"The Cosmic Calculator Course" - Summary of Book 1

Introduction 1
1) Arithmetic 3

2) Digit Sums and the Nine-Point Circle 5     
The Number Nine 6     
The 9-Point Circle 6     
Your Lucky Number 9     
Digit Sum Game 9      GAME     
Digit Sum Problems 10

3) Large Numbers 11     
Restructuring Numbers 11     
Reading and Writing Large Numbers 13     
Millions 14     
Billions 16     
Make a Number Game 16      GAME

4) Digit Sum Check 17     
Addition from Right to Left 17     
Sums Involving 'Carries' 18     
The Digit Sum Check 18     
Subtraction 20     
Checking Subtraction Sums 22

5) Number Nine 23     
By Addition and By Subtraction 24

6) Numbers with Shapes 27     
Square Numbers 28     
Factor Pairs 29     
Factor Rectangles 30     
Prime Numbers 31     
The Sieve of Eratosthenes 31     
Triangular Numbers32     
Cube Numbers 32     
Summary of Number Sequences 34
REVISION Test 1

7) Geometry 35     
The Right Angle 35     
Right-Angles Game 36      GAME     
Parallel Lines 36     
Drawing Geometrical Shapes 37     
Right-angled and Equilateral Triangles 40

8) Symmetry 41     
Polygons 43             WORKSHEET 1     
Rotational Symmetry 45

9) Angles and Triangles 46     
Finding Angles 48     
Triangles 49

REVISION Test 2

MAGIC SQUARES 52

10) By the Completion 54     
Completing the Whole- Fractions 55     
Completing the Whole- Shapes 56

11) Doubling and Halving 58     
Extending the Multiplication Tables 60

12) Divisibility 62     
Divisibility by 2, 5, 10 62     
Divisibility by 3 and 9 64     
Summary 64     
Divisibility by 4 66     
Divisibility by 6 67     
Divisibility by 15 68

13) Short Multiplication and Division 71     
Multiplication 71     
Multiplication by 11 72     
Division 73     
The Digit Sum Check for Division 74     
Division by 9 75

14) Powers of Ten and Decimals 77     
Adding and Subtracting Decimal Numbers 78     
Multiplying and Dividing Decimal Numbers 79     
Multiplying & Dividing by Powers of 10 79     
Multiplying & Dividing Decimals by 10, 100 etc 81     
Metric Units 83
REVISION Test 3

15) Number Splitting 85     
Addition 85     
Subtraction 87     
Multiplication 87     
Division 88     
Checking Devices 89     
Checking Calculations 90

16) Polygons and Coordinates 91     
Quadrilaterals 92     
Diagonals of Quadrilaterals 93

17) Regular Polygons and Perimeters 95     
To Construct an Equilateral Triangle 96     
To Construct a Regular Hexagon 96     
To Construct a Square 97     
To Construct a Regular Octagon 98     
Perimeters 98     
Perimeter Problems 99

18) All from 9 and the Last From 10 101     
All from 9 101     
All from 9 and the Last from 10 102     
First Extension 103     
Second Extension 104     
Combining the First and Second Extensions 105

REVISION Test 4

PASCAL'S TRIANGLE 107

19) Bar Numbers 109     
Bar Numbers Game 111      GAME     
All from 9 and the Last from 10 111     
Subtraction 112     
Creating Bar Numbers 113

20) On the Flag 115     
Addition 115     
Multiplication 118

21) Prime and Composite Numbers 120     
Factor Trees 121     
An Alternative Method 122     
Highest Common Factor: HCF 123     
By Addition and by Subtraction 124

22) Proportionately 126     
Equal Ratios 126     WORKSHEET 2     
Simplifying Ratios 127     
Finding Equal Ratios 128     
Ratio Problems 129     
Splitting in a Ratio 130     
Extended Ratios 130
REVISION Test 5

23) By One More than the One Before 132     
Squaring Numbers that end in 5 132     
Multiplying by Numbers whose First Figures are the Same and whose Last Figures Add up to 10, 100 etc 133     
Rounding 135       WORKSHEET 3
24) Algebra 138     
Using Letters 138     
Brackets 140     Factorising 141     
Substitution 142     
Multiple Substitutions 144

25) Area 145     
Rectangles and Squares 145     
Irregular Shapes 147     
Composite Shapes 149     
Parallelograms 150     
Triangles 152     
Units of Area 154

26) Volume 155     
Capacity 157

27) Planets 160     
Planet Sizes 160     
Orbits of Planets 161

REVISION Test 6

FLEXAGONS 164

HISTORICAL NOTES 166