Algebra 1 To the Teacher... xi Instructional Units UNIT 1: PATTERN AND EQUATIONS Planning the Unit... 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 Planning the Unit... 63a Unit 2 Overview... 63 Getting Ready... 64 Activity 5 Function 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 2014 College Board. All Rights. SpringBoard Mathematics Algebra 1
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 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 UNIT 3: EXTENSIONS OF LINEAR CONCEPTS Planning the Unit...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, POLYNOMIALS Planning the Unit...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 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 2014 College Board. All Rights. SpringBoard Mathematics Algebra 1
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 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 Planning the Unit...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 Quadratics 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 Activity 32 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 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 Functions 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 Modeling with Functions Photo App... 495 Lesson 34-1 Constructing Models... 495 Lesson 34-2 Comparing Models... 500 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 2014 College Board. All Rights. SpringBoard Mathematics Algebra 1
UNIT 6: PROBABILITY AND STATISTICS Planning the Unit...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... 640