| Preface |
|
| Overview of materials |
i |
| Index of key problems |
vii |
| Acknowledgments |
xi |
About the authors
|
xii |
| I. What is Mathematical Investigation? |
1 |
|
Problem solving and problem posing |
3 |
| You’ve got a conjecture-now what? |
7 |
| Do it yourself |
14 |
| You know the answer? Prove it. |
17 |
Discerning what is; predicting what might be
|
23 |
II. Dissections and Area
|
33 |
Be a mathematical cut-up
|
34 |
Making assumptions, checking procedures
|
41 |
Thinking about area
|
46 |
Areas of nonpolygonal area
|
55 |
Transformations and area
|
64 |
| III. Linearity and Proportional Reasoning |
72 |
| Mix it up |
73 |
| Filling in the gaps |
80 |
Guess my rule
|
89 |
Functions of two variables
|
98 |
From cups to vectors
|
106 |
| IV. Pythagoras and Cousins |
112 |
| What would Pythagoras do? |
114 |
Puzzling out some proofs
|
121 |
Pythagoras’s second cousins
|
131 |
Pythagorean triples (and cousins)
|
139 |
More classroom cousins
|
146 |
V. Pascal's Revenge: Combinatorial Algebra
|
153 |
Trains of thought
|
156 |
Getting there
|
162 |
Trains and paths and triangles, oh my!
|
170 |
Binomial theorem connection
|
179 |
Supercalifragilisticgeneratingfunctionology
|
187 |
VI. Problems for the Classroom (with solutions)
|
195 |
VII. Answers to Selected Problems (Chapter I-V)
|
231 |
