The Play's the Thing

Alan Lipp

Description

Presents 18 mathematical games and develops the concepts of game analysis and winning strategies.

The book presents 18 games and develops the concepts of game analysis and winning strategies. Students are encouraged to play these mathematical games together, collect data developed through their play, and analyze the data to develop a winning strategy. The book provides the basis for a six- to eight-week unit on mathematical games. Each chapter also functions as a self-contained and independent exploration so that selected chapters may be used as supplementary classroom investigations or as independent projects. The book includes both familiar games (such as Quadrangles and Nim) and many others that will be new and exciting to most readers. Through the exploration of mathematical games, ‘The Play’s the Thing’ introduces teachers and students to the fun of play and to the mathematics behind the fun.

Acknowledgements; Prologue: To the Teacher; Act 0: To the Student; Act 1: Blockers; Act 2: Nimble; Act 3: More Variations; Act 4: Take Away 1, 2, 3; Act 5: Two Piles:  A Hidden Game; Act 6: Two Piles 1, 2, 3; Act 7: Nim; Act 8: Flit; Act 9: Mr Flit; Act 10: Landis; Act 11: Add’em Up; Act 12: Connect-the-Dots; Act 13: Boxes; Act 14: Hold That Line; Act 15: The Fifteen Game; Act 16: Sliders; Act 17: Lynch; Act 18: Progression: Down and Up; Act 19: Harder Stuff; Answers

Sujets

• Mathematics

Informations

• Publié par: Anthem Press
• Date de parution: 01 février 2011
• Nombre de lectures: 0
• EAN13: 9780857288714
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

The Play’s the Thing

The Play’s the Thing

Mathematical Games for the Classroom and Beyond

Alan Lipp

Anthem Press An imprint of Wimbledon Publishing Company www.anthempress.com

This edition rst published in UK and USA 2011 by ANTHEM PRESS 75-76 Blackfriars Road, London SE1 8HA, UK or PO Box 9779, London SW19 7ZG, UK and 244 Madison Ave. #116, New York, NY 10016, USA

Copyright © Alan Lipp 2011

The author asserts the moral right to be identied as the author of this work.

All rights reserved. Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without the prior written permission of both the copyright owner and the above publisher of this book.

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library.

Library of Congress Cataloging in Publication Data Lipp, Alan. The plays the thing : mathematical games for the classroom and beyond / Alan Lipp. p. cm. ISBN 978-0-85728-666-6 (papercover : alk. paper) 1. Mathematical recreations. 2. MathematicsStudy and teaching. I. Title. QA95.L764 2011 510.71 dc22 2010051140

ISBN-13: 978 0 85728 666 6 (Pbk) ISBN-10: 0 85728 666 8 (Pbk)

This title is also available as an eBook.

Dedication

To my brother Michael who rst taught me to love mathematics, and to my father Sunny who taught me to love teaching.

The Acts

Acknowledgments

Prologue To the Teacher

Act 0

Act 1

Act 2

Act 3

Act 4

Act 5

To the Student

Blockers Act 1 Exercises

Nimble Act 2 Exercises

More Variations Act 3 Exercises

Take Away 1, 2, 3 Looking for a Strategy Act 4 Exercises

Two Piles: A Hidden Game Scene 1 Scene 2 Scene 3 Scene 3 Exercises

vii

x

i

xiii

xv

1 2

5 6

9 10

13 13 14

17 17 17 18 19

viii

Act 6

Act 7 Act 8

Act 9

Act 10

Act 11

Two Piles 1, 2, 3 Scene 1 Scene 2 Scene 2 Exercises Scene 3 Scene 3 Exercises Scene 4 Scene 4 Exercises Scene 5 Scene 5 Exercises

Nim Scene 1 Scene 1 Exercises Scene 2 Scene 2 Exercises Scene 3 Scene 3 Exercises Bouton’s Strategy

Flit Act 8 Exercises

Mr Flit Scene 1 Scene 1 Exercises Scene 2 Scene 2 Exercises

Landis Act 10 Exercises

Add’em Up Act 11 Exercises

The Play’s the Thing

21 21 21 22 22 23 23 23 24 26

29 29 30 30 31 32 33 35

37 38

41 41 42 42 43

47 48

51 52

The Acts

Act 12

Act 13

Act 14

Act 15

Act 16

Act 17

Act 18

Act 19

Answers

ConnecttheDots Act 12 Exercises

Boxes Act 13 Exercises

Hold That Line Act 14 Exercises

The Fifteen Game Act 15 Exercises

Sliders Act 16 Exercises

Lynch Act 17 Exercises

Progression: Down and Up Scene 1: Going Down Scene 1 Exercises Scene 2: Growing Up Scene 2 Exercises Scene 3: Staircase Scene 3 Exercises

Harder Stuff Scene 1: Nimble Scene 2: Variations of Take Away 1, 2, 3 Scene 3: Blockers Scene 4: Take Away 1, 2, 3 Scene 5: Two Piles 1, 2, 3 Scene 6: Nim Scene 7: Flit

ix

55 55

59 60

65 66

69 70

73 75

76 78

81 81 82 83 83 85 85

87 87 89 89 90 90 92 94

9

7