Quantitative Reasoning

Alicia Sevilla has a Ph.D. in mathematics from Cornell University and is Professor of Mathematics at Moravian College, where she has taught for over 20 years. She participated in the two FIPSE projects that produced the COMPANION TO CALCULUS and mentored other institutions to adopt the integrated approach. She recently served as Chair of the Department of Mathematics and Computer Science, and was co-director of a National Science Foundation grant to develop and implement a quantitative reasoning course. She is an active member of the Mathematical Association of America, and serves as Coordinat.

Annotated Contents xi

Preface xvii

To the Student xxiii

To the Instructor xxv

Acknowledgments xxvii

Section I: Numerical Reasoning

Topic 1: Organizing Information Pictorially Using Charts and Graphs 2

Activity 1.1: World Motor Vehicle Production: Bar Graphs and Pie Charts 27

Activity 1.2: Medical Data and Class Data: Graphs with Excel 35

Activity 1.3: SATs and the Super Bowl: Creating and Interpreting Histograms 43

Topic 2: Bivariate Data 52

Activity 2.1: Estimating Dates: Scatterplots 69

Activity 2.2: State Governors’ Salaries and Per Capita Income: More on Scatterplots 75

Topic 3: Graphs of Functions 82

Activity 3.1: Temperature Patterns: Functions and Line Graphs 105

Activity 3.2: Rates of Change and Concavity 111

Topic 4: Multiple Variable Functions 118

Activity 4.1: Blood Alcohol Levels and Credit Cards: Working with More Than Two Variables 133

Topic 5: Proportional, Linear, and Piecewise Linear Functions 140

Activity 5.1: Rates of Change and Linear Functions 159

Topic 6: Modeling with Linear and Exponential Functions 166

Activity 6.1: The Genie’s Offer: Exponential Growth and Linear Growth 185

Activity 6.2: Lines of Best Fit 191

Topic 7: Logarithms and Scientific Notation 198

Activity 7.1: Richter Scale and Logarithms 213

Activity 7.2: Estimations, Scientifc Notation, and Properties of Logarithms 219

Topic 8: Indexes and Ratings 224

Activity 8.1: Measurement Difficulties and Indexes 243

Activity 8.2: Consumer Indexes 249

Topic 9: Personal Finances 256

Activity 9.1: Mortgages 277

Topic 10: Introduction to Problem Solving 284

Activity 10.1: Savings and Loans: Problem Solving and Using Scroll Bars 299

Activity 10.2: Asking and Answering a Research Question 305

Section II: Logical Reasoning

Topic 11: Decision Making 308

Activity 11.1: Ranking Cities: Ratings and Decisions 325

Topic 12: Inductive Reasoning 332

Activity 12.1: Analyzing Studies: Inductive Reasoning 345

Topic 13: Deductive Reasoning 354

Activity 13.1: Code-Breaking and Deductive Reasoning 375

Activity 13.2: Compound Statements Used in Reasoning 381

Activity 13.3: Quantified Statements and Deductive Reasoning: Direct and Indirect Reasoning 389

Topic 14: Apportionment 394

Activity 14.1: Methods of Apportionment: Quota Methods 409

Activity 14.2: Apportionment: Divisor Methods 415

Topic 15: More on Problem Solving 422

Activity 15.1: Making a Purchase Decision 433

Section III: Statistical Reasoning

Topic 16: Averages and Five-Number Summary 436

Activity 16.1: Visualizing Football Scores: Measures of Center and Spread 457

Topic 17: Standard Deviation, z-Score, and Normal Distributions 462

Activity 17.1: Coins, Presidents, and Justices: Normal Distributions and z-Scores 485

Topic 18: Basics of Probability 492

Activity 18.1: Simulations 511

Activity 18.2: Finding Probabilities 517

Topic 19: Conditional Probability and Tables 522

Activity 19.1: Diagnostic Testing and Conditional Probability 543

Topic 20: Sampling and Surveys 550

Activity 20.1: Sampling and Surveys 569

Topic 21: More on Decision Making 578

Activity 21.1: To Purchase a Warranty or Not: Making a Decision 593

Appendix

Excel Commands by Activity 597

Index 603