Often the Remainder’s position around the Wheel highlights and illumes

knowledge on how to read numerals in a Number with Cyclic Addition. This may take

practise from current day methods, however it yields that role that a number plays amongst

all. Also the Remainder itself may contribute like knowledge to the Count. This is amysterious part of Cyclic Addition. Where the Count is mapped to its nearest 7×Multiple.


21/245

21

See 2 pdf text ‘A New Invention’ and ‘A Prophetic Design’ and Sphere #3 for illustrations

and guide.

Laws Step 5: 7×Multiple

This is the final Step culminating in the receive of the 7×Multiple. The next Count follows.

Once the Remainder is determined, and Subtracted from the Count the 7×Multiple appears.This is from the universal formula ‘Count ̶ Remainder = 7×Multiple’.

Actually the 7×Multiple sits transparently underneath the Cylinder Count. Like the many

Patterns of the Cylinder serving and Addition or Subtraction of two Counts, in Pattern,

equalling a 7×Multiple. Consider the unity of these Patterns and Step 5: 7×Multiple.

The 7×Multiple is a Number that can be found by Counting around the next higher Tier

Wheel. For example Counting with Tier 1 Common Multiple 2 Wheel ‘2 6 4 12 8 10’

presents 7×Multiples from the Tier 2 Common Multiple 14 Wheel ’14 42 28 84 56 70’.

Typically the end of Cycle Count has no Remainder and equals a 7×Multiple. The Cylinder

clearly presents this as a Ring of 6 identical 7×Multiples.

The creation of the 7×Multiple unites the lower Tier with the next higher Tier for Cyclic

Addition. In fact the higher Tier Wheel should be present whilst performing Cyclic Additionwith the lower Tier Wheel. See Wheels pdf for the first 7 Tiers of all Common Multiples.

Cylinder Patterns of the 7×Multiple are detailed in Sphere #5 text.

The Count, Remainder and 7×Multiple all share the same Common Multiple.

The 7×Multiple acts as a unseen framework beneath the Count to enhance the Count’s

numerals forming Number, Pattern of the Common Multiple, and a Reference point for the

Count. So one is mathematically informed as to the Count’s place, position and Order

amongst other Counts on the Cylinder, and other Cylinders with the same Count.

The 7×Multiple thus aids scale, ratio, magnitude, size and proportion of the Count.

There is a maximum of 6 unique Counts with Remainder utilizing one 7×Multiple. The

seventh multiple is where the Count = 7×Multiple without Remainder.

All 7×Multiples are shown as an end of Cycle, Count = 7×Multiple, from Tier 2 and above.

The Order and Hierarchy of Cyclic Addition 5 Steps introduces and unites the next higher

Order with the lower order. So the skill in working with the lower Order is presenting the

higher Order in conjunction with the lower Order Cyclic Addition 5 Steps.

Before moving to a higher Order Wheel and Cyclic Addition, make sure of your confidence

in this presentation of the higher Order within the lower Order 5 Steps. This is the test of

Mathematical ability required to shift to a higher Order Wheel.

The range of 7×Multiple in a 7 Cycle Count is about a complete Cycle with the next higher

Tier.

One can introduce oneself with Patterns found in higher Tier Wheels. This shows the starting

point from the Wheel’s Reference Page from the Wheels pdf on the CD-Rom. These Wheelsare in straight line form and can be rewritten in a Circular Form for Cyclic Addition 5 Steps.

The whole search for the 7×Multiple, found on the next higher Tier Wheel, again preserves

the Circle and Sequence.

Note the number of occurrences of a 7×Multiple within a Spiral Count on a Cylinder. This is

akin to the Remainder Pattern each Cycle. This number of a distinct 7×Multiple repeats each

Cycle. There is either 1, 2, 3 or 4 identical 7×Multiple in any complete Cycle of 1 Spiral.

Finding an accurate 7×Multiple is a perfect sign as to all the Mathematics of the other Steps.

Again the Count choice, Place Value Set choice, Move Tens Circle, Remainder Patterning to

derive the 7×Multiple shows mastery of Cyclic Addition 5 Steps with this accuracy.

Thus the Cyclic Addition Mathematics is a journey that continually perfects the higher Order by applying ToolKit Mathematics to the lower Order. The Mathematics of the lower Order is


22/245

22

adequate preparation to receive the next higher Order. From a glimpse of the Wheels pdf

showing 7 Tiers for each Common Multiple, one asks how to join consecutive Tiers. The

Cyclic Addition 5 Steps, the ToolKit and the Cylinder answers this connection completely.

The Mathematics of Cyclic Addition matures the Student’s Number, discarding guesswork,

gambling and magical tricks with Number, in preference to completeness of mastering the 5Steps with the ToolKit.

After going through a few Cylinders with Cyclic Addition 5 Steps one realises the inherent

perfection of a Number System that is guided by such Laws. A Number System that provides

freedom and creativity to express Number, with beauty and perfection, by natural Laws.

These natural Laws guide and instruct the newcomer to Cyclic Addition, to effectively

challenge all prior beliefs, in how to use the 10 Hindu-Arabic Numerals forming Number.

Imagine finding these 10 numerals in an Order of Cyclic Addition 1000’s of years ago.

Etched into a stone tablet found at a historical monument. The transition to merge Cyclic

Addition Number with current day Number would be simple. Today with competing forces todistract our attention away from the big picture, away from the whole view, the eternal view

of the subject matter, ones powers of truth, reason and discernment are limited by current day

propaganda.

Laws of Cyclic Addition Cylinder

Cylinder Creation and Form

Cyclic Addition and the Mathematical and Numerical ‘Cylinder’ are one.

Cyclic Addition Mathematics is only complete with the mathematical study of the Cylinder.

As mentioned in the Chapter Structure the Cylinder contains 4 visual forms. These are a

Spiral Clockwise, a Spiral anti-clockwise, a Ring and Vertically aligned Number.The Cyclic Addition 5 Steps are applied to any or all of the Spirals forming a Cylinder.

Cyclic Addition recommends that the core activity of using a Cylinder is with any or all of

the 5 Steps of Cyclic Addition. And treat the Pattern making and exploration of a Common

Multiple as a supplementary activity. This allows consistent concentration on a Spiral with

the purpose of Cyclic Addition 5 Steps in mind. Sure Patterns form along the way however to

remain true to the long term use of the Cylinder one should always return to the 5 Steps.

The form of the Cylinder is a 7 Cycle Count with each Spiral down and around the Cylinder.

The paper Cylinder is about 32 Counts or 5 Cycles designed for an A4 piece of paper.

The form of the Cylinder has 6 members to a Ring, for Tier 1. The first, third and fifth Rings

in any Cycle are Vertically Aligned. So to the second, fourth and sixth Rings. These form 12

points Vertically aligned, equally spaced, all the way down the Cylinder.The Tier 1 Common Multiple Cylinder has 12 Counts on 1 Cylinder created with 1 Wheel.

The Tier 2 Common Multiple Cylinder has 28 Counts on 4 Cylinders created with 2 Wheels.

The Tier 3 and above Common Multiple Cylinder has 42 Counts on 4 complete Cylinders

created with 3 Wheels. As per Cyclic Addition Law of creating a Count Sequence.

The Tier 2 Wheel is exactly 7× Tier 1 Wheel. The Tier 3 Wheel is exactly 7× Tier 2 Wheel.

From the formula of any Wheel ‘Common Multiple’×‘1 3 2 6 4 5’×7(n-1) . When n=Tier.

Each new Ring of 6 Numbers is the next Count. The smaller Cylinder, Tier 2 and up, has a

Ring of 3 Numbers, where the next Ring down is also the next Count.

The spacing of Counts on any Spiral is generated by the Wheel in either clockwise or anti-

clockwise direction.

Counting all Counts of a Tier with Cylinder(s) presents completeness with the CommonMultiple for that Tier.


23/245

23

Teaching and Learning the 6 Spheres of Number Mandala

Sphere #1 The Book of Wheels

The Wheels pdf shows all Wheels for every Common Multiple 1 to 69 and presenting 7

Tiers. Each page is a single Common Multiple. This is called a Reference Page used

continuously to manage inter-Tier Cyclic Addition Mathematics. One can draw a Circular Wheel to construct a Count Sequence or simply use the Reference Page. Even both can be

used.

The Wheels Reference Pages contain 3 parts of Cyclic Addition. The top row of 22 numerals

is part of the Pure Circular Fraction 69. The diagonal numbers beginning with the Common

Multiple are exponentials of 7. i.e. ‘Common Multiple’×7(n-1) where n= Tiered Exponential.

Underneath the exponentials are the 6 number Wheels where the first leftmost number match

the exponentials above. Sphere #1 gives 7 examples of Reference Pages to familiarise one

with the simpler Common Multiples 1 to 7.

This Reference Page, or Circular Wheel, is an unmatchable Tool used with all 5 Steps of Cyclic Addition. To move around the Wheel and Add the next member of the Wheel with

Step 1: Counting. To construct a Place Value Set for each position units, tens and hundreds

with Step 2: Place Value. To use hands around the Wheel, to physically move tens to units or

place value sets, condensed to one Remainder number, around the Wheel in a clockwise

motion. To further Pattern final units Wheel members to reveal a single Number Remainder

with Step 3 and 4: Move Tens and Remainder combined. To Subtract the Remainder from the

Count to link the next higher Tier Wheel Number to the Count, with Step 5: 7×Multiple.

Sphere #1B shows Mathematics of Remainder Patterns common to most Common Multiples.

Sphere #1C asks one to construct the new Pure Circular Fractions. Teaching all fractions of

these special circular sequences of Rational Number. These are constructed wholly from one

number. For example Pure Circular Fraction 19 uses a 2 to construct the whole fraction and

remainder. The Fraction can be formed with Operations +× from right to left or

Operations ̶ ÷ from left to right. This teaches Mathematics of Number 2 and the citing of the

fraction Sequence prepares one for Cyclic Addition with the Common Multiple 2.

The Pure Circular Fraction 19 also present perfect exponentials of 2 see Sphere #1D. To

master a number’s exponential Order with the formula ‘multiple ’×Exponential Number (n-1)

One merely perfectly connects all exponentials to the Fraction. This Mathematical Feat of

numerical engineering allows one to put Order to a home and a Reference for exponentials.

Sphere #1F shows Cyclic Addition Count Numbers and matching them to a Pure Circular

Fraction 19. So a special Cyclic Addition Count can form all parts of the Fraction Sequence.

This is demonstrated in further Spheres #1 to show how Whole Number created from Cyclic

Addition Wheels is perfectly able to present Rational Number.

Complete Rational Number has 3 types. A Pure Circular Fraction perfectly presented with

Cyclic Addition. And a fixed length Decimal Fraction which has a denominator of 2n×5m

Where n and m are positive integers. These Fractions always produce a fixed length Decimal

and the Mathematics of multiples of 5 and 2 can be created with a Cyclic Addition Wheel.

Thus are excluded from Cyclic Addition Mathematics. The third type is a mixed Fraction.

These have the qualities of both types of Fraction above. Most numerators show a decimalfixed portion and a repeating or circulating portion in the Fraction. Thus are obsolete and are


24/245

24

excluded from a study of Number. Little is to be gained by studying Pure Circular Fraction

19 and then denominator 38 or 76. These types are discussed in Rational Number Sphere #1.

Cyclic Addition exploration and discovery into Rational Number is with Pure Circular

Fractions only. These special denominators with any numerator forming a perfectly Circular

Decimal Fraction from 0 to 1 are the purpose of Number Mandala. Other omitted Rational Number Mathematics can be found in a Text book anywhere.

There are perfect and pure Mathematical Skills to be learnt by working with Pure Circular

Fractions. With Denominators 9, 19, 29, 39, 49, 59 and 69 the working number is +1 and tens

only to the denominator i.e. 1, 2, 3, 4, 5, 6 and 7. This proves Circular Mathematics of

creating these Fractions has a major and significant role to play with Rational Number. See

the two pages of fraction sequences formed by Pure Circular Fraction 399 in Sphere #1J.

Consider the Circular Place Value Skills in constructing perfect Fractions. See Sphere #1.

Any fraction formed is Circular, merely move along the Sequence of a Pure Circular Fraction

to find the numerator and begin circling from there. The diagonal staggering of Exponentials,there corresponding remainder from multiples of the denominator and there vertical Addition

to equal the fraction sequence presents perfect Mathematics. Note how the diagonal

Exponentials form with any numerator along the circular Sequence. This Design, Order and

Numeracy is recognised formally as Cyclic Addition Mathematics. Thus also present on a

Reference Page. In fact Pure Circular Fraction 69 is fundamental to Cyclic Addition Wheels.

Remainder Sequences define a Circular Sequence of Number that show the Cyclic Addition

Step 3: Move Tens to Units from another Multiple. See Sphere #1K. These are, from the

authors view of Number Mandala, considered to be lengthy sequences that are difficult to

remember and apply mathematically. Often Patterns moving from one Remainder to the next

is of more use. For example Remainder Sequence 19 one can apply mathematics of creating a

Pure Circular Fraction and produce the same result. So in perspective, these Remainder

Sequences are completely overshadowed by the Cyclic Addition 6 Number Wheel.

Sphere #2 The Wheels within the Wheel

The start of Cyclic Addition for a pre-school child or early primary is with Object Count.

Cyclic Addition constructs Sphere #2A with Circle, Cycle, Sequence, Number, Word name

for number, and a Count in groups, then progressing to Counting in multiple groups around

the Circle. That simple. Teaching all of these qualities from scratch from new. This prepares

the child to receive down the schooling track the 6 number Cyclic Addition Wheel. Thus the

Circle, Wheel and nature of both with Number are familiar in later primary schooling. Of course any Object can replace the pictured 21 Stars either 2D or 3D shapes that have a similar

Counting ability with them.

The Number alone starts with Sphere #2B. This list is derived from the Wheel at the top.

Simply all 60 mini-Wheels, with some repeating Wheels, are contained in the Table. The

Table groups a Cycle Total or Addition of all numbers in the mini-Wheel together. Then

Count. Counting with Sphere #2C shows the regular NumberGrid in 1’s, yes 1’s. The length

of each Row of the NumberGrid matches the Cycle Total of all mini-Wheels above. To make

it work simply start anywhere around a single mini-Wheel and finger Count, write on another

piece of paper, or colour in the journey around and around and around the mini-Wheel.


25/245

25

This teaches beginner Circle, Cycle, Sequence, Number, Common Multiple and Remainder

Mathematics. The Remainders are the Numbers in between the right most Common

Multiples. This relationship with essentially fancy, elaborate, skip Counting and the

NumberGrid builds a Number found on a Wheel and its Order with the Table and Common

Multiple. Patterns formed from familiar Times Tables are made perfect with these mini-

Wheels onto NumberGrids. Spacing of Number, which Cyclic Addition perfectly achieves, begins here.

For teachers who ask for a believable nexus between Current Day Base 10 Number and

Cyclic Addition Number Sphere #2F was created. There are 5 Tables. The first is used to

form any 4 digit Base 10 Number. Pick at most one number from each of the 4 rows. Simple.

The second Table converts Base 10 to Base 7. Same Pattern as the first Table, however our

Base 10 Number temporarily disappears. For example 1+20+300+4000=(1×70)+ (2×71)+

(3×72)+ (4×73)= Base 10 Number of 1+14+147+1372=1534. The third Table converts all

Numbers in the second Table back to Base 10. Note the Zero as a Place value Marker has

disappeared. So Cyclic Addition converts the linear Table into Circular Wheel in the fourth

and fifth Table. The fifth Table is simply a construction of a multiple of the fourth Table. i.e.Common Multiple 21 Wheels for Tier 1 to 4. From here the Cyclic Addition Wheel performs

the 5 Steps mentioned in Laws above. Simple. Actually there is a lot of hard work to search

for a Whole Number truth this important, however the journey is simple to Teach. Making

the transition from Current-Day to Cyclic Addition a little easier.

Sphere #3 The Creation of Whole Number

This Sphere #3 is the nuts and bolts of the 5 Steps of Cyclic Addition. The labelled

illustrations communicate how to teach these 5 Steps. The Order again for the 5 Steps is

Counting, Place Value, Move Tens, Remainder and 7×Multiple.

Sphere #3A is a 12 way Count down the page. Showing Counting forwards and Counting

backwards for 2 Cycles with the Wheel of ‘1 3 2 6 4 5’. This is the start of the Common

Multiple 1’s. The Cylinder of 1’s shows these Counts all inter-meshed with one another. This

vertical Counting shows especially the spacing of each Sequence. This Count spacing may

seem new to some, however it allows incredible perfection and Pattern to be formed on the

Cylinder of 1’s shown in Sphere #3B.

Sphere #3C is also vertical Counts showing a beginning to Common Multiple 1 Tier 2. This

shows only clockwise Counting. All possible clockwise Counts are created with Tier 1 and

Tier 2 Wheels. 6 Counts are simply Tier 2 alone, 2 others show no Tier 3 end-of-cycle and

the remaining 6 show the other Tier 3 end-of-cycles with the spaced Counting in-between.Sphere #3D is also vertical Counts showing a beginning to Common Multiple 1 Tier 3 or

Common Multiple 49. Note the 6+6+6+3=21 Counts and how they’re formed. The first 6 a

Tier 3 alone. The second and third 6+6=12 use Tier 1 and Tier 2 and Tier 3 Wheels to present

all Clockwise Counts with an end-of-cycle 343 and 686. This spacing of 49’s shows 6 Counts

for every multiple between 1029 and 2058. The next Count from any number is all 6 Wheel

members from ‘49 147 98 294 196 245’. To find the remaining 21 anti-clockwise Counts see

the 4 Cylinders for Common Multiple 49 on the CD-Rom.

This connection between Tier 1, Tier 2, Tier 3 and Tier 4 Number is the original making of

Cyclic Addition complete Counting for Common Multiple 49 or Tier 3 of Common Multiple

1. To move to a higher Tier, according to Cyclic Addition Law, one Counts with the lower Tier first and when there is no Remainder, such that the Count = 7×Multiple, one can begin


26/245

26

Counting with the next higher Tier. Thus Sphere #3D shows this connection between Tier 1,

2 and 3 of Common Multiple 1. This also represents a seamless Count with two or more

Tiers. All of the Cylinders, both paper and pdf, use only 1 Wheel for set of (1 or 4) Cylinders.

This aids simplification and concentration of Count Sequences with again 1 Wheel.

Step 1: Counting essentially completely links the Wheel with the Cylinder. Every incrementon a Cylinder from one Ring to the next is with a Wheel member. Counting builds other

mathematical talents like scale, ratio, proportion, magnitude and gaining the ability to use all

Counting Numbers rather than a zero dominated or rounded Number. Counting is the thread

of each Spiral Count Sequence, every Spiral and every Count Sequence, without exception.

Counting with Addition and the Wheel trains one to use the Common Multiple perfectly.

Place Value is called as such because Cyclic Addition requires a way to build each Number

from each place value position, typically units, tens and hundreds. Most Wheels have

overlapping numerals into a higher place value position. See the two Steps Counting and

Place Value in Sphere #3I. This building is with Wheel, is with Circle and ‘kind of’ replaces

Base 10 association with numerals in a place value position. The purpose of which is to prepare Wheel Numbers to find a single Number Step 4: Remainder.

Other Mathematics, during the Place Value Step, is accomplished. The Count is confirmed to

belong to the Common Multiple Wheel, as all Place Values in units and tens and hundreds

originate from the Wheel. Thus proving the Count is a multiple of the Common Multiple.

Very valuable Mathematics to see a Number and connect a Common Multiple to it. The Place

Value Step also encourages manipulation of place value positions with Wheel members. The

basics of which enhance traditional carrying or gluing numeral aside numeral Number. This

determines that Number remains as Mathematical Number rather than symbol. One of the

formal primary outcomes of Number Mandala with Cyclic Addition Mathematics.

Sphere #3F is 30 mini-Wheels complete. This is an invaluable Tool to aid visualising how to

perform the Step 2: Place Value. One need only select a mini-Wheel and Count in a

clockwise rotation for 1 to 5 numbers as per Laws. This Circle and Wheel with 30 mini-

Wheels applies mathematical dexterity to form a Place Value Set. With a little practise with

Common Multiple 1 Wheel ‘1 3 2 6 4 5’ one can see how the Wheel reveals many options for

a choice of a Place Value Set. Note Sphere #3G for all Place Value Sets totalling 9, 10 and 11

for Common Multiple 1 Wheel. This Sphere shows mathematical perfection and creativity

with the Wheel to choose a Place Value Set. Look at Sphere #3H and the 45 Patterns of Place

Value Sets. Note the mini-Wheels all start with 1, and show all corresponding possible Place

Value Sets. Visualise the mini-Wheel and Circling around it to create a Place Value Set. The30 mini-Wheels generate 45×6=270 possible Place Value Sets for any 1 Wheel.

Sphere #3J shows all possible Place Value Sets with all Wheels for the Number 144. All

Place Value Sets are unique and show a scale of how to form 144 from a Wheel. This tests

the child’s Circle, Number and mini-Count Total from the Wheel. A perfectly unique and

universal feature of the Cyclic Addition Wheel. As the effort put into simple Wheels can be

transferred to higher Tier or highe

Teach Number Mandala with Cyclic Addition Mathematics

Documents

Transcript of Teach Number Mandala with Cyclic Addition Mathematics