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Creative Secondary School Mathematics: 125 Enrichment Units For Grades 7 To 12 [Pehme köide]

(City University Of New York, Usa)
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Creative Secondary School Mathematics: 125 Enrichment Units For Grades 7 To 12Suurem pilt
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There are many topics within the scope of the secondary school mathematics curriculum that are clearly of a motivational sort, and because of lack of time they are usually not included in the teaching process. This book provides the teacher 125 individual units — ranging from grades 7 through 12 — that can be used to enhance the mathematics curriculum. Each unit presents a preassessment, instructional objectives, and a detailed description of the topic as well as teaching suggestions. Each unit has a post-assessment. This is the sort of instructional intervention that can make students love mathematics!

About the Author v
Preface xiii
Introduction 1(4)
Cross-Catalog of Enrichment Units
5
Unit 1 Constructing Odd-Order Magic Squares
12(4)
Unit 2 Constructing Even-Order Magic Squares
16(5)
Unit 3 Introduction to Alphametics
21(5)
Unit 4 A Checkerboard Calculator
26(5)
Unit 5 The Game of Nim
31(3)
Unit 6 The Tower of Hanoi
34(4)
Unit 7 What Day of the Week Was It?
38(10)
Unit 8 Palindromic Numbers
48(3)
Unit 9 The Fascinating Number Nine
51(6)
Unit 10 Unusual Number Properties
57(5)
Unit 11 Enrichment With a Calculator
62(4)
Unit 12 Symmetric Multiplication
66(5)
Unit 13 Variations On a Theme --- Multiplication
71(6)
Unit 14 Ancient Egyptian Arithmetic
77(4)
Unit 15 Napier's Rods
81(2)
Unit 16 Unit Pricing
83(2)
Unit 17 Successive Discounts and Increases
85(4)
Unit 18 Prime and Composite Factors of a Whole Number
89(4)
Unit 19 Prime Numeration System
93(4)
Unit 20 Repeating Decimal Expansions
97(4)
Unit 21 Peculiarities of Perfect Repeating Decimals
101(3)
Unit 22 Patterns in Mathematics
104(4)
Unit 23 Googol and Googolplex
108(4)
Unit 24 Mathematics of Life Insurance
112(3)
Unit 25 Geometric Dissections
115(4)
Unit 26 The Klein Bottle
119(3)
Unit 27 The Four-Color Map Problem
122(4)
Unit 28 Mathematics On a Bicycle
126(5)
Unit 29 Mathematics and Music
131(4)
Unit 30 Mathematics in Nature
135(6)
Unit 31 The Birthday Problem
141(3)
Unit 32 The Structure of the Number System
144(4)
Unit 33 Excursions in Number Bases
148(3)
Unit 34 Raising Interest
151(4)
Unit 35 Reflexive, Symmetric, and Transitive Relations
155(4)
Unit 36 Bypassing An Inaccessible Region
159(4)
Unit 37 The Inaccessible Angle
163(3)
Unit 38 Triangle Constructions
166(5)
Unit 39 The Criterion of Constructibility
171(5)
Unit 40 Constructing Radical Lengths
176(2)
Unit 41 Constructing a Pentagon
178(3)
Unit 42 Investigating the Isosceles Triangle Fallacy
181(4)
Unit 43 The Equiangular Point
185(4)
Unit 44 The Minimum-Distance Point of a Triangle
189(4)
Unit 45 The Isosceles Triangle Revisited
193(4)
Unit 46 Reflective Properties of the Plane
197(5)
Unit 47 Finding the Length of a Cevian of a Triangle
202(5)
Unit 48 A Surprising Challenge
207(3)
Unit 49 Making Discoveries in Mathematics
210(2)
Unit 50 Tessellations
212(4)
Unit 51 Introducing the Pythagorean Theorem
216(7)
Unit 52 Trisection Revisited
223(4)
Unit 53 Proving Lines Concurrent
227(5)
Unit 54 Squares
232(2)
Unit 55 Proving Points Collinear
234(4)
Unit 56 Angle Measurement With a Circle
238(4)
Unit 57 Trisecting a Circle
242(4)
Unit 58 Ptolemy's Theorem
246(4)
Unit 59 Constructing Π
250(4)
Unit 60 The Arbelos
254(4)
Unit 61 The Nine-Point Circle
258(3)
Unit 62 The Euler Line
261(3)
Unit 63 The Simson Line
264(4)
Unit 64 The Butterfly Problem
268(4)
Unit 65 Equicircles
272(5)
Unit 66 The Inscribed Circle and the Right Triangle
277(5)
Unit 67 The Golden Rectangle
282(5)
Unit 68 The Golden' Triangle
287(5)
Unit 69 Geometric Fallacies
292(5)
Unit 70 Regular Polyhedra
297(4)
Unit 71 An Introduction to Topology
301(4)
Unit 72 Angles On a Clock
305(3)
Unit 73 Averaging Rates --- the Harmonic Mean
308(4)
Unit 74 Howlers
312(4)
Unit 75 Digit Problems Revisited
316(3)
Unit 76 Algebraic Identities
319(4)
Unit 77 A Method for Factoring Trinomials of the Form Ax1 + Bx + C
323(3)
Unit 78 Solving Quadratic Equations
326(5)
Unit 79 The Euclidean Algorithm
331(4)
Unit 80 Prime Numbers
335(4)
Unit 81 Algebraic Fallacies
339(5)
Unit 82 Sum Derivations With Arrays
344(5)
Unit 83 Pythagorean Triples
349(5)
Unit 84 Divisibility
354(5)
Unit 85 Fibonacci Sequence
359(5)
Unit 86 Diophantine Equations
364(3)
Unit 87 Continued Fractions and Diophantine Equations
367(5)
Unit 88 Simplifying Expressions Involving Infinity
372(5)
Unit 89 Continued Fraction Expansion of Irrational Numbers
377(5)
Unit 90 The Farey Sequence
382(3)
Unit 91 The Parabolic Envelope
385(5)
Unit 92 Application of Congruence to Divisibility
390(5)
Unit 93 Problem Solving --- a Reverse Strategy
395(6)
Unit 94 Decimals and Fractions in Other Bases
401(2)
Unit 95 Polygonal Numbers
403(8)
Unit 96 Networks
411(5)
Unit 97 Angle Trisection --- Possible Or Impossible?
416(3)
Unit 98 Comparing Means
419(5)
Unit 99 Pascal's Pyramid
424(4)
Unit 100 The Multinomial Theorem
428(4)
Unit 101 Algebraic Solution of Cubic Equations
432(5)
Unit 102 Solving Cubic Equations
437(7)
Unit 103 Calculating Sums of Finite Series
444(5)
Unit 104 A General Formula for the Sum of Series of the Former
449(6)
Unit 105 A Parabolic Calculator
455(4)
Unit 106 Constructing Ellipses
459(5)
Unit 107 Constructing the Parabola
464(5)
Unit 108 Using Higher Plane Curves to Trisect An Angle
469(4)
Unit 109 Constructing Hypocycloid and Epicycloid Circular Envelopes
473(4)
Unit 110 The Harmonic Sequence
477(3)
Unit 111 Transformations and Matrices
480(6)
Unit 112 The Method of Differences
486(4)
Unit 113 Probability Applied to Baseball
490(3)
Unit 114 Introduction to Geometric Transformations
493(6)
Unit 115 The Circle and the Cardioid
499(5)
Unit 116 Complex-Number Applications
504(5)
Unit 117 Hindu Arithmetic
509(4)
Unit 118 Proving Numbers Irrational
513(3)
Unit 119 How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems
516(3)
Unit 120 The Three Worlds of Geometry
519(7)
Unit 121 The Mix
526(2)
Unit 122 Graphical Iteration
528(3)
Unit 123 The Feigenbaum Plot
531(3)
Unit 124 The Sierpinski Triangle
534(3)
Unit 125 Fractals
537