Cover -- Title page -- Preface -- Chapter 1. Numbers as Geometric Shapes -- Examples of Figurate Numbers -- Square Numbers -- Rectangular Arrangements -- Triangular Numbers -- Quick Summations -- Cubic Numbers -- Pyramids -- Chapter 2. Combinatorics -- Coloring Beads -- Mumbo Language -- Ice Cream Cones -- Nowhere York City -- The Handshake Problem -- Sides and Diagonals -- Same Problems with 10 Objects -- Apples, Oranges, and More -- Problems about Numbers -- Harder Problems -- Chapter 3. Fibonacci Numbers -- Building Strips with Squares and Dominoes -- Parking Problems -- Counting Routes -- Fibonacci Sequence in Nature -- Extension to the Left -- Even/Odd Pattern -- Divisibility by 3 -- Sum of the First n Consecutive Fibonacci Numbers -- Fibonacci Rectangles and Fibonacci Spiral -- Honeybees' Ancestral Tree -- Chapter 4. Pascal's Triangle -- Paths in Mouseville -- Hockey Stick Pattern -- Diagonals in Pascal's Triangle -- Rows in Pascal's Triangle -- Extending Pascal's Triangle -- Fibonacci Numbers in Pascal's Triangle -- Sierpinski Triangle -- Counting Odd and Even Numbers in Pascal's Triangle -- Pascal's Triangle Modulo 3 -- Chapter 5. Area -- Playing with Squares -- Areas of Similar Shapes -- SAME SHAPE SAME SIZE -- Rotation by a Right Angle -- Area of a Tilted Square -- Pythagorean Theorem -- Area of a Parallelogram and Area of a Triangle -- Pick's Formula -- Chapter 6. Selected Warmup and Challenging Problems -- Handouts -- Bibliography -- Index -- Back Cover This book is based on selected topics that the authors taught in math circles for elementary school students at the University of California, Berkeley; Stanford University; Dominican University (Marin County, CA); and the University of Oregon (Eugene). It is intended for people who are already running a math circle or who are thinking about organizing one. It can be used by parents to help their motivated, math-loving kids or by elementary school teachers. We also hope that bright fourth or fifth graders will be able to read this book on their own. The main features of this book are the logical sequence of the problems, the description of class reactions, and the hints given to kids when they get stuck. This book tries to keep the balance between two goals: inspire readers to invent their own original approaches while being detailed enough to work as a fallback in case the teacher needs to prepare a lesson on short notice. It introduces kids to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors chose topics with deep mathematical context. These topics are just as engaging and entertaining to children as typical "recreational math" problems, but they can be developed deeper and to more advanced levels. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession