Elementary School Mathematics For Parents And Teachers - Volume 2 available in Hardcover, Paperback, eBook
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Elementary School Mathematics For Parents And Teachers - Volume 2
- ISBN-10:
- 9813108932
- ISBN-13:
- 9789813108936
- Pub. Date:
- 05/23/2017
- Publisher:
- World Scientific Publishing Company, Incorporated
- ISBN-10:
- 9813108932
- ISBN-13:
- 9789813108936
- Pub. Date:
- 05/23/2017
- Publisher:
- World Scientific Publishing Company, Incorporated
![Elementary School Mathematics For Parents And Teachers - Volume 2](http://img.images-bn.com/static/redesign/srcs/images/grey-box.png?v11.9.4)
Elementary School Mathematics For Parents And Teachers - Volume 2
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$48.00Overview
MAA ReviewsThis book covers the elementary school mathematics curriculum common in most parts of the world. Its aim is to serve educators (teachers and parents) as a guide for teaching mathematics at elementary school level. The book focuses both on content knowledge and on pedagogical content knowledge. It bridges the gap between fundamental mathematical principles and good teaching practices. It also offers the reader a glimpse on how mathematicians perceive elementary mathematics and presents ideas for specific mathematical activities.Volume 2 focuses on content taught in the higher grades of elementary school. It covers the following topics: multiplication and division of multi-digit numbers, divisibility and primality, divisibility signs, sequences, fractions and their representations, and fraction arithmetic.The author is also a co-founder of Matific, an adaptive game-based teaching and learning tool for primary school mathematics. Independent studies have shown Matific to improve test scores, reduce maths anxiety, and increase motivation. Matific is available in 26 languages and aligned to mathematics curricula in 46 countries. Awards include Best Mathematics Instructional Solution, Best Game-Based Curriculum Solution and Best Educational App. For a trial, visit https://www.matific.com.
Product Details
ISBN-13: | 9789813108936 |
---|---|
Publisher: | World Scientific Publishing Company, Incorporated |
Publication date: | 05/23/2017 |
Pages: | 304 |
Product dimensions: | 7.00(w) x 9.90(h) x 0.60(d) |
Table of Contents
Preface v
Acknowledgments xi
19 Multiplication of Multi-Digit Numbers 1
19.1 Repeated addition 2
19.1 Products of one-significant-digit numbers 3
19.2 Products of a single-digit number and a multi-digit number 6
19.3.1 Using the distributive property 6
19.3.2 Multiplication without regrouping 10
19.3.3 Multiplication with regrouping 12
19.4 Products of multi-digit numbers 14
19.4.1 Using the distributive property 14
19.4.2 Multiplication with regrouping 16
19.5 Mental calculations 19
19.6 Other multiplication algorithms 19
19.6.1 Napier bones 20
19.6.2 The binary algorithm 22
19.6.3 The peasants' algorithm 23
20 Division of Multi-Digit Numbers 29
20.1 Division without regrouping 32
20.1.1 Using the distributive property 32
20.1.2 Algorithm 33
20.2 Division with regrouping 34
20.2.1 First regroup and then evaluate 34
20.2.2 Illustrating the division process 36
20.2.3 Long division: Step-by-step 40
20.3 Division by a multi-digit number 43
20.4 Chunking 45
21 The Order of Operations 49
21.1 Problem statement 50
21.2 From computation networks to arithmetic expressions 52
21.3 Parentheses 53
21.4 Precedence of operations 55
21.4.1 Deleting redundant parentheses 57
22 Division with a Remainder 61
22.1 Remainders 62
22.1.1 Notation 64
22.1.2 The range of the remainder 65
22.1.3 Inverse multiplication equation 66
22.2 Word problems 68
22.3 Evaluating division with a remainder 70
22.4 Arithmetic of remainders 72
22.4.1 Odd and even numbers 72
22.4.2 Modulo-3 classification of integers 74
22.4.3 Modulo-3 addition 76
22.4.4 Modulo-3 multiplication 78
23 Prime and Composite Numbers 85
23.1 Multiples and divisors 85
23.1.1 Properties of multiples and divisors 87
23.1.2 Enumerating the divisors of a given number 88
23.2 Prime numbers 89
23.2.1 Prime and composite numbers 89
23.2.2 The fundamental theorem of arithmetic 90
23.2.3 Why is 1 not a prime number? 94
23.2.4 Prime number factorization: The fingerprints of natural numbers 95
23.3 Enumerating the divisors of a given number 96
23.4 Prime numbers and rectangular arrays 97
23.5 More on prime numbers 99
23.5.1 The sieve of Eratosthenes 99
23.5.2 There are infinitely many prime numbers 101
23.5.3 Large prime numbers 103
23.5.4 The density of prime numbers 103
23.5.5 Twin prime numbers 104
23.5.6 Goldbach's conjecture 105
24 Common Multiples and Common Divisors 109
24.1 Least common multiple 109
24.1.1 Common multiples 109
24.1.2 Evaluation of the least common multiple 110
24.2 Greatest common divisor 113
24.2.1 Common divisors 113
24.2.2 Evaluation of the greatest common divisor 114
24.3 Relation between least common multiple and greatest common divisor 120
25 Divisibility Rules 123
25.1 The principles underlying divisibility rules 124
25.1.1 Remainder arithmetic 124
25.1.2 Subtraction of a multiple does not change the remainder 125
25.1.3 Prime number factorization 126
25.2 Divisibility rules 126
25.2.1 Divisibility by 10 126
25.2.2 Divisibility by 5 127
25.2.3 Divisibility by 4 128
25.2.4 Divisibility by 8 130
25.2.5 Divisibility by 9 131
25.2.6 Divisibility by 3 132
25.2.7 Divisibility by 7 133
25.2.8 Divisibility by 11 135
25.3 Divisibility by composite numbers 137
25.3.1 Divisibility by 6 137
25.3.2 Divisibility by 4 138
25.3.3 Divisibility by 12 138
25.4 Validation using divisibility tests 139
26 Sequences 143
26.1 Some examples 144
26.1 Arithmetic progressions 145
26.2.1 Finding the element at a given location 145
26.2.2 Arithmetic series 146
26.3 Geometric progressions 149
26.3.1 Exponential growth 150
26.3.1 Exponential decay 150
26.3.1 Geometric progressions in daily life 150
26.4 Square numbers 151
26.4 Triangular numbers 152
26.4 The Fibonacci sequence 153
26.6.1 Fibonacci numbers in daily life 154
26.6.1 The golden ratio 156
26.7 The isoperimetric problem 157
26.8 The sequence of factorials 159
27 Fractions 163
27.1 Natural numbers and fractions 164
27.1.1 Natural numbers as quantifiers 164
27.1.2 Fractions as quantifiers 166
27.2 Unit fractions 168
27.2.1 Definition 168
27.2.2 Quantifying with unit fractions 169
27.3 General fractions 173
27.3.1 Definition 173
27.3.2 Quantifying with general fractions 174
27.3.3 The rational numbers 176
27.4 Fractions in early history 177
27.5 Fractions as part of a quantity 178
28 Quotients of Natural Numbers 181
28.1 Division of natural numbers 182
28.2 Equivalent fractions 184
28.2.1 Equivalent fractions and multiplicative scaling 185
28.2.2 Infinitude of equivalent fractions 186
28.2.3 Natural numbers as fractions 187
28.2.4 Expansion and reduction 189
28.3 Improper fractions and mixed numbers 191
28.3.1 Improper fractions 191
28.3.2 Mixed numbers 191
28.3.3 From improper fractions to mixed numbers 192
28.3.4 From mixed numbers to improper fractions 193
29 Fraction Comparison 195
29.1 Order relations and inclusion 196
29.2 Fraction comparison 197
29.2.1 Comparison using concrete models 198
29.2.2 Fractions with like denominators 201
29.2.3 Fractions with like numerators 202
29.2.4 Finding a common denominator 203
29.2.5 Finding a common numerator 206
29.2.6 Comparison using an intermediary 207
29.3 Factions on the number line 208
29.4 Density of the rational numbers 209
29.5 McKay's theorem 210
30 Fraction Addition and Subtraction 215
30.1 The meaning of fraction addition 216
30.2 The meaning of fraction subtraction 218
30.3 Evaluation of fraction addition and subtraction 220
30.3.1 Using concrete models 220
30.3.2 Fractions with like denominators 223
30.3.3 Fractions with unlike denominators 225
30.4 Fractions in ancient Egypt 227
31 Fraction Multiplication 231
31.1 Numbers and multiplication revisited 232
31.1.1 The number concept revisited 232
31.1.2 Multiplication revisited 234
31.2 Evaluating products 239
31.2.1 Fractions multiplied by natural numbers 240
31.2.2 Natural numbers multiplied by fractions 241
31.2.3 Fractions multiplied by fractions 245
31.3 Multiplicative inverses 250
31.4 Is multiplication a magnifying operation? 252
32 Fraction Division 257
32.1 Division revisited 258
32.1.1 Quotients of natural numbers 259
32.1.2 Quotients of fractions 263
32.1.3 Division is inverse to multiplication 264
32.2 Evaluating quotients 266
32.2.1 Fractions divided by whole numbers 266
32.2.2 Whole number divided by fractions 268
32.2.3 Fractions divided by fractions 271
32.3 Misconceptions 275
32.3.1 Divided by two, divided by hall 275
32.3.2 Is division a reducing operation? 275
Index 279
Common Core Index 283