2020;
402 pp;
Softcover

MSC: Primary 97; 00;

**Print ISBN: 978-1-4704-5675-7
Product Code: MBK/131**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

**Electronic ISBN: 978-1-4704-6004-4
Product Code: MBK/131.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

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#### Supplemental Materials

# Rational Numbers to Linear Equations

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*Hung-Hsi Wu*

This is the first of three volumes that,
together, give an exposition of the mathematics of grades 9–12
that is simultaneously mathematically correct and grade-level
appropriate. The volumes are consistent with CCSSM (Common Core State
Standards for Mathematics) and aim at presenting the mathematics of
K–12 as a totally transparent subject.

The present volume begins with fractions, then rational numbers,
then introductory geometry that can make sense of the slope of a line,
then an explanation of the correct use of symbols that makes sense of
“variables”, and finally a systematic treatment of linear
equations that explains why the graph of a linear equation in two
variables is a straight line and why the usual solution method for
simultaneous linear equations “by substitutions” is correct.

This book should be useful for current and future teachers of
K–12 mathematics, as well as for some high school students and
for education professionals.

#### Readership

Teachers of middle school mathematics; students and professionals interested in mathematical education.

#### Table of Contents

# Table of Contents

## Rational Numbers to Linear Equations

- Cover Cover11
- Title page iii4
- Contents vii8
- Contents of the Companion Volumes and Structure of the Chapters ix10
- Preface xi12
- To the Instructor xxvii28
- To the Pre-Service Teacher xli42
- Prerequisites xlv46
- Some Conventions xlvii48
- Chapter 1. Fractions 150
- Overview of Chapters 1 and 2 150
- 1.1. Definition of a fraction 453
- 1.2. Equivalent fractions 1968
- 1.3. Adding and subtracting fractions 3281
- 1.4. Multiplying fractions 4392
- 1.5. Dividing fractions 54103
- 1.6. Complex fractions 68117
- 1.7. Percent, ratio, and rate problems 72121
- 1.8. Appendix: The basic laws 86135

- Chapter 2. Rational Numbers 89138
- Chapter 3. The Euclidean Algorithm 137186
- Chapter 4. Basic Isometries and Congruence 157206
- Overview of Chapters 4 and 5 157206
- 4.1. The basic vocabulary, Part 1 164213
- 4.2. The basic vocabulary, Part 2 180229
- 4.3. Transformations of the plane 199248
- 4.4. The basic isometries: Rotations 216265
- 4.5. The basic isometries: Reflections and translations 229278
- 4.6. Congruence, SAS, and ASA 239288
- 4.7. A brief pedagogical discussion of proofs 252301

- Chapter 5. Dilation and Similarity 255304
- Chapter 6. Symbolic Notation and Linear Equations 297346
- 6.1. Symbolic expressions 298347
- 6.2. Solving linear equations in one variable 322371
- 6.3. Setting up coordinate systems 331380
- 6.4. Lines in the plane and their slopes 337386
- 6.5. The graphs of linear equations in two variables 351400
- 6.6. Parallelism and perpendicularity 363412
- 6.7. Simultaneous linear equations 373422

- Glossary of Symbols 385434
- Bibliography 387436
- Index 391440
- Back Cover Back Cover1452