| Part 1. Introduction |
1 |
| Chapter 1. Preliminaries |
3 |
| 1.1. Sets, natural numbers, and whole
numbers |
3 |
| 1.2. Variables, constants, and
grouping symbols |
8 |
| 1.3. Inductive reasoning and
deductive reasoning |
13 |
| 1.4. Properties of whole number
addition and multiplication |
16 |
| 1.5. Mind stretches* |
26 |
| |
| Chapter 2. Integers |
33 |
| 2.1. What are the integers? |
33 |
| 2.2. Absolute value and addition |
37 |
| 2.3. Opposite and subtraction |
46 |
| 2.4. Implicit addition and order |
52 |
| 2.5. Multiplication and division |
57 |
| 2.6. Properties of integer addition,
multiplication, and equality |
66 |
| 2.7. Story problems |
71 |
| 2.8. Mind stretches* |
77 |
| |
| Chapter 3. First taste of algebra |
83 |
| 3.1. Exponents |
83 |
| 3.2. Terms and expressions |
87 |
| 3.3. Combining like terms |
95 |
| 3.4. Opposite of an expression |
99 |
| 3.5. Mind stretches* |
105 |
| |
| Chapter 4. Rational numbers I:
multiplication and division |
111 |
| 4.1. What are the rational numbers? |
111 |
| 4.2. Multiplication |
127 |
| 4.3. Reducing and building fractions |
133 |
| 4.4. Prime factorization * |
144 |
| 4.5. Reciprocal and division |
150 |
| 4.6. Mind stretches* |
161 |
| |
| Chapter 5. Rational numbers II:
addition and subtraction |
167 |
| 5.1. Absolute value, opposite,
addition, and subtraction |
167 |
| 5.2. More addition and subtraction,
order |
176 |
| 5.3. Properties of rational addition,
multiplication, and equality |
188 |
| 5.4. Mind stretches* |
194 |
| |
| Part 2. Application |
197 |
| Chapter 6. Linear equations and story
problems |
199 |
| 6.1. Equations and solutions |
199 |
| 6.2. Linear equations in one
variable: part 1 |
202 |
| 6.3. Linear equations in one
variable: part 2 |
218 |
| 6.4. Story problems |
224 |
| 6.5. Mind stretches* |
234 |
| |
| Chapter 7. Mixed numbers and decimals
numbers |
241 |
| 7.1. Mixed number representation of a
rational number |
241 |
| 7.2. Addition and subtraction of
mixed numbers |
248 |
| 7.3. Multiplication and division of
mixed numbers |
256 |
| 7.4. Decimal number representation of
a rational number |
260 |
| 7.5. The four basic operations on
decimal numbers |
273 |
| 7.6. Rounding decimal numbers and
order |
281 |
| 7.7. Small talk on using a scientific
calculator * |
286 |
| 7.8. More linear equations in one
variable |
292 |
| 7.9. Story problems |
294 |
| 7.10. Mind stretches* |
298 |
| |
| Chapter 8. Square roots and
Pythagoras’s theorem |
309 |
| 8.1. What are the real numbers? |
309 |
| 8.2. Perfect squares and square roots |
313 |
| 8.3. Pythagoras’s theorem |
324 |
| 8.4. Story problems |
333 |
| 8.5. Mind stretches* |
338 |
| |
| Chapter 9. Linear equations in two
variables and graphing |
347 |
| 9.1. Linear equations in two
variables |
347 |
| 9.2. Graphing linear equations in two
variables |
353 |
| 9.3. Mind stretches* |
363 |
| |
| Chapter 10. Ratio, proportion , and
percent |
373 |
| 10.1. Ratios |
373 |
| 10.2. Proportions |
377 |
| 10.3. Percents |
380 |
| 10.4. Story problems |
389 |
| 10.5. Mind stretches* |
396 |
| |
| Chapter 11. Of things geometric |
405 |
| 11.1. Units of measure and rates |
405 |
| 11.2. Angle |
412 |
| 11.3. Perimeter |
417 |
| 11.4. Area |
429 |
| 11.5. Story problems |
438 |
| 11.6. Mind stretches* |
443 |
| |
| Index |
447 |
