Fletcher / Howell / Plumpton Mathematics with Understanding

1. Auflage 2014
ISBN: 978-1-4832-8079-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 190 Seiten, Web PDF

Mathematics with Understanding, Book 1 provides a guide for teaching primary mathematics. This book consists of nine main topics-aims of a modern approach; language of sets; relations and sorting; recording of number and use of different bases; open sentences, number facts and pictorial representation; natural numbers and addition; subtraction; multiplication; and division. In these topics, this text specifically discusses the union and intersection of two sets, Cardinal number of a set, and recording by means of a mapping. The collection of data, fundamental operations for natural numbers, and subtraction algorithm are also deliberated. This compilation likewise covers the Cartesian product of two sets and properties of division. This publication is recommended for math teachers intending to acquire a deeper understanding of the structure behind many mathematical ideas and processes.

Autoren/Hrsg.

Fletcher, Harold

Howell, Arnold A.

Plumpton, C.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematics with Understanding: Book 1;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. THE AIMS OF A MODERN APPROACH;10
6.1;Introduction;10
6.2;Understanding;11
6.3;Structure;13
6.4;Discovery;14
6.5;Discussion;18
6.6;Flexibility;20
6.7;Power Skill;23
6.8;Pattern;24
6.9;Pleasure, Purpose and Purity;26
6.10;Techniques and Practice;27
7;CHAPTER 2. THE LANGUAGE OF SETS;28
7.1;Sets and Subsets;28
7.2;Recording: Set Notation;29
7.3;Set Builder Form;30
7.4;Empty Set;31
7.5;Subsets;32
7.6;Universal Set;33
7.7;Union and Intersection of Two Sets;34
7.8;Disjoint Sets;35
7.9;Cardinal Number of a Set;35
7.10;Partition of a Set;36
7.11;Venn Diagrams;37
7.12;Venn Diagrams to illustrate Logical Arguments;40
7.13;Revision Exercises;42
8;CHAPTER 3. RELATIONS AND SORTING;46
8.1;Cartesian Product;47
8.2;Mapping;50
8.3;Equivalence Relations (Equals Relations);53
8.4;Equivalence Classes;55
8.5;Equivalent Sets. Cardinal Number of a Set;57
8.6;The Infant Classroom Situation;59
8.7;Number Games;71
8.8;Partitioning Sets;72
9;CHAPTER 4. RECORDING OF NUMBER AND USE OF DIFFERENT BASES;74
9.1;Bases Other Than Ten;76
9.2;Base Six;76
9.3;Number Bases for Junior Children;78
9.4;Children's Activities;79
9.5;Recording by Means of a Mapping;79
9.6;Operations Using Bases Other Than Ten;81
9.7;Decomposition;84
9.8;Equal Addition;85
9.9;Multiplication in Different Bases;86
9.10;Algorithm for Changing to Base Ten from Base Four and vice versa;87
9.11;Russian Multiplication;90
9.12;Reason Why the Method Gives the Correct Result;92
9.13;Bicimals;93
9.14;Pattern in Other Bases;95
10;CHAPTER 5. OPEN SENTENCES, NUMBER FACTS AND PICTORIAL REPRESENTATION;99
10.1;Open Sentence;99
10.2;Number Facts (Number Bonds);101
10.3;Counting;103
10.4;Pictorial Representation;107
10.5;Collection of Data;108
10.6;Mapping;108
10.7;Tally Chart;118
11;CHAPTER 6. NATURAL NUMBERS AND ADDITION;120
11.1;Fundamental Operations for Natural Numbers;121
11.2;Essential Property of an Operation;123
11.3;Special Properties under Addition;125
11.4;The Commutative Property;126
11.5;The Associative Property;128
11.6;Summary;131
11.7;Counting Experience;133
11.8;The Story of Number;136
12;CHAPTER 7. SUBTRACTION (GENERAL THOUGHTS);150
12.1;Summary;152
12.2;The Subtraction Algorithm;153
12.3;Using Bundles or the Abacus;157
13;CHAPTER 8. MULTIPLICATION;160
13.1;Sets: The Cartesian Product of Two Sets;160
13.2;Properties of Multiplication;165
13.3;Developing a method for multiplication;172
13.4;Situations which Lead to Discussion of Multiplication;177
14;CHAPTER 9. DIVISION;178
14.1;Defining Division: its Properties;178
14.2;Summary;184
14.3;Discussing Division in Class;187
15;INDEX;190