**MSRI Mathematical Circles Library**

Volume: 21;
2018;
171 pp;
Softcover

MSC: Primary 00; 97;

**Print ISBN: 978-1-4704-4785-4
Product Code: MCL/21**

List Price: $25.00

AMS Member Price: $20.00

MAA Member Price: $22.50

**Electronic ISBN: 978-1-4704-4998-8
Product Code: MCL/21.E**

List Price: $25.00

AMS Member Price: $20.00

MAA Member Price: $22.50

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#### Supplemental Materials

# Math Circle by the Bay: Topics for Grades 1–5

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*Laura Givental; Maria Nemirovskaya; Ilya Zakharevich*

A co-publication of the AMS and the Mathematical Sciences Research Institute

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.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

#### Readership

Elementary and middle school teachers, organizers of math circles for elementary school students, and parents of such students.

#### Table of Contents

# Table of Contents

## Math Circle by the Bay: Topics for Grades 1-5

- Cover Cover11
- Title page i2
- Preface vii8
- Chapter 1. Numbers as Geometric Shapes 114
- Chapter 2. Combinatorics 2538
- Chapter 3. Fibonacci Numbers 4154
- Building Strips with Squares and Dominoes 4154
- Parking Problems 4457
- Counting Routes 4861
- Fibonacci Sequence in Nature 4962
- Extension to the Left 5164
- Even/Odd Pattern 5265
- Divisibility by 3 5568
- Sum of the First n Consecutive Fibonacci Numbers 5972
- Fibonacci Rectangles and Fibonacci Spiral 6174
- Honeybees’ Ancestral Tree 6477

- Chapter 4. Pascal’s Triangle 6982
- Paths in Mouseville 6982
- Hockey Stick Pattern 7487
- Diagonals in Pascal’s Triangle 7588
- Rows in Pascal’s Triangle 7790
- Extending Pascal’s Triangle 7992
- Fibonacci Numbers in Pascal’s Triangle 8396
- Sierpinski Triangle 8497
- Counting Odd and Even Numbers in Pascal’s Triangle 89102
- Pascal’s Triangle Modulo 3 94107

- Chapter 5. Area 99112
- Chapter 6. Selected Warmup and Challenging Problems 135148
- Handouts 163176
- Bibliography 169182
- Index 171184
- Back Cover Back Cover1186