Crossing the River with Dogs: Problem Solving for College Students, 3rd Edition

Crossing the River with Dogs: Problem Solving for College Students, 3rd Edition promotes the philosophy that students learn best by working in groups and the skills required for real workplace problem solving are those skills of collaboration. The text aims to improve students’ writing, oral communication, and collaboration skills while teaching mathematical problem-solving strategies. Focusing entirely on problem solving and using issues relevant to college students for examples, the authors continue their approach of explaining classic as well as non-traditional strategies through dialogs among fictitious students. This text is appropriate for a problem solving, quantitative reasoning, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.

Preface vii

Instructor Resources x

Acknowledgments xi

Introduction 1

1 Draw a Diagram 11

2 Make a Systematic List 27

3 Eliminate Possibilities 47

4 Use Matrix Logic 73

5 Look for a Pattern 115

6 Guess and Check 145

7 Identify Subproblems 175

8 Analyze the Units 199

9 Solve an Easier Related Problem 233

10 Create a Physical Representation 267

11 Work Backwards 297

12 Draw Venn Diagrams 323

13 Convert to Algebra 351

14 Evaluate Finite Differences 383

15 Organize Information in More Ways 417

16 Change Focus in More Ways 447

17 Visualize Spatial Relationships 473

Appendix 503

Unit Analysis

Adding, Subtracting, Multiplying, and Dividing Fractions

Area and Volume Formulas

Properties of Triangles

Properties of Numbers

Glossary 511

Bibliography 519

Index of Problem Titles 521

General Index 529

Photo Credits 539

Answers to More Practice Problems 541