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Tables of Contents for Mathematical Investigations
Chapter/Section Title
Page #
Page Count
Preface
v
CHAPTER 1 What Is Mathematics?
1
70
1.1 Learning Mathematics
1
12
1.2 Thinking Mathematically
13
15
1.3 Using Variables to Generalize
28
15
1.4 Expanding the Notion of Variable
43
18
1.5 Making Connections: What Does It Mean to Do Mathematics?
61
10
CHAPTER 2 Whole Numbers: Introducing a Mathematical System
71
72
2.1 Whole Number Domains
71
16
2.2 Order of Operations with Whole Numbers
87
17
2.3 Algebraic Extensions of the Whole Numbers
104
12
2.4 Properties That Change the Order of Operations
116
19
2.5 Making Connections: What Does It Mean to Generalize?
135
8
CHAPTER 3 Functional Relationships
143
98
3.1 Investigating Relationships Numerically
143
18
3.2 Function: Algebraic Representation
161
15
3.3 Function: Notation for Algebraic Representations
176
12
3.4 Function: Geometric Interpretations
188
15
3.5 Triangular Numbers
203
16
3.6 Power and Factorial Functions
219
13
3.7 Making Connections: What Is a Function?
232
9
CHAPTER 4 Integers: Expanding a Mathematical System
241
107
4.1 Integers and the Algebraic Extension
241
16
4.2 Operations on Integers
257
24
4.3 The Absolute Value Function
281
18
4.4 Graphing with Integers
299
11
4.5 Using a Graphing Utility
310
16
4.6 Functions over the Integers
326
13
4.7 Making Connections: How Do Integers Expand the Mathematics?
339
9
CHAPTER 5 Rational Numbers: Further Expansion of a Mathematical System
348
89
5.1 Rates of Change
348
20
5.2 Rational Numbers and Proportional Reasoning
368
16
5.3 Investigating Rational Number Operations
384
20
5.4 Reciprocal and Power Functions
404
16
5.5 Integer Exponents
420
10
5.6 Making Connections: Is There Anything Rational About Functions?
430
7
CHAPTER 6 Real Numbers: Completing a Mathematical System
437
97
6.1 Real Numbers and the Algebraic Extension
437
12
6.2 The Square Root Function
449
14
6.3 Classes of Basic Functions
463
22
6.4 Linear Functions
485
24
6.5 Quadratic Functions
509
16
6.6 Making the Connections: Is There REALly a Completion to the Number System?
525
9
CHAPTER 7 Answering Questions with Linear and Quadratic Functions
534
87
7.1 Linear Equations and Inequalities in One Variable
534
21
7.2 Systems of Equations
555
17
7.3 Finding Zeros of Quadratic Functions by Factoring
572
21
7.4 Additional Factoring Experiences
593
19
7.5 Making Connections: Linking Multiple Representations of Functions
612
9
Glossary
621
13
Index
634