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.