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1、 Resources for Teaching Mathematics: 1416 T h i r d P r o o f t y p e s e t b y P i n d a r N Z Also available from Continuum 50 Mathematics Lessons, Colin Foster 100+ Ideas for Teaching Mathematics, Mike Ollerton Getting the Buggers to Add Up, 2nd edition, Mike Ollerton Resources for Teaching Mathe
2、matics: 1416 Colin Foster A companion website to accompany this book is available online at: Please visit the link and register with us to receive your password and to access these downloadable resources. If you experience any problems accessing the resources, please contact Continuum at: info Conti
3、nuum International Publishing Group Th e Tower Building 80 Maiden Lane, Suite 704 11 York Road New York, NY 10038 London SE1 7NX Colin Foster 2010 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photoc
4、opying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. Colin Foster has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identi- fi ed as Author of this work. British Library Cataloguing-in-Publication D
5、ata A catalogue record for this book is available from the British Library. ISBN: 9780826436030 (paperback) Library of Congress Cataloging-in-Publication Data Foster, Colin. Resources for teaching mathematics 1416 / Colin Foster. p. cm. (Resources for teaching) Includes index. ISBN 978-0-8264-3603-0
6、 (pbk.) 1. MathematicsStudy and teaching (Secondary) 2. Curriculum planning. 3. Lesson planning. I. Title. II. Series. QA11.F69 2010 510.71 2dc22 Typeset by Pindar NZ, Auckland, New Zealand Printed and bound in Great Britain by Bell released into the public domain by the author, who disclaims any le
7、gal liability arising from its use . I would like to thank the teams at Continuum and Pindar for all their hard work and I would particularly like to thank John Cooper and Tim Honeywill, among many other wonderful col- leagues, for numerous extremely helpful conversations and some solutions! Most of
8、 all, I would also like to thank the many learners who have put their energy into these tasks and taught me more about how people learn mathematics. And thank you to Megan Gay (Year 10) for the drawing on page 158. ix Introduction Resources For Teaching Mathematics: 1416 comprises 70 lesson plans co
9、vering many topics com- monly encountered at this age. Th e lessons seek to draw learners into thinking about the various ideas by posing questions and tasks that are not straightforward or routine. Learners of any level of prior attainment can gain satisfaction from thinking carefully about worthwh
10、ile mathematics, and although some lessons mainly target a Higher Tier GCSE (or IGCSE) topic, in the hands of a skilful teacher, many would work well for all learners, however they are grouped or setted. Much of the material is designed to be divergent, with learners self-diff erentiating according
11、to their current skills, interest, speed or mood. It is to be expected that diff erent learners, beginning with the same starting point, will fi nish in quite diff erent places. Answers are given for the teacher s convenience rather than to suggest that they should be the optimum endpoint for everyo
12、ne. It helps if the teacher is not too rigid in his/her mind about what the proper route should be or how far learners must get during a particular lesson. Th e notion of fi nishing off is problematic for many mathematics teachers when working with rich tasks, since when a mathematician answers one
13、question they are likely to fi nd themselves asking others. Th e lessons are described under headings that indicate a possible beginning of the lesson ( Lesson Starter ), a middle (referred to as Main Lesson ) and a suggested whole-class discussion to end ( Plenary ), but clearly a successful mathem
14、atics lesson does not have to follow that pattern slavishly. Beginning with a plenary or having one or more plenaries in the middle, or omitting a starter, etc., are all viable options, so there is no need to be too regimented about such matters. Th e teacher should not feel dictated to by resources
15、 such as this book and must be free to adapt, respond- ing professionally to learners progress, comments, questions and interests, and using their skills to lead the lesson in the most benefi cial way possible. Photocopiable task sheets are provided for each lesson to help learners engage with the t
16、asks at their own pace. Likely outcomes and objectives are indicated to help the teacher to think in advance about what may arise and what opportunities are available. Possible homework tasks are suggested, as are ways of extending the ideas for early fi nishers or those very confi dent with the topic. Th ere are also suggestions of ways that a learner who fi nds the work particularly diffi cult might begin. On many occasions in these lessons, learners
