Acknowledgments 

ii  
The University of Chicago School Mathematics Project 

iv  


vi  
To the Student 

1  (3) 


4  (66) 


6  (5) 


11  (6) 


17  (6) 


23  (4) 


27  (4) 

Square Roots and Variables 


31  (6) 


37  (8) 

Inclass Activity: Patterns with Squares and Right Triangles 


44  (1) 


45  (8) 

Inclass Activity: Variables and Tables 


52  (1) 


53  (17) 


60  (2) 


62  (1) 


63  (2) 


65  (4) 


69  (1) 

Multiplication in Algebra 


70  (70) 

Areas, Arrays, and Volumes 


72  (7) 

Special Numbers in Multiplication 


79  (6) 

Inclass Activity: Multiplying Algebraic Fractions 


84  (1) 

Multiplying Algebraic Fractions 


85  (6) 


91  (5) 

Products and Powers with Negative Numbers 


96  (6) 


102  (7) 

Special Numbers in Equations 


109  (5) 


114  (5) 

The Multiplication Counting Principle 


119  (6) 

Factorials and Permutations 


125  (15) 


131  (2) 


133  (1) 


134  (2) 


136  (3) 


139  (1) 


140  (74) 

Models and Properties of Addition 


142  (7) 

More Properties of Addition 


149  (6) 


155  (8) 


163  (7) 


170  (7) 

Inclass Activity: Using Algebra Tiles to Add Expressions 


176  (1) 

The Distributive Property and Adding Like Terms 


177  (6) 

The Distributive Property and Removing Parentheses 


183  (5) 

Writing Linear Expressions 


188  (7) 

Adding Algebraic Fractions 


195  (5) 


200  (14) 


205  (2) 


207  (1) 


208  (2) 


210  (3) 


213  (1) 


214  (68) 

Subtraction of Real Numbers 


216  (5) 


221  (6) 

Solving Sentences Involving Subtraction 


227  (5) 


232  (8) 

The Opposite of a Sum or Difference 


240  (6) 

Graphing x + y = k and x  y = k 


246  (7) 

Sums and Differences in Geometry 


253  (7) 

Inclass Activity: The Triangle Inequality 


259  (1) 


260  (7) 


267  (15) 


274  (2) 


276  (1) 


277  (1) 


278  (4) 


282  (66) 

Horizontal and Vertical Lines 


284  (7) 

Using Tables to Compare Linear Expressions 


291  (6) 


297  (7) 

Using Graphs to Compare Linear Expressions 


304  (6) 

Using an Automatic Grapher 


310  (7) 


317  (5) 


322  (5) 

Advanced Solving Technique I: Multiplying Through 


327  (6) 

Advanced Solving Technique II: Chunking 


333  (15) 


338  (2) 


340  (1) 


341  (2) 


343  (4) 


347  (1) 


348  (68) 

The Algebraic Definition of Division 


350  (6) 


356  (6) 


362  (8) 

Inclass Activity: Relative Frequencies and Probabilities 


368  (2) 

Relative Frequency and Probability 


370  (6) 

Solving Percent Problems Using Equations 


376  (5) 

Probability Without Counting 


381  (6) 


387  (7) 


394  (8) 

Inclass Activity: Similar Figures 


401  (1) 


402  (14) 


408  (2) 


410  (1) 


411  (1) 


412  (4) 


416  (68) 


418  (7) 


425  (7) 


432  (7) 

SlopeIntercept Equations for Lines 


439  (6) 

Equations for Lines with a Given Point and Slope 


445  (5) 

Equations for Lines Through Two Points 


450  (8) 

Inclass Activity: Latitude and Temperature 


456  (2) 


458  (5) 


463  (6) 

Graphing Linear Inequalities 


469  (15) 


476  (2) 


478  (1) 


479  (1) 


480  (4) 


484  (62) 


486  (6) 


492  (6) 

Comparing Constant Increase and Exponential Growth 


498  (7) 


505  (5) 

Products and Powers of Powers 


510  (5) 


515  (6) 


521  (6) 

Powers of Products and Quotients 


527  (6) 

Remembering Properties of Exponents and Powers 


533  (13) 


539  (2) 


541  (1) 


542  (1) 


543  (3) 

Quadratic Equations and Square Roots 


546  (68) 


548  (6) 

Graphing y = ax2 + bx + c 


554  (8) 

Inclass Activity: Graphing Parabolas with an Automatic Grapher 


561  (1) 

Graphing Parabolas with an Automatic Grapher 


562  (5) 

Quadratic Equations and Projectiles 


567  (6) 


573  (6) 

Analyzing Solutions to Quadratic Equations 


579  (7) 

Square Roots and Products 


586  (7) 

Absolute Value, Distance, and Square Roots 


593  (6) 


599  (15) 


605  (2) 


607  (2) 


609  (1) 


610  (4) 


614  (50) 


616  (5) 

Investments and Polynomials 


621  (6) 

Multiplying a Polynomial by a Monomial 


627  (6) 


633  (6) 

Inclass Activity: Modeling Multiplication of Binomials with Tiles 


638  (1) 


639  (7) 

Special Binomial Products 


646  (5) 


651  (13) 


657  (2) 


659  (1) 


660  (1) 


661  (3) 


664  (54) 

An Introduction to Systems 


666  (6) 

Solving Systems Using Substitution 


672  (4) 

More Uses of Substitution 


676  (5) 

Solving Systems by Addition 


681  (6) 

Solving Systems by Multiplication 


687  (7) 

Systems and Parallel Lines 


694  (5) 

Situations Which Always or Never Happen 


699  (5) 


704  (14) 


711  (2) 


713  (1) 


714  (1) 


715  (3) 


718  (54) 

Factoring Integers into Primes 


720  (6) 

Common Monomial Factoring 


726  (7) 

Inclass Activity: Factoring Trinomials 


732  (1) 


733  (5) 

Solving Some Quadratic Equations by Factoring 


738  (6) 


744  (5) 

How Was the Quadratic Formula Found? 


749  (5) 

Rational Numbers and Irrational Numbers 


754  (5) 

Which Quadratic Expressions Are Factorable? 


759  (13) 


765  (2) 


767  (1) 


768  (1) 


769  (3) 


772  (52) 


774  (4) 


778  (6) 


784  (5) 


789  (6) 

Inclass Activity: Results of Tossing Two Dice 


794  (1) 


795  (5) 


800  (7) 

Inclass Activity: Ratios of Sides in Right Triangles 


806  (1) 


807  (5) 

Functions on Calculators and Computers 


812  (12) 


817  (2) 


819  (1) 


820  (1) 


821  (3) 
Appendix A: Scientific Calculators 

824  (5) 
Appendix B: Scientific Notation 

829  (5) 
Appendix C: BASIC 

834  (4) 
Selected Answers 

838  (28) 
Glossary 

866  (8) 
Index 

874  (11) 
List of Symbols 

885  (1) 
Photo Acknowledgments 

886  