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 conjecturenow 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 cutup

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 IV)

231 