Modeling with Mathematics: A Bridge to Algebra II

Description

Bridge 2e helps students solidify their understanding of Algebra I and Geometry in preparation for Algebra II by providing a different kind of experience. This experience consists of modeling of real-world applications with a functions approach that will give them a deeper grasp of the necessary concepts. Focusing on topics essential to success in Algebra II, the authors have revamped the content to insure that all prerequisite topics for Algebra II are addressed. Cover Page Title Page Copyright Page About the Authors Contents Chapter 1 MATHEMATICAL MODELING What Is a Mathematical Model? 1.1 Activity: Animal Populations 1.2 Proportions as Models 1.3 R.A.P. (Review And Practice) 1.4 Investigation: Patterns and Explanations Modeling Project A Picture Is Worth a Thousand Words Chapter Review Chapter 2 DIRECT VARIATION How Is Mathematics Related to Bungee Jumping? 2.1 Activity: Bungee Jumping 2.2 Investigation: Proportional Relationships 2.3 Direct Variation Functions 2.4 R.A.P. 2.5 Slope Modeling Project It’s Only Water Weight Chapter Review Extension Inverse Variation Chapter 3 SOLVING EQUATIONS AND INEQUALITIES How Can We Care for Our Forests? 3.1 Activity: Tree Growth 3.2 Investigation: From Expression to Equation 3.3 Using Arrow Diagrams and Tables to Solve Equations 3.4 R.A.P. 3.5 Investigation: Solving Multi-Step Equations 3.6 Investigation: Solving Inequalities 3.7 Compound Inequalities Modeling Project Algebra’s Next Top Model Chapter Review Chapter 4 MEASUREMENT: PERIMETER, AREA, AND VOLUME Why Is Package Design Important? 4.1 Polygons 4.2 Investigation: Formulas and Literal Equations 4.3 Activity: Area and Package Design 4.4 Investigation: Volumes of Solid Figures 4.5 R.A.P. 4.6 Activity: Surface Area 4.7 Investigation: Similar Figures—Perimeter, Area, and Volume Modeling Project Building a Better Box Chapter Review Extension Constructing the Net of a Cone Chapter 5 FUNCTIONS AND THEIR REPRESENTATIONS How Can You Find the Value of an Unknown Quantity? 5.1 Investigation: Representing Functions 5.2 Activity: Linear Relationships 5.3 Investigation: Identifying Linear Functions 5.4 R.A.P. 5.5 Graphing Linear Equations 5.6 Investigation: Writing Equations of Lines 5.7 Slopes of Parallel and Perpendicular Lines Modeling Project It’s in the News Chapter Review Extension Special Functions Chapter 6 DESCRIBING DATA How Does the Census Help Us Understand Our Country? 6.1 Investigation: Graphs of Data 6.2 Activity: The Center of a Data Set 6.3 Stem-and-Leaf Diagrams and Box Plots 6.4 R.A.P. 6.5 Activity: Sampling Modeling Project What a State You’re In! Chapter Review Extension Frequency Tables and Histograms Chapter 7 LINEAR MODELS FROM DATA What Happened to Amelia Earhart? 7.1 Activity: Bones and Height 7.2 Investigation: Fitting Lines to Data 7.3 Investigation: Residuals and Judging the Quality of Fit 7.4 Investigation: Predicting from Linear Models 7.5 R.A.P. 7.6 Activity: Linear Regression 7.7 Comparing Models Modeling Project Who Am I? Chapter Review Extension Correlation Chapter 8 SYSTEMS OF EQUATIONS AND INEQUALITIES How Are Business Decisions Made? 8.1 Investigation: Using Tables and Graphs to Compare Linear Models 8.2 Solving Systems of Two Equations Using Substitution 8.3 Investigation: Solving Systems of Two Equations Using Elimination 8.4 R.A.P. 8.5 Graphing Inequalities in Two Variables 8.6 Investigation: Systems of Linear Inequalities Modeling Project Sizing Up the Mail Chapter Review Extension Linear Programming Chapter 9 SYMMETRY AND TRANSFORMATIONS How Do Archaeologists Use Mathematics When Studying Past Civilizations? 9.1 Activity: Symmetry 9.2 Transformations and Rigid Motions 9.3 Investigation: Rigid Motions and Patterns 9.4 R.A.P. 9.5 Activity: Rigid Motions in the Coordinate Plane Modeling Project It’s a Masterpiece! Chapter Review Extension Perspective in Art Chapter 10 EXPONENTIAL FUNCTIONS Will the World Have Enough Water? 10.1 Activity: Nonlinear Change 10.2 Properties of Exponents 10.3 Investigation: Negative Exponents 10.4 R.A.P. 10.5 Investigation: Modeling Exponential Growth 10.6 Investigation: Modeling Exponential Decay Modeling Project My, How You’ve Grown! Chapter Review Extension Newton’s Law of Cooling Chapter 11 QUADRATIC FUNCTIONS Is It a Parabola? 11.1 Investigation: Parabolas–A Geometric Look 11.2 Activity: Parabolas–An Algebraic Look 11.3 Investigation: Graphing Quadratic Functions 11.4 R.A.P. 11.5 Polynomial Arithmetic 11.6 Investigation: Solving Quadratic Equations 11.7 Investigation: The Quadratic Formula 11.8 Modeling with Quadratic Functions Modeling Project Designing a Hero’s Fall Chapter Review Extension Exploring Quadratic Data Chapter 12 INDIRECT MEASUREMENT How Can You Determine the Height of a ModelRocket? 12.1 Investigation: Right Triangles 12.2 Investigation: Distance and Midpoint Formulas 12.3 Activity: Similar Triangles as Models 12.4 Investigation: Trigonometric Ratios 12.5 Using Trigonometric Ratios 12.6 R.A.P. 12.7 Investigation: Finding Acute Angles Modeling Project What’s Your Angle? Chapter Review Extension Measuring Angles of Elevation Chapter 13 PERIODIC FUNCTIONS AND SOUND How Are Music and Repeated Motion Related? 13.1 Activity: Periodic Motion 13.2 Activity: Frequency and Pitch 13.3 Investigation: Modeling with Sound Waves 13.4 R.A.P. Modeling Project Bottle Harmony Chapter Review Extension Sinusoidal Functions Chapter 14 PROBABILITY What Are the Chances? 14.1 Activity: Determining Probability 14.2 Activity: Conditional Probability 14.3 Investigation: Joint Probabilities 14.4 R.A.P. 14.5 Activity: Binomial Experiments Modeling Project Let the Good Times Roll Chapter Review Chapter 15 THE MATHEMATICS OF PERSONAL FINANCE How Much Income Do I Need to Cover My Expenses? 15.1 Investigation: Budgeting Expenses 15.2 Investigation: Income and Taxes 15.3 Investigation: Implementing a Budget 15.4 Investigation: Saving 15.5 R.A.P. 15.6 Investigation: Borrowing Modeling Project Money for Life Chapter Review Extension Annuities APPENDICES A Fractions B Decimals C Ratios D Proportions E Percents as Fractions or Decimals F Percent Calculations G Absolute Value H Order of Operations I Operations with Positive and Negative Numbers J Properties of Real Numbers K Scientific Notation L Solving One- and Two-Step Linear Equations M Simplifying Radicals N Mean, Median, Mode, and Range O Coordinate Plane P Square Roots Photo Credits Index