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

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