Preface v
Introduction vii
1 Multiplication: Part one 1
2 Using a reference number 6
3 Multiplying numbers above and below the reference number 14
4 Checking answers: Part one 18
5 Multiplication: Part two 25
6 Multiplying decimals 41
7 Multiplying using two reference numbers 47
8 Addition 59
9 Subtraction 66
10 Squaring numbers 75
11 Short division 89
12 Long division by factors 94
13 Standard long division 100
14 Direct division 106
15 Division by addition 117
16 Checking answers: Part two 135
17 Estimating square roots 141
18 Calculating square roots 151
19 Fun shortcuts 162
20 Adding and subtracting fractions 180
21 Multiplying and dividing fractions 186
22 Direct multiplication 192
23 Estimating answers 199
24 Estimating hypotenuse 203
25 Memorising numbers 208
26 Phonetic pegs 215
27 Memorising long numbers 223
28 Logarithms 229
29 Using what you have learned 240
Afterword 248
Appendix A Frequently asked questions 250
Appendix B Estimating cube roots 256
Appendix C Finding any root of a number 263
Appendix D Checks for divisibility 267
Appendix E Why our methods work 283
Appendix F Casting out nines - why it works 289
Appendix G Squaring feet and inches 291
Appendix H How do you get students to enjoy mathematics? 294
Appendix I Solving problems 298
Glossary 300
Index 303
