2011;
551 pp;
Hardcover

MSC: Primary 97; 00;

Print ISBN: 978-0-8218-5260-6

Product Code: MBK/79

List Price: $83.00

AMS Member Price: $66.40

MAA member Price: $74.70

**Electronic ISBN: 978-1-4704-1210-4
Product Code: MBK/79.E**

List Price: $83.00

AMS Member Price: $66.40

MAA member Price: $74.70

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#### Supplemental Materials

# Understanding Numbers in Elementary School Mathematics

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*Hung-Hsi Wu*

This is a textbook for pre-service elementary school teachers and for
current teachers who are taking professional development courses. By
emphasizing the precision of mathematics, the exposition achieves a
logical and coherent account of school mathematics at the appropriate
level for the readership. Wu provides a comprehensive treatment of
all the standard topics about numbers in the school mathematics
curriculum: whole numbers, fractions, and rational numbers. Assuming
no previous knowledge of mathematics, the presentation develops the
basic facts about numbers from the beginning and thoroughly covers the
subject matter for grades K through 7.

Every single assertion is established in the context of elementary
school mathematics in a manner that is completely consistent with the
basic requirements of mathematics. While it is a textbook for
pre-service elementary teachers, it is also a reference book that
school teachers can refer to for explanations of well-known but
hitherto unexplained facts. For example, the sometimes-puzzling
concepts of percent, ratio, and rate are each given a treatment that
is down to earth and devoid of mysticism. The fact that a negative
times a negative is a positive is explained in a leisurely and
comprehensible fashion.

Solutions to the activities are available electronically on the
Supplemental Materials page.

Selected solutions are available electronically for instructors
only. Please send email to textbooks@ams.org for more
information.

#### Readership

Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics.

#### Reviews & Endorsements

[This book] delivers the mathematical knowledge that elementary-grades teachers need.

-- American Educator

#### Table of Contents

# Table of Contents

## Understanding Numbers in Elementary School Mathematics

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xv16 free
- Acknowledgments xxi22 free
- To the reader xxv26 free
- Some conventions in this book xxxi32 free
- Part 1. Whole numbers 134 free
- Place value 538
- The basic laws of operations 3972
- The standard algorithms 5790
- The addition algorithm 6194
- The subtraction algorithm 71104
- The multiplication algorithm 85118
- The long division algorithm 95128
- The number line and the four operations revisited 127160
- What is a number? 135168
- Some comments on estimation 139172
- Numbers in base 𝑏 155188
- Part 2. Fractions 171204
- Definitions of fraction and decimal 177210
- Equivalent fractions and FFFP 203236
- Addition of fractions and decimals 221254
- Equivalent fractions: further applications 235268
- Subtraction of fractions and decimals 253286
- Multiplication of fractions and decimals 261294
- Division of fractions 283316
- Complex fractions 309342
- Percent 319352
- Fundamental Assumption of School Mathematics (FASM) 331364
- Ratio and rate 335368
- Some interesting word problems 357390
- On the teaching of fractions in elementary school 367400
- Part 3. Rational numbers 373406
- The (two-sided) number line 375408
- A different view of rational numbers 379412
- Adding and subtracting rational numbers 381414
- Adding and subtracting rational numbers redux 395428
- Multiplying rational numbers 403436
- Dividing rational numbers 413446
- Ordering rational numbers 421454
- Part 4. Number theory 431464
- Divisibility rules 435468
- Primes and divisors 445478
- The Fundamental Theorem of Arithmetic (FTA) 455488
- The Euclidean algorithm 463496
- Applications 473506
- Pythagorean triples 487520
- Part 5. More on decimals 491524
- Why finite decimals are important 495528
- Review of finite decimals 497530
- Scientific notation 505538
- Decimals 511544
- Decimal expansions of fractions 525558
- Bibliography 541574
- Index 545578 free
- Back Cover Back Cover1586