EQUATIONS AND INEQUALITIES Planning the Unit Unit 1 Overview 1 Getting Ready 2

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1 i-xvi_sb_a1_te_fm.indd Page 5 7/9/13 7:25 PM dksharma wgf To the Teacher Instructional Units UNIT 1 EQUATIONS AND INEQUALITIES 1a Unit 1 Overview 1 Getting Ready 2 Activity 1 Investigating Patterns Cross-Country Adventures 3 Lesson 1-1 Numeric and Graphic Representations of Data 3 Lesson 1-2 Writing Expressions 8 Activity 1 Practice 14 Activity 2 Solving Equations What s My Number? 15 Lesson 2-1 Writing and Solving Equations 15 Lesson 2-2 Equations with Variables on Both Sides 19 Lesson 2-3 Solving More Complex Equations 22 Lesson 2-4 Equations with No Solution or Infinitely Many Solutions 25 Lesson 2-5 Solving Literal Equations for a Variable 28 Activity 2 Practice 31 Embedded Assessment 1 Patterns and Equations Of Music and Money 33 Activity 3 Solving Inequalities Physical Fitness Zones 35 Lesson 3-1 Inequalities and Their Solutions 35 Lesson 3-2 Solving Inequalities 38 Lesson 3-3 Compound Inequalities 43 Activity 3 Practice 47 Activity 4 Absolute Value Equations and Inequalities Student Distances 49 Lesson 4-1 Absolute Value Equations 49 Lesson 4-2 Absolute Value Inequalities 54 Activity 4 Practice 59 Embedded Assessment 2 Inequalities and Absolute Value Diet and Exercise 61 UNIT 2 FUNCTIONS 63a Unit 2 Overview 63 Getting Ready 64 Activity 5 Functions and Function Notation Vending Machines 65 Lesson 5-1 Relations and Functions 65 Lesson 5-2 Domain and Range 71 Lesson 5-3 Function Notation 76 Activity 5 Practice 79 Activity 6 Interpreting Graphs of Functions Shake, Rattle, and Roll 81 Lesson 6-1 Key Features of Graphs 81 Lesson 6-2 More Complex Graphs 87 Lesson 6-3 Graphs of Real-World Situations 92 Activity 6 Practice 95 xi v

2 i-xvi_sb_a1_te_fm.indd Page 6 7/9/13 7:25 PM dksharma wgf continued Activity 7 Graphs of Functions Experiment Experiences 97 Lesson 7-1 The Spring Experiment 97 Lesson 7-2 The Falling Object Experiment 101 Lesson 7-3 The Radioactive Decay Experiment 105 Activity 7 Practice 109 Activity 8 Transformations of Functions Transformers 111 Lesson 8-1 Exploring f(x) + k 111 Lesson 8-2 Exploring f(x + k) 115 Activity 8 Practice 119 Embedded Assessment 1 Representations of Functions Bryce Canyon Hiking 121 Activity 9 Rates of Change Ramp It Up 123 Lesson 9-1 Slope 123 Lesson 9-2 Slope and Rate of Change 128 Lesson 9-3 More About Slopes 133 Activity 9 Practice 137 Activity 10 Linear Models Stacking Boxes 139 Lesson 10-1 Direct Variation 139 Lesson 10-2 Indirect Variation 144 Lesson 10-3 Another Linear Model 148 Lesson 10-4 Inverse Functions 152 Activity 10 Practice 157 Activity 11 Arithmetic Sequences Picky Patterns 159 Lesson 11-1 Identifying Arithmetic Sequences 159 Lesson 11-2 A Formula for Arithmetic Sequences 162 Lesson 11-3 Arithmetic Sequences as Functions 166 Activity 11 Practice 171 Embedded Assessment 2 Linear Functions and Equations Text Message Plans 173 Activity 12 Forms of Linear Functions Under Pressure 175 Lesson 12-1 Slope-Intercept Form 175 Lesson 12-2 Point-Slope Form 179 Lesson 12-3 Standard Form 183 Lesson 12-4 Slopes of Parallel and Perpendicular Lines 187 Activity 12 Practice 191 Activity 13 Equations from Data Pass the Book 193 Lesson 13-1 Scatter Plots and Trend Lines 193 Lesson 13-2 Linear Regression 197 Lesson 13-3 Quadratic and Exponential Regressions 200 Activity 13 Practice 205 Embedded Assessment 3 Linear Models and Slope as Rate of Change A 10K Run 207 vi SpringBoard Mathematics with Meaning Algebra 1

3 i-xvi_sb_a1_te_fm.indd Page 7 7/9/13 7:25 PM dksharma wgf UNIT 3 EXTENSIONS OF LINEAR CONCEPTS 209a Unit 3 Overview 209 Getting Ready 210 Activity 14 Piecewise-Defined Linear Functions Breakfast for Bowser 211 Lesson 14-1 Function Notation and Rate of Change 211 Lesson 14-2 Writing Functions and Finding Domain and Range 215 Lesson 14-3 Evaluating Functions and Graphing Piecewise-Defined Linear Functions 219 Lesson 14-4 Comparing Functions 221 Activity 14 Practice 225 Activity 15 Comparing Equations A Tale of a Trucker 227 Lesson 15-1 Writing Equations from Graphs and Tables 227 Lesson 15-2 Comparing Functions with Inequalities 231 Lesson 15-3 Writing Equations from Verbal Descriptions 235 Activity 15 Practice 237 Activity 16 Inequalities in Two Variables Shared Storage 239 Lesson 16-1 Writing and Graphing Inequalities in Two Variables 239 Lesson 16-2 Graphing Inequalities in Two Variables 242 Activity 16 Practice 247 Embedded Assessment 1 Graphing Inequalities and Piecewise-Defined Functions Earnings on a Graph 249 Activity 17 Solving Systems of Linear Equations A Tale of Two Truckers 251 Lesson 17-1 The Graphing Method 251 Lesson 17-2 Using Tables and the Substitution Method 256 Lesson 17-3 The Elimination Method 261 Lesson 17-4 Systems Without a Unique Solution 264 Lesson 17-5 Classifying Systems of Equations 267 Activity 17 Practice 271 Activity 18 Solving Systems of Linear Inequalities Which Region Is It? 273 Lesson 18-1 Representing the Solution of a System of Inequalities 273 Lesson 18-2 Interpreting the Solution of a System of Inequalities 278 Activity 18 Practice 281 Embedded Assessment 2 Systems of Equations and Inequalities Tilt the Scales 283 UNIT 4 EXPONENTS, RADICALS, AND POLYNOMIALS 285a Unit 4 Overview 285 Getting Ready 286 Activity 19 Exponent Rules Icebergs and Exponents 287 Lesson 19-1 Basic Exponent Properties 287 Lesson 19-2 Negative and Zero Powers 291 Lesson 19-3 Additional Properties of Exponents 294 Activity 19 Practice 297 vii

4 i-xvi_sb_a1_te_fm.indd Page 8 7/9/13 7:25 PM dksharma wgf continued Activity 20 Operations with Radicals Go Fly a Kite 299 Lesson 20-1 Radical Expressions 299 Lesson 20-2 Adding and Subtracting Radical Expressions 304 Lesson 20-3 Multiplying and Dividing Radical Expressions 307 Activity 20 Practice 311 Activity 21 Geometric Sequences Go Viral! 313 Lesson 21-1 Identifying Geometric Sequences 313 Lesson 21-2 Formulas for Geometric Sequences 316 Activity 21 Practice 321 Embedded Assessment 1 Exponents, Radicals, and Geometric Sequences Taking Stock 323 Activity 22 Exponential Functions Protecting Your Investment 325 Lesson 22-1 Exponential Functions and Exponential Growth 325 Lesson 22-2 Exponential Decay 329 Lesson 22-3 Graphs of Exponential Functions 333 Activity 22 Practice 339 Activity 23 Modeling with Exponential Functions Growing, Growing, Gone 341 Lesson 23-1 Compound Interest 341 Lesson 23-2 Population Growth 347 Activity 23 Practice 351 Embedded Assessment 2 Exponential Functions Family Bonds 353 Activity 24 Adding and Subtracting Polynomials Polynomials in the Sun 355 Lesson 24-1 Polynomial Terminology 355 Lesson 24-2 Adding Polynomials 359 Lesson 24-3 Subtracting Polynomials 364 Activity 24 Practice 367 Activity 25 Multiplying Polynomials Tri-Com Computers 369 Lesson 25-1 Multiplying Binomials 369 Lesson 25-2 Special Products of Binomials 376 Lesson 25-3 Multiplying Polynomials 379 Activity 25 Practice 381 Embedded Assessment 3 Polynomial Operations Measuring Up 383 Activity 26 Factoring Factors of Construction 385 Lesson 26-1 Factoring by Greatest Common Factor (GCF) 385 Lesson 26-2 Factoring Special Products 388 Activity 26 Practice 391 Activity 27 Factoring Trinomials Deconstructing Floor Plans 393 Lesson 27-1 Factoring x 2 + bx + c 393 Lesson 27-2 Factoring ax 2 + bx + c 398 Activity 27 Practice 401 Activity 28 Simplifying Rational Expressions Totally Rational 403 Lesson 28-1 Simplifying Rational Expressions 403 viii SpringBoard Mathematics with Meaning Algebra 1

5 i-xvi_sb_a1_te_fm.indd Page 9 7/9/13 7:25 PM dksharma wgf Lesson 28-2 Dividing Polynomials 406 Lesson 28-3 Multiplying and Dividing Rational Expressions 411 Lesson 28-4 Adding and Subtracting Rational Expressions 413 Activity 28 Practice 417 Embedded Assessment 4 Factoring and Simplifying Rational Expressions Rock Star Demands 419 UNIT 5 QUADRATIC FUNCTIONS 421a Unit 5 Overview 421 Getting Ready 422 Activity 29 Introduction to Quadratic Functions Touchlines 423 Lesson 29-1 Modeling with a Quadratic Function 423 Lesson 29-2 Graphing and Analyzing a Quadratic Function 427 Activity 29 Practice 431 Activity 30 Graphing Quadratic Functions Transformers 433 Lesson 30-1 Translations of the Quadratic Parent Function 433 Lesson 30-2 Stretching and Shrinking the Quadratic Parent Function 440 Lesson 30-3 Multiple Transformations of the Quadratic Parent Function 444 Activity 30 Practice 451 Embedded Assessment 1 Graphing Quadratic Functions Parabolic Paths 453 Activity 31 Solving Quadratic Equations by Graphing and Factoring Trebuchet Trials 455 Lesson 31-1 Solving by Graphing or Factoring 455 Lesson 31-2 The Axis of Symmetry and the Vertex 459 Lesson 31-3 Graphing a Quadratic Function 462 Activity 31 Practice 465 Activity 32 Algebraic Methods of Solving Quadratic Equations Keeping It Quadratic 467 Lesson 32-1 The Square Root Method 467 Lesson 32-2 Completing the Square 471 Lesson 32-3 The Quadratic Formula 474 Lesson 32-4 Choosing a Method and Using the Discriminant 477 Lesson 32-5 Complex Solutions 480 Activity 32 Practice 483 Activity 33 Applying Quadratic Equations Rockets in Flight 485 Lesson 33-1 Fitting Data with a Quadratic Function 485 Lesson 33-2 Interpreting Solutions of Quadratic Equations 488 Activity 33 Practice 491 Embedded Assessment 2 Solving Quadratic Equations Egg Drop 493 Activity 34 Graphs of Functions Photo App 495 Lesson 34-1 Constructing Models 495 Lesson 34-2 Comparing Models 500 ix

6 i-xvi_sb_a1_te_fm.indd Page 10 7/9/13 7:25 PM dksharma wgf continued Lesson 34-3 Extending Models 503 Activity 34 Practice 507 Activity 35 Systems of Equations Population Explosion 509 Lesson 35-1 Solving a System Graphically 509 Lesson 35-2 Solving a System Algebraically 513 Activity 35 Practice 517 Embedded Assessment 3 Solving Systems of Equations Sports Collector 519 UNIT 6 PROBABILITY AND STATISTICS 521a Unit 6 Overview 521 Getting Ready 522 Activity 36 Measures of Center and Spread To Text, or Not to Text 523 Lesson 36-1 Mean, Median, Mode, and MAD 523 Lesson 36-2 Another Measure of Variability 532 Activity 36 Practice 536 Activity 37 Dot and Box Plots and the Normal Distribution Disturbing Coyotes 537 Lesson 37-1 Dot Plots and Box Plots 537 Lesson 37-2 Modified Box Plots 543 Lesson 37-3 Normally Distributed 548 Activity 37 Practice 554 Embedded Assessment 1 Comparing Univariate Distributions Splitting the Bill 557 Activity 38 Correlation What s the Relationship? 559 Lesson 38-1 Scatter Plots 559 Lesson 38-2 Correlation Coefficient 564 Activity 38 Practice 569 Activity 39 The Best-Fit Line Regressing Linearly 571 Lesson 39-1 Line of Best Fit 571 Lesson 39-2 Residuals 577 Lesson 39-3 Interpreting the Slope and Intercept of the Best-Fit Line 582 Lesson 39-4 Plotting Residuals 588 Activity 39 Practice 594 Activity 40 Bivariate Data Categorically Speaking 595 Lesson 40-1 Bivariate Categorical Data 595 Lesson 40-2 Presenting Relative Frequency Data Graphically 600 Activity 40 Practice 607 Embedded Assessment 2 Bivariate Distributions Dear Traveling Tooth 609 RESOURCES 613 Formulas 614 Learning Strategies 618 Glossary 621 Academic Vocabulary Graphic Organizers 626 x SpringBoard Mathematics with Meaning Algebra 1