E-Book, Englisch, 258 Seiten, Web PDF
Fletcher / Howell / Plumpton Mathematics with Understanding
1. Auflage 2014
ISBN: 978-1-4831-5340-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
The Commonwealth and International Library: Mathematical Topics, Volume 2
E-Book, Englisch, 258 Seiten, Web PDF
ISBN: 978-1-4831-5340-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Mathematics with Understanding: Book 2 is an eight-chapter book that begins with an explanation of the number systems. Fractions, rational numbers, systems of integers, algebraic relations, shape, and measurement are then described. The modular arithmetic and groups as well as probability are also explained. This book will be useful to students and teachers for a deeper understanding of the structure behind many mathematical ideas and processes.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Mathematics With Understanding: Book 2 ;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. NUMBER SYSTEMS;10
6.1;Introduction;10
6.2;Binary Operations;12
6.3;Closure;14
6.4;The Whole Numbers and the Integers;16
6.5;The Rationale;18
6.6;The Rational Numbers on a Number Line;20
6.7;The Irrational Numbers;22
6.8;Rational and Irrationals expressed in Decimal Form;25
7;CHAPTER 2. FRACTIONS AND RATIONAL NUMBERS;30
7.1;Introduction;30
7.2;The Fraction Symbol;31
7.3;Developing the Idea of a Fraction;32
7.4;Equivalent Fractions;39
7.5;Mixed Numerals;50
7.6;Addition of Fractions;55
7.7;The Subtraction Idea;61
7.8;Multiplication;63
7.9;Division of Fractions;66
7.10;Summary;69
8;CHAPTER 3. THE SYSTEM OF INTEGERS;71
8.1;Introduction;71
8.2;Into the Classroom;71
8.3;Addition;73
8.4;Negative Integers;75
8.5;Summary;79
8.6;Subtraction;81
8.7;Summary;87
8.8;Further Notes;89
9;CHAPTER 4. ALGEBRAIC RELATIONS;92
9.1;Introduction;92
9.2;Cartesian Products (or Cartesian Cross-products);94
9.3;Relations as Subsets of Cartesian Products;95
9.4;Graphs from a "Two-table";98
9.5;Graphs of Inequalities;103
9.6;Continuous Straight-line Graphs;106
9.7;Exercises;108
9.8;Worked Solutions to Exercises;109
9.9;Straight-line Graphs;113
9.10;Discovering Relations;119
9.11;Discovery of p;120
9.12;Distance-Time Graphs;122
9.13;Some Curved Graphs;124
9.14;Exercises;128
9.15;Solutions to Exercises;128
10;CHAPTER 5. SHAPE;132
10.1;Symmetry;136
10.2;Rigidity;147
10.3;Tessellations;150
10.4;Geometrical Models;156
10.5;Similarity;157
10.6;Pattern;161
11;CHAPTER 6. MEASUREMENT;167
11.1;Introduction;167
11.2;The Early Stages;168
11.3;The Theory of Measures;170
11.4;The Classroom Situation;172
11.5;Applications of General Principles to Length, Area and Angular Measurement;175
12;CHAPTER 7. MODULAR ARITHMETIC AND GROUPS;186
12.1;3+1 = 0 ???;186
12.2;Leading to the Idea of a Type of Structure known as a Group;197
12.3;The Distributive Property of Multiplication over Addition;199
12.4;Closure;202
13;CHAPTER 8. PROBABILITY;210
13.1;Introduction;210
13.2;Simple Ideas on Probability Theory;213
13.3;Non-equiprobable Sample Spaces;216
13.4;Double Experiments;220
13.5;Mutually Exclusive Events;224
13.6;Independent Events;225
13.7;Conditional Probability;228
13.8;Probability Trees;232
13.9;The Classroom Situation;237
13.10;Experiments;238
14;APPENDIX A ASSIGNMENT CARDS;241
15;APPENDIX B CHECK CARDS;248
15.1;Sample Discussion Checks;248
16;INDEX;258
