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Real-Life Math: Everyday Use of Mathematical Concepts PDF

180 Pages·2002·1.502 MB·English
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Real-Life Math Real-Life Math everyday use of mathematical concepts ▼ ▲ ▲ EVAN M. GLAZER and JOHN W. McCONNELL An Oryx Book GREENWOODPRESS Westport,Connecticut • London Library of Congress Cataloging-in-Publication Data Glazer, Evan, 1971– . Real-life math : everyday use of mathematical concepts / Evan M. Glazer and John W. McConnell. p. cm. Includes bibliographical references. ISBN 0-313-31998-7 (alk. paper) 1. Mathematics—Popular works. I. McConnell, John W. II. Title. QA93 .G45 2002 510—dc21 2001058635 British Library Cataloguing in Publication Data is available. Copyright ©2002 by Evan M. Glazer and John W. McConnell All rights reserved. No portion of this book may be reproduced, by any process or technique, without the express written consent of the publisher. Library of Congress Catalog Card Number: 2001058635 ISBN: 0-313-31998-7 First published in 2002 Greenwood Press, 88 Post Road West, Westport, CT06881 An imprint of Greenwood Publishing Group, Inc. www.greenwood.com Printed in the United States of America The paper used in this book complies with the Permanent Paper Standard issued by the National Information Standards Organization (Z39.48-1984). 10 9 8 7 6 5 4 3 2 1 DEDICATED TO the mathematics teachers at Glenbrook South High School who were fearless in adapting real-world applications to their lessons, and who generously shared their best teaching ideas with us Contents ▼ ▲ ▲ Introduction, ix MATHEMATICALCONCEPTS Angle, 1 Asymptote, 7 Cartesian Coordinates, 10 Circles, 12 Circumference, 16 Complex Numbers, 16 Conic Sections, 18 Counting, 21 Derivative, 23 Equations, 23 Expected Value, 26 Exponential Decay, 28 Exponential Growth, 30 Fibonacci Sequence, 35 Imaginary Numbers, 37 Integration, 37 Inverse (Multiplicative), 43 Inverse Function, 45 Inverse Square Function, 47 viii CONTENTS Linear Functions, 49 Logarithms, 55 Logistic Functions, 58 Matrices, 61 Perimeter, 64 Periodic Functions, 67 Plane, 70 Polar Coordinates, 72 Polynomial Functions, 75 Probability, 77 Proportions, 82 Pythagorean Theorem, 87 Quadratic Functions, 89 Quadrilaterals, 93 Rates, 96 Ratio, 102 Reflections, 107 Rotations, 111 Sequences, 114 Series, 117 Similarity, 121 Slope, 124 Square Roots, 124 Standard Deviation, 127 Step Functions, 130 Surface Area, 133 Symbolic Logic, 136 Symmetry, 138 Tangent, 141 Translations, 144 Triangle Trigonometry, 146 Variation, 150 Vectors, 154 Volume, 159 Bibliography, 163 Introduction ▼ ▲ ▲ “When are we ever going to use this?” This plaintive question from frustrated mathematics students is heard in schools around our country as they wrestle with pages of abstract mathematics and learn algorithms that appear to go nowhere. They study real numbers, but don’t find any reason to believe that they are real. Thousands of American students still work from textbooks that limit applications to age problems and mixtures of nuts. Despite the call from the National Council of Teachers of Mathematics in the Principles and Standards for School Mathematics (2000) for meaningful learning through study of realistic applications, many students will find that the only modernization of content over their grandparents’ math books is that jet planes have replaced the trains that used to travel at different rates between cities. The twentieth century saw an explosion of applications of mathematics. It is now hard to find a field of study that does notuse mathematical tools. Biologists use differential equations. Chemists use solid geometry to describe molecules. Set designers in theaters use trigonometry to determine the best lighting for a play. Historians determine authorship of obscure documents through statistical analysis of words. Governments, international corporations, and individual in- vestors use mathematical rules to determine production, employment, and prices. Everybody uses computers. Unfortunately, even good students don’t know how mathematics affects their lives. Few understand the power of compound interest. Few realize that the compound interest embedded in credit cards can bring adults to bankruptcy. Few know the mathematical implications of public policies that will affect their lives. Even fewer know how to make best decisions based on the probabilities of risk rather than blind gambles. The secondary-school mathematics curriculum is faced with multiple chal- lenges. What should students know and be able to do? Proficiency in some algo- rithms is important. Abstraction in mathematics—stripping concepts of all but

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