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

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

Ken Johnson, Ted Herr, Judy Kysh

ISBN: 978-1-119-29873-1

Apr 2018

572 pages

Description

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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.

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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

  •  Rewrote the language in several problems to make the problems easier to understand, or to make the problem situation more modern.
  • Added new problems to Problem Set A in several chapters.
  • Added problems to the More Practice section in several chapters.
  • Replaced many Problem Set B problems with new problems.
  • Examples are solved as dialogues between fictitious students so students can see common errors and learn to avoid pitfalls.
  • Each chapter includes relevant examples of the strategy presented.
  • Chapters conclude with problem sets made up of three levels: A (routine), B (lengthy), and Classic Problems whose level can be determined by instructors.
  • Over a dozen distinct problem-solving strategies are developed in depth, including classic strategies as well as more contemporary strategies.
  • Icons appear to indicate examples, important information, and difficult material.