Mathematical Activities: A Resource Book For Teachers (cambridge Educational)

This page intentionally left blank MATHEMATICAL ACTIVITIES A resource book for teachers Brian Bolt CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521285186 © Cambridge University Press 1982 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 1982 ISBN-13 978-0-511-41362-9 eBook (EBL) ISBN-13 paperback 978-0-521-28518-6 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Page numbers in italics refer to the commentary. Preface xi Introduction xii 1. Three in a line (a geometric investigation) 1 133 2. Pawns on a chessboard (an extension of Activity 1) 2 134 3. Avoid three (a geometric game for two players) 2 134 4. Curves of pursuit (a geometric construction) 3 134 5. The misguided missiles (an extension of Activity 4) 4 134 6. Pattern (a geometric pattern based on Activity 5) 5 134 7. Two halves make a whole (a geometric puzzle) 5 135 8. Make your own dice (a three-dimensional puzzle) 6 135 9. Matchstick triangles (a matchstick puzzle) 6 135 10. The farmer's sheep-pens (a geometric puzzle) 6 136 11. Map folding (a paper folding puzzle) 7 136 12. A tricky river crossing (a spatial puzzle) 7 136 13. Stretching a circle (a geometric construction) 8 136 14. The ellipse (an environmental investigation) 9 136 15. Paper-folding an ellipse (a geometric constructions) 10 136 16. An ellipse using string and drawing pins (a practical geometric construction) 11 136 17. The sliding ladder (a practical geometric construction and investigation) 11 136 18. The growing network (a spatial game for two players) 13 137 19. Cubism (a three-dimensional puzzle) 14 137 20. Matchstick squares (a matchstick puzzle) 14 137 21. The square, cross and circle (a three-dimensional puzzle) 15 138 22. The baffled engine driver (a railway shunting puzzle) 15 138 23. The ingenious milkman (a measuring puzzle) 15 138 24. The army's predicament (a river-crossing puzzle) 16 138 25. Curves of constant breadth (a geometric investigation) 16 139 26. The Mobius band (a practical geometric activity) 18 139 27. Inside or outside (a spatial investigation) 20 139 28. Rolling along (a geometric investigation) 21 140 29. Which way is the wheel moving? (a geometric investigation) 22 140 30. Gear trains (analysing the mathematics of gear wheels) 22 141 31. Hex (a spatial game for two players) 24 32. The knights' dance (a spatial puzzle) 26 142 33. The railway sidings (an intriguing shunting puzzle) 26 143 34. The multi-coloured cube (a tricky three-dimensional puzzle) 27 143 35. The jealous husbands (another boat puzzle) 27 144 36. The extension lead (a shortest route puzzle) 27 145 37. The economical gardener (a geometrical puzzle) 28 146 38. Perimeter and area (a pinboard investigation) 28 146 39. Tessel