Math Games Cover [Converted].pdf 1 12/7/10 10:12 AM • • MULTICULTURAL FUN for AGES 9 & up M a t h G a “Connects youngsters with ‘friends’ around the globe m and through time in compelling math play.” e s ——Dr. Lorraine Whitman, Executive Director, Salvadori Center & A c t M i v i ath, history, art, and world cultures come together in this delightful t i book for kids. e s More than seventy math games, puzzles, and projects from all over the f r world encourage kids to hone their math skills as they use geometry to o m design game boards, probability to analyze the outcomes of games of chance, and logical thinking to devise strategies for the games. A r o Many of the games have been played for centuries, like Tic-tac-toe, played u n in ancient Egypt; Nine Men’s Morris, once played in England with living game d pieces; and Mankala, the oldest and most popular game in the world. Kids t will learn that math is everywhere, from the geometry reflected in buildings h e to the border patterns of Eskimo parkas. Activities include building a model W pyramid, testing the golden ratio of the Parthenon, and working mazelike o African network puzzles. r l d Claudia Zaslavsky is the author of many books for children and adults, including Africa Counts, Multicultural Math, and Fear of Math. Z a $16.95 (CAN $18.95) s l ISBN 978-1-55652-287-1 a v 51695 s k y IPG 9 781556 522871 Front matter_Front matter 12/7/10 10:43 AM Page i Math Games & Activities from around the World Claudia Zaslavsky Front matter_Front matter 12/7/10 10:43 AM Page ii Zaslavsky, Claudia. Math games and activities from around the world / Claudia Zaslavsky p. cm. Includes bibliographical references (p. 144 – 145). Summary: Presents games and other activities from different countries and cultures that teach a variety of basic mathematical concepts. ISBN 1-55652-287-8 1. Mathematical recreations—Juvenile literature. [1. Mathematical recreations 2. Games.] I. Title. QA95.z37 1998 793.7'4—dc21 Cover, interior design, and illustrations by Mel Kupfer Photo credits: p. 20—D. W. Crowe; p. 102 courtesy of the Kenya Mission to the U. N.; pp. 21, 52, 133—Sam Zaslavsky. Figure credits: Figs. 61a and b reprinted by permission of Claudia Zaslavsky: The Multicultural Math Classroom: Bringing in the World (Heinemann, A Division of Reed Elsevier, Inc., Portsmouth, NH, 1996). Figs. 43b and 57a, b, and c courtesy of J. Weston Walch, reprinted from Multicultural Mathematics by Claudia Zaslavsky. Copyright 1987, 1993. © 1998 by Claudia Zaslavsky All rights reserved First Edition Published by Chicago Review Press, Incorporated 814 North Franklin Street Chicago, Illinois 60610 ISBN 1-55652-287-8 Printed in the United States of America 5 4 3 2 Front matter_Front matter 12/7/10 10:43 AM Page iii This book is dedicated to all the children of the world. May they have a bright future and enjoy peaceful games. Front matter_Front matter 12/7/10 10:43 AM Page iv Front matter_Front matter 12/7/10 10:43 AM Page v ACKNOWLEDGMENTS I want to thank the many educators who shared their expertise to make this book possible. In particular, Judith Hankes contributed her material about the dream catcher; Esther Ilutsik shared her knowledge of Yup’ik border patterns; Marcia Ascher set me straight on the solution to the river-crossing puzzle involving the jealous husbands; and Beverly Ferrucci shared Japanese paper-cutting and several games. I am grateful to the authors of the many books listed in the Bibliography that were a source of information and inspiration for this collection. Cynthia Sherry was a most concerned and involved editor; she played all the games and carried out the activities, pointing out my mistakes and occasional lack of clarity. I take full responsibility for any remaining errors. Front matter_Front matter 12/7/10 10:43 AM Page vi Table Contents of INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . viii 4: GAMES OF CHANCE . . . . . . . . . . . . . . . . . . . . . . 44 Lu-lu from the Hawaiian Islands . . . . . . . . . 46 1: THREE-IN-A-ROW GAMES. . . . . . . . . . . . . . . . . . 2 Native American Games . . . . . . . . . . . . . . . . 48 The Game of Dish, Native American. . . . . . . 49 Shisima from Kenya. . . . . . . . . . . . . . . . . . . . 4 Stick Game, Native American. . . . . . . . . . . . 51 Tapatan from the Philippines. . . . . . . . . . . . . 6 Igba-Ita from Nigeria . . . . . . . . . . . . . . . . . . 52 Tsoro Yematatu from Zimbabwe. . . . . . . . . . . 8 Spin the Dreidel, Jewish . . . . . . . . . . . . . . . 54 Picaría, Native American . . . . . . . . . . . . . . . 10 Toma-Todo from Mexico. . . . . . . . . . . . . . . . 56 9 Men’s Morris from England. . . . . . . . . . . . 12 Trigrams & Good Luck from East Asia. . . . . 58 Trique from Colombia . . . . . . . . . . . . . . . . . 15 The Hexagrams of I Ching from China . . . . . 59 Nerenchi from Sri Lanka . . . . . . . . . . . . . . . 16 Dara from Nigeria. . . . . . . . . . . . . . . . . . . . . 18 5: PUZZLES WITH NUMBERS. . . . . . . . . . . . . . . . . . 60 2: MANKALA: BOARD GAMES OF TRANSFER . . . . . . . 20 Secret Code, Part I, Ancient Hebrew & Greek. . . . . . . . . . . . . . 61 Easy Oware from Ghana . . . . . . . . . . . . . . . 22 Secret Code, Part II, The Real Oware Game from Ghana . . . . . . . 24 Ancient Hebrew & Greek. . . . . . . . . . . . . . 63 Sungka from the Philippines . . . . . . . . . . . . 26 Magic Squares, Part I, from West Africa . . . . 64 Giuthi from Kenya . . . . . . . . . . . . . . . . . . . . 28 Magic Squares, Part II, from China . . . . . . . 66 Magic Squares, Part III. . . . . . . . . . . . . . . . . 68 3: MORE BOARD GAMES. . . . . . . . . . . . . . . . . . . . . 30 Counting Your Ancestors . . . . . . . . . . . . . . . 70 Pong Hau K’i from Korea & China . . . . . . . . 32 Rice Multiplies from Asia . . . . . . . . . . . . . . . 72 Mu Torere from New Zealand. . . . . . . . . . . . 34 Dividing the Camels from North Africa. . . . . 73 Pentalpha from Crete. . . . . . . . . . . . . . . . . . 36 The Ishango Bone from Congo . . . . . . . . . . . 75 Kaooa from India . . . . . . . . . . . . . . . . . . . . . 38 Postal Codes from the U.S.A. . . . . . . . . . . . . 76 Awithlaknannai, Native American. . . . . . . . . 39 Butterfly from Mozambique . . . . . . . . . . . . . 41 Yoté from West Africa . . . . . . . . . . . . . . . 42 Front matter_Front matter 12/7/10 10:43 AM Page vii 6: PUZZLES WITHOUT NUMBERS . . . . . . . . . . . . . . . 78 8: DESIGNS & SYMMETRY . . . . . . . . . . . . . . . . . . 110 Crossing the River in the Sea Islands. . . . . . 79 Masks and Faces from the U.S.A.. . . . . . . . 112 Crossing the River in Liberia . . . . . . . . . . . . 81 Native American Masks . . . . . . . . . . . . . . . 114 Crossing the River with Jealous Husbands Hopi Flat Baskets, Native American . . . . . . 116 from Kenya . . . . . . . . . . . . . . . . . . . . . . . . 82 Pennsylvania Dutch Love Pattern Crossing the River in Colonial America. . . . . 83 from the U.S.A.. . . . . . . . . . . . . . . . . . . . 118 The Snake & the Swallow’s Nest Mon-Kiri Cutouts from Japan. . . . . . . . . . . 120 from Angola . . . . . . . . . . . . . . . . . . . . . . . 84 The Chokwe Storytellers from Angola. . . . . . 85 9: REPEATING PATTERNS. . . . . . . . . . . . . . . . . . . 122 Decorations on the Walls from Angola . . . . . 87 Yup’ik Eskimo Border Patterns How the World Began from Angola. . . . . . . . 88 from Alaska. . . . . . . . . . . . . . . . . . . . . . . 123 Children’s Networks from Congo . . . . . . . . . 90 The Covenant Belt, Native American. . . . . . 125 African Patterns from Congo . . . . . . . . . . . 127 7: GEOMETRY ALL AROUND US . . . . . . . . . . . . . . . . 92 Patchwork Quilts from the U.S.A.. . . . . . . . 130 The Olympic Games Symbol. . . . . . . . . . . . . 94 Adinkra Cloth from Ghana. . . . . . . . . . . . . 133 The Yin-Yang Symbol from China. . . . . . . . . 95 Tessellations in Islamic Culture . . . . . . . . . 135 The Dream Catcher, Native American. . . . . . 96 Polygon Patterns, Islamic . . . . . . . . . . . . . . 136 The Tipi, Native American . . . . . . . . . . . . . . 98 Be a Tessellation Artist, Islamic . . . . . . . . . 138 Round Houses in Kenya. . . . . . . . . . . . . . . 100 Cone-Cylinder Houses in Kenya . . . . . . . . . 101 10: SELECTED ANSWERS. . . . . . . . . . . . . . . . . . . 140 Tangram Polygons from China . . . . . . . . . . 103 The Pyramids of Ancient Egypt. . . . . . . . . . 105 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . 144 The Parthenon in Greece . . . . . . . . . . . . . . 107 Pueblo Buildings in the U.S.A. . . . . . . . . . . 108 A WORD ABOUT UNICEF . . . . . . . . . . . . . . . . . . . 146 Front matter_Front matter 12/7/10 10:43 AM Page viii Introduction D id you know that some of You will exercise your brain as Most of the activities are self- the games that kids play you solve puzzles like the African checking—you will know whether were invented hundreds, children’s network that a they are correct. See Chapter 10 even thousands, of years ago? European scientist said was for the answers to some of these Today you can play computer “impossible.” You will follow the activities, but you probably won’t versions of Tic-tac-toe and Oware, lead of Islamic artists who made need them. It’s much more games that go back at least 3,300 beautiful patterns using only a satisfying to work out the solution years to ancient Egypt. compass and a straightedge yourself, even if it takes a while. The games, puzzles, and (unmarked ruler). You will design In this book you will read about projects in this book come from all and decorate game boards and two types of games for two or parts of the world—Africa, Asia, make the game pieces you will more people—games of strategy Europe, North America, and the need to play some of the games. and games of chance. Some island nations of Hawaii, the You will make models of the games require a game board and Philippines, and New Zealand homes that different people certain types of playing pieces or (called Aotearoa by the Maori around the world live in. counters. Players must decide how people who first lived there). These In all of these activities you will they are going to move their pieces activities will introduce you to the be using math. Many of these on the board. These are called people who played the games, who math ideas are probably different games of strategy. Another kind of solved the puzzles, and who from the math you learn in game depends upon the way the designed the art. school. If a puzzle or activity pieces fall. The players have no doesn’t work out at first, just keep control over the outcome of the N O I trying. Read the hints and game, and such games are called T C suggestions carefully. You might games of chance. U D want to discuss the problem with O R T a friend, teacher, or family N I member. Two heads are better than one! viii Front matter_Front matter 12/7/10 10:43 AM Page ix It is interesting to see how a Many of these games call for two In traditional games of strategy game changes as it travels from kinds of counters or markers. for two players, one side wins and one place to another and is Kings and princes used to play the other side loses. Each player passed along from ancient times with beautiful pieces made of gold should have an equal chance of to the present. Three-in-a-row and ivory. Ordinary people used winning. In some games the first games and mankala games are pebbles, seeds, or bits of twig, player to move is more likely to good examples. You will learn peeled and unpeeled. You can use win. Players should take turns several versions of each of these red and black checkers or two going first in this type of game. games. kinds of coins, beans, or buttons. Perhaps you can figure out The games of strategy require Or you might like to make your changes in the rules so that both several types of game boards. own special counters. players are winners. Cooperation Although you can draw them on Most of the games of strategy may be more rewarding than paper, you will probably want are for two players or two teams. competition. boards that last for a while. Use You can also play them by your- You may want to vary the sections of cardboard or mat self. Pretend that you are two games. A slight change in the board, and draw the lines neatly people, and play on both sides of rules, or in the shape of the game with the help of a ruler. It’s a good the board. This is a good way to board, or in the number of idea to make a pattern on a sheet learn a new game or to work out counters may call for an entirely of scratch paper first. Be sure you the fine points of strategy, as different strategy. Just be sure measure carefully. though you were solving a puzzle. that both players agree on the Some people play games just to new rules before the game starts. win and get upset when they lose. Most important—have fun! Playing a game should be fun. When one player always wins, the other player must always lose and may give up after a while. Helping an opponent to improve his or her skills makes the game more interesting for both players. I N T R O D U C T I O N ix