Softcover ISBN:  9781470447854 
Product Code:  MCL/21 
List Price:  $35.00 
MAA Member Price:  $31.50 
AMS Member Price:  $28.00 
eBook ISBN:  9781470449988 
Product Code:  MCL/21.E 
List Price:  $30.00 
MAA Member Price:  $27.00 
AMS Member Price:  $24.00 
Softcover ISBN:  9781470447854 
eBook: ISBN:  9781470449988 
Product Code:  MCL/21.B 
List Price:  $65.00 $50.00 
MAA Member Price:  $58.50 $45.00 
AMS Member Price:  $52.00 $40.00 
Softcover ISBN:  9781470447854 
Product Code:  MCL/21 
List Price:  $35.00 
MAA Member Price:  $31.50 
AMS Member Price:  $28.00 
eBook ISBN:  9781470449988 
Product Code:  MCL/21.E 
List Price:  $30.00 
MAA Member Price:  $27.00 
AMS Member Price:  $24.00 
Softcover ISBN:  9781470447854 
eBook ISBN:  9781470449988 
Product Code:  MCL/21.B 
List Price:  $65.00 $50.00 
MAA Member Price:  $58.50 $45.00 
AMS Member Price:  $52.00 $40.00 

Book DetailsMSRI Mathematical Circles LibraryVolume: 21; 2018; 171 ppMSC: Primary 00; 97
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, mathloving 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 copublished with the Mathematical Sciences Research Institute (MSRI).
ReadershipElementary and middle school teachers, organizers of math circles for elementary school students, and parents of such students.

Table of Contents

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


Additional Material

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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, mathloving 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 copublished with the Mathematical Sciences Research Institute (MSRI).
Elementary and middle school teachers, organizers of math circles for elementary school students, and parents of such students.

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