Modeling with Mathematics: A Bridge to Algebra II

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