Download M AT H E X P L O... t a b l e o f ...

M AT H E X P L O R AT I O N S
table of contents
PREFACE AND INTRODUCTION
viii
CH. 1 EXPLORING INTEGERS ON THE NUMBER LINE 1
Section 1.1 Building Number Lines............................................... 1
Section 1.2 Less Than and Greater Than....................................... 9
Section 1.3 Distance Between Points, Absolute Value................... 15
Review Problems............................................................................ 18
Challenge Problems........................................................................ 20
CH. 2 ADDING AND SUBTRACTING ON THE NUMBER LINE
21
Section 2.1 Addition of Integers................................................... 21
Section 2.2 Subtraction of Integers.............................................. 27
Section 2.3 Adding and Subtracting Larger Numbers.................... 33
Section 2.4 Integer Properties and Terminology............................ 39
Section 2.5 The Chip Model......................................................... 46
Review Problems............................................................................ 51
Challenge Problems........................................................................ 53
CH. 3 MODELING PROBLEMS ALGEBRAICALLY
55
Section 3.1 Variables and Expressions.......................................... 55
Section 3.2 Equations.................................................................. 60
Section 3.3 Solving Equations with Subtraction............................ 69
Section 3.4 Solving Equations with Addition................................. 76
Section 3.5 Equations and Inequalities on Number Line................ 86
Review Problems............................................................................ 92
Challenge Problems........................................................................ 95
Copyright © 2014 Texas State Mathworksiii
M AT H E X P L O R AT I O N S
table of contents
CH. 4 MULTIPLICATION AND DIVISION
96
Section 4.1 Multiplication of Integers........................................... 96
Section 4.2 Area Model for Multiplication and the
Distributive Property.................................................. 105
Section 4.3 Applications of Multiplication..................................... 116
Section 4.4 The Linear Model for Division..................................... 121
Section 4.5 The Division Algorithm............................................... 128
Section 4.6 Solving Equations...................................................... 134
Review Problems............................................................................ 143
Challenge Problems........................................................................ 145
CH. 5 PATTERNS AND FUNCTIONS
147
Section 5.1 Graphing on the Coordinate Plane.............................. 147
Section 5.2 Translations and Reflections....................................... 154
Section 5.3 Functions.................................................................. 166
Section 5.4 Graphing Functions................................................... 174
Section 5.5 Applications of Linear Functions................................. 183
Section 5.6 Patterns and Sequences............................................. 191
Review Problems............................................................................ 198
Challenge Problems........................................................................ 201
CH. 6 DECIMAL REPRESENTATION AND OPERATIONS
203
Section 6.1 Decimals.................................................................... 203
Section 6.2 Multiplication of Decimals.......................................... 209
Section 6.3 Long Division............................................................. 217
Section 6.4 Division of Decimals................................................... 227
Review Problems............................................................................ 234
Challenge Problems........................................................................ 236
Copyright © 2014 Texas State Mathworksiv
M AT H E X P L O R AT I O N S
table of contents
CH. 7 NUMBER THEORY
237
Section 7.1 Divisibility, Factors, and Multiples............................... 237
Section 7.2 Prime and Composite Numbers.................................. 247
Section 7.3 Exponents and Order of Operations............................ 256
Section 7.4 Square Numbers and Square Roots............................. 264
Section 7.5 Unique Prime Factorization......................................... 270
Review Problems............................................................................ 276
Challenge Problems........................................................................ 279
CH. 8 ADDING AND SUBTRACTING FRACTIONS
281
Section 8.1 GCF and Equivalent Fractions..................................... 281
Section 8.2 Unit Fractions and Mixed Numbers............................ 296
Section 8.3 Common Multiples and the LCM................................ 303
Section 8.4 Addition and Subtraction of Fractions........................ 313
Section 8.5 Common Denominators and Mixed Numbers.............. 324
Review Problems............................................................................ 332
Challenge Problems........................................................................ 336
CH. 9 MULTIPLYING AND DIVIDING FRACTIONS
339
Section 9.1 Multiplication of Fractions.......................................... 339
Section 9.2 Division of Fractions.................................................. 350
Section 9.3 Fraction, Decimal and Percent Equivalents.................. 360
Section 9.4 Fractions and Alternatives.......................................... 372
Review Problems............................................................................ 380
Challenge Problems........................................................................ 382
Copyright © 2014 Texas State Mathworksv
M AT H E X P L O R AT I O N S
table of contents
CH. 10 RATES, RATIOS, AND PROPORTIONS
383
Section 10.1 Rates and Ratios...................................................... 383
Section 10.2 Rates of Change and Linear Functions...................... 393
Section 10.3 Proportions............................................................. 407
Section 10.4 Percents and Proportions......................................... 420
Section 10.5 Scaling.................................................................... 434
Section 10.6 Scaling and Similarity............................................... 443
Review Problems............................................................................ 453
Challenge Problems........................................................................ 457
CH. 11 GEOMETRY
459
Section 11.1 Measuring Angles.................................................... 459
Section 11.2 Angles in a Triangle.................................................. 469
Section 11.3 Two-Dimensional Figures.......................................... 483
Section 11.4 Pythagorean Theorem.................................................. 499
Section 11.5 Circles...................................................................... 505
Section 11.6 Three-Dimensional Shapes....................................... 516
Section 11.7 Surface Area and Nets.............................................. 528
Review Problems............................................................................ 541
Challenge Problems........................................................................ 547
CH. 12 DATA ANALYSIS
549
Section 12.1 Measures of Central Tendency.................................. 549
Section 12.2 Graphing Data......................................................... 560
Section 12.3 Probability............................................................... 581
Section 12.4 Independent Events................................................. 597
Review Problems............................................................................ 608
Challenge Problems........................................................................ 612
Copyright © 2014 Texas State Mathworksvi
M AT H E X P L O R AT I O N S
table of contents
CH. 13 PERSONAL FINANCE
Section 13.1 Simple and Compound Interest................................. 615
Section 13.2 Making up a Personal Budget.................................. 621
Section 13.3 Taxes....................................................................... 627
GLOSSARY629
INDEX669
APPENDIX (FINANCE)
Copyright © 2014 Texas State Mathworksvii
A-1