Acknowledgments 

ii  
The University of Chicago School Mathematics Project 

iv  


vi  
To the Student 

1  (3) 


4  (58) 

Decimals for Whole Numbers 


6  (4) 

Decimals for Numbers Between Whole Numbers 


10  (6) 

Estimating by Rounding Up or Rounding Down 


16  (5) 

Estimating by Rounding to the Nearest 


21  (5) 


26  (5) 

Decimals for Simple Fractions 


31  (6) 

Decimals for Mixed Numbers 


37  (4) 


41  (5) 


46  (4) 


50  (12) 


55  (2) 


57  (1) 


58  (1) 


59  (3) 


62  (54) 

Multiplying by 10, 100, . . . 


64  (4) 


68  (5) 

Scientific Notation for Large Numbers 


73  (5) 

Multiplying by 1/10, 1/100, . . . 


78  (6) 


84  (5) 

From Decimals to Fractions and Percents 


89  (4) 


93  (6) 


99  (6) 

Inclass Activity: Scientific Notation for Small Numbers 


104  (1) 

Scientific Notation for Small Numbers 


105  (11) 


109  (2) 


111  (1) 


112  (1) 


113  (3) 


116  (58) 


118  (7) 


125  (5) 

Weight and Capacity in the Customary System of Measurement 


130  (5) 

The Metric System of Measurement 


135  (5) 

Converting Between Systems 


140  (5) 


145  (8) 

Inclass Activity: Kinds of Angles 


152  (1) 


153  (5) 


158  (5) 


163  (11) 


167  (2) 


169  (1) 


170  (1) 


171  (3) 


174  (62) 


176  (6) 

Describing Patterns with Variables 


182  (5) 

Translating Words to Algebraic Expressions 


187  (6) 

Evaluating Algebraic Expressions 


193  (4) 


197  (6) 


203  (5) 


208  (6) 

Inclass Activity: Relative Frequency 


213  (1) 


214  (5) 


219  (5) 


224  (12) 


229  (2) 


231  (1) 


232  (1) 


233  (3) 

Patterns Leading to Addition 


236  (64) 


238  (6) 


244  (4) 

Rules for Adding Positive and Negative Numbers 


248  (6) 

Inclass Activity: Combining Turns 


253  (1) 


254  (6) 

Adding Positive and Negative Fractions 


260  (6) 


266  (5) 

The Commutative and Associative Properties 


271  (5) 


276  (7) 

Inclass Activity: Polygons 


282  (1) 


283  (5) 


288  (12) 


293  (2) 


295  (1) 


296  (1) 


297  (3) 

ProblemSolving Strategies 


300  (44) 

Being a Good Problem Solver 


302  (5) 


307  (4) 


311  (4) 


315  (5) 


320  (5) 


325  (7) 

Special Cases and Simpler Numbers 


332  (12) 


338  (2) 


340  (1) 


341  (1) 


342  (2) 

Patterns Leading to Subtraction 


344  (62) 

Two Models for Subtraction 


346  (6) 

The Slide Model for Subtraction 


352  (6) 


358  (4) 


362  (5) 

Counting and Probability with Overlap 


367  (8) 

Inclass Activity: Angles and Lines 


374  (1) 


375  (6) 

Angles and Parallel Lines 


381  (6) 


387  (6) 

The TriangleSum Property 


393  (13) 


399  (2) 


401  (1) 


402  (1) 


403  (3) 


406  (60) 

Graphs and Other Displays 


408  (7) 


415  (6) 


421  (7) 


428  (7) 

Inclass Activity: Translations (Slides) 


434  (1) 


435  (5) 


440  (6) 


446  (6) 


452  (14) 


458  (2) 


460  (1) 


461  (2) 


463  (3) 

Patterns Leading to Multiplication 


466  (62) 

The Area Model for Multiplication 


468  (8) 

Volumes of Rectangular Solids 


476  (6) 

Multiplication of Fractions 


482  (6) 

Multiplying Probabilities 


488  (5) 

The Rate Factor Model for Multiplication 


493  (6) 

Multiplication with Negative Numbers and Zero 


499  (6) 

Size ChangesExpansions 


505  (6) 

Size ChangesContractions 


511  (5) 

Picturing Multiplication with Negative Numbers 


516  (12) 


521  (2) 


523  (1) 


524  (1) 


525  (3) 

Multiplication and Other Operations 


528  (62) 

Multiplication as Shortcut Addition 


530  (5) 


535  (5) 


540  (4) 


544  (6) 

Solving ax + b = c when a Is Negative 


550  (5) 

The Distributive Property 


555  (6) 

The Surface Area of a Box 


561  (5) 


566  (5) 


571  (6) 


577  (13) 


582  (2) 


584  (1) 


585  (2) 


587  (3) 

Patterns Leading to Division 


590  (50) 


592  (5) 

The Rate Model for Division 


597  (4) 


601  (5) 

Division with Negative Numbers 


606  (5) 

The Ratio Comparison Model for Division 


611  (4) 


615  (5) 

The MeansExtremes Property 


620  (6) 

Inclass Activity: Proportions in Similar Figures 


625  (1) 

Proportions in Similar Figures 


626  (4) 


630  (10) 


634  (2) 


636  (1) 


637  (1) 


638  (2) 

Real Numbers, Area, and Volume 


640  (50) 

Converting Decimals to Fractions 


642  (4) 


646  (6) 

Inclass Activity: The Pythagorean Theorem 


651  (1) 


652  (6) 

Inclass Activity: The Circumference of a Circle 


657  (1) 

The Circumference of a Circle 


658  (6) 


664  (6) 

Surface Areas of Cylinders and Prisms 


670  (5) 

Volumes of Cylinders and Prisms 


675  (5) 


680  (10) 


684  (2) 


686  (1) 


687  (1) 


688  (2) 

Coordinate Graphs and Equations 


690  (42) 


692  (7) 

Inclass Activity: Using an Automatic Grapher 


698  (1) 

Situations Leading to ax + b = cx + d 


699  (5) 


704  (5) 

Fractions and Relative Frequencies Revisited 


709  (5) 


714  (5) 

Graphs of Equations with Symbols for Rounding 


719  (13) 


725  (2) 


727  (1) 


728  (1) 


729  (3) 
Selected Answers 

732  (23) 
Glossary 

755  (9) 
Index 

764  (9) 
List of Symbols 

773  (1) 
Photo Acknowledgments 

774  