Preface 

vii  
To The Student 

xix  


1  (68) 


4  (7) 

An Introduction to Problem Solving 


11  (5) 

Polya's ProblemSolving Principles 


16  (12) 

More ProblemSolving Strategies 


28  (22) 

Additional ProblemSolving Strategies 


50  (19) 


63  (2) 


65  (2) 


67  (2) 


69  (70) 

Sets and Operations on Sets 


72  (12) 

Sets, Counting, and the Whole Numbers 


84  (14) 

Addition and Subtraction of Whole Numbers 


98  (15) 

Multiplication and Division of Whole Numbers 


113  (26) 


134  (2) 


136  (1) 


137  (2) 

Numeration and Computation 


139  (88) 

Numeration Systems Past and Present 


141  (14) 

Nondecimal Positional Systems 


155  (8) 

Algorithms for Adding and Subtracting Whole Numbers 


163  (16) 

Algorithms for Multiplication and Division of Whole Numbers 


179  (16) 

Mental Arithmetic and Estimation 


195  (13) 

Getting the Most Out of Your Calculator 


208  (19) 


222  (2) 


224  (1) 


225  (2) 


227  (54) 

Divisibility of Natural Numbers 


230  (16) 


246  (9) 

Greatest Common Divisors and Least Common Multiples 


255  (14) 

Codes and Credit Card Numbers: Connections to Number Theory 


269  (12) 


277  (1) 


278  (1) 


279  (2) 


281  (62) 

Representations of Integers 


283  (11) 

Addition and Subtraction of Integers 


294  (22) 

Multiplication and Division of Integers 


316  (11) 


327  (16) 


337  (2) 


339  (2) 


341  (2) 

Fractions and Rational Numbers 


343  (64) 

The Basic Concepts of Fractions and Rational Numbers 


345  (19) 

The Arithmetic of Rational Numbers 


364  (22) 

The Rational Number System 


386  (21) 


402  (2) 


404  (1) 


405  (2) 

Decimals and Real Numbers 


407  (66) 


410  (21) 

Computations with Decimals 


431  (14) 


445  (11) 


456  (17) 


470  (1) 


471  (1) 


472  (1) 

Algebraic Reasoning and Representation 


473  (58) 

Algebraic Expressions and Equations 


477  (12) 


489  (15) 

Graphing Functions in the Cartesian Plane 


504  (27) 


526  (1) 


527  (2) 


529  (2) 

Statistics: The Interpretation of Data 


531  (62) 

The Graphical Representation of Data 


533  (24) 

Measures of Central Tendency and Variability 


557  (18) 


575  (18) 


589  (1) 


590  (1) 


591  (2) 


593  (60) 


595  (14) 


609  (18) 


627  (26) 


649  (2) 


651  (1) 


652  (1) 


653  (88) 


657  (22) 

Curves and Polygons in the Plane 


679  (21) 


700  (20) 


720  (21) 


734  (2) 


736  (3) 


739  (2) 


741  (82) 


743  (18) 


761  (22) 


783  (10) 


793  (30) 


815  (2) 


817  (2) 


819  (4) 

Transformations, Symmetries, and Tilings 


823  (66) 

Rigid Motions and Similarity Transformations 


826  (25) 


851  (15) 

Tilings and EscherLike Designs 


866  (23) 


883  (2) 


885  (1) 


886  (3) 

Congruence, Constructions, and Similarity 


889  


891  

Constructing Geometric Figures 


911  


931  


948  


950  


952  
Appendices 


Appendix A Manipulatives in the Mathematics Classroom 


955  


959  

Appendix C Graphing Calculators 


965  

Appendix D A Brief Guide to The Geometer's Sketchpad 


979  


990  
Answers to Selected Problems 

1  (56) 
Acknowledgments 

57  (2) 
Mathematical Lexicon 

59  (2) 
Index and Pronunciation Guide 

61  