Mathematics in Action: An Introduction to Algebraic, Graphical, and Numerical Problem Solving (6th Edition)

Cover
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgments
Resources for Success
To The Student
CHAPTER 1 Number Sense
	CLUSTER 1 Introduction to Problem Solving
		ACTIVITY 1.1 The Bookstore
		Steps in Problem Solving
		Objectives: 1. Develop problem-solving skills
		2. Organize information
		3. Practice communication skills
		4. Write a solution in sentences
		ACTIVITY 1.2 The Classroom
		Problem-Solving Strategies
		Objectives: 1. Develop problem-solving strategies
			Organize information
			Draw a picture
			Recognize a pattern
			Do a simpler problem
		2. Communicate problem-solving ideas
		ACTIVITY 1.3 Properties of Arithmetic
		Properties and Vocabulary for Arithmetic Calculations
		Objectives: 1. Identify and use the commutative property in calculations
		2. Use the associative property to evaluate arithmetic expressions
		3. Use the order of operations convention to evaluate arithmetic expressions
		4. Identify and use the properties of exponents in calculations
		5. Convert numbers to and from scientific notation
		What Have I Learned?
		How Can I Practice?
	CLUSTER 2 Problem Solving with Fractions and Decimals (Rational Numbers)
		ACTIVITY 1.4 Top Chef
		Operations with Fractions and Mixed Numbers
		Objectives: 1. Add and subtract fractions
		2. Multiply and divide fractions
		PROJECT 1.5 Course Grades and Your GPA
		Problem Solving Using Fractions and Decimals
		Objectives: 1. Recognize and calculate a weighted average
		2. Express fractions in decimal format
		What Have I Learned?
		How Can I Practice?
	CLUSTER 3 Comparisons and Proportional Reasoning
		ACTIVITY 1.6 Everything Is Relative
		Ratios as Fractions, Decimals, and Percents
		Objectives: 1. Distinguish between absolute and relative measure
		2. Write ratios in fraction, decimal, and percent formats
		3. Determine equivalence of ratios
		ACTIVITY 1.7 Antidepressant Use
		Proportional Reasoning
		Objective: Use proportional reasoning to apply a known ratio to a given piece of information
		ACTIVITY 1.8 Who Really Did Better?
		Actual and Relative Change, Percent Increase and Decrease
		Objectives: 1. Define actual and relative change
		2. Distinguish between actual and relative change
		3. Calculate relative change as a percent increase or percent decrease
		ACTIVITY 1.9 Going Shopping
		Growth and Decay Factors
		Objectives: 1. Define growth factor
		2. Determine growth factors from percent increases
		3. Apply growth factors to problems involving percent increases
		4. Define decay factor
		5. Determine decay factors from percent decreases
		6. Apply decay factors to problems involving percent decreases
		ACTIVITY 1.10 Take an Additional 20% Off
		Consecutive Growth and Decay Factors
		Objectives: 1. Define consecutive growth and decay factors
		2. Determine a consecutive growth or decay factor from two or more consecutive percent changes
		3. Apply consecutive growth and/or decay factors to solve problems involving percent changes
		ACTIVITY 1.11 Fuel Economy
		Rates and Unit Analysis
		Objectives: 1. Apply rates directly to solve problems
		2. Use unit or dimensional analysis to solve problems that involve consecutive rates
		What Have I Learned?
		How Can I Practice?
	CLUSTER 4 Problem Solving with Signed Numbers
		ACTIVITY 1.12 Celsius Thermometers
		Addition and Subtraction of Integers
		Objectives: 1. Identify signed numbers
		2. Use signed numbers to represent quantities in real-world situations
		3. Compare signed numbers
		4. Calculate the absolute value of numbers
		5. Identify and use properties of addition and subtraction of signed numbers
		6. Add and subtract signed numbers using absolute value
		ACTIVITY 1.13 Shedding the Extra Pounds
		Multiplication and Division of Integers
		Objective: Multiply and divide signed numbers
		ACTIVITY 1.14 Order of Operations Revisited
		Negative Exponents and Scientific Notation
		Objectives: 1. Use the order of operations convention to evaluate expressions involving signed numbers
		2. Evaluate expressions that involve negative exponents
		3. Distinguish between such expressions as -5⁴ and (-5)⁴
		4. Write very small numbers in scientific notation
		What Have I Learned?
		How Can I Practice?
	Chapter 1 Summary
	Chapter 1 Gateway Review
CHAPTER 2 Variable Sense
	CLUSTER 1 Symbolic Rules and Expressions
		ACTIVITY 2.1 Symbolizing Arithmetic
		Formulas and Algebraic Expressions
		Objectives: 1. Generalize from an arithmetic calculation to a symbolic representation by utilizing variables
		2. Evaluate algebraic expressions
		ACTIVITY 2.2 Blood Alcohol Levels
		Represent a Two-Variable Relationship Algebraically, Numerically, and Graphically
		Objectives: 1. Identify input and output in situations involving two variable quantities
		2. Determine the replacement values for a variable within a given situation
		3. Represent and interpret an input/output relationship algebraically by formula, numerically as data pairs in a table, and graphically as points on a graph
		ACTIVITY 2.3 College Expenses
		Symbolic Rules
		Objectives: 1. Write verbal rules that represent relationships between input and output variables
		2. Translate verbal rules into symbolic rules
		3. Determine input/output values from a graph
		ACTIVITY 2.4 Are They the Same?
		Equivalent Expressions and Grouping Symbols
		Objectives: 1. Identify equivalent algebraic expressions by examining their outputs
		2. Identify equivalent algebraic expressions by comparing their graphs
		3. Write algebraic expressions that involve grouping symbols
		What Have I Learned?
		How Can I Practice?
	CLUSTER 2 Solving Equations
		ACTIVITY 2.5 Let’s Go Shopping
		Solve an Equation Containing One Operation
		Objectives: 1. Solve an equation of the form ax = b, a ≠ 0, for x using an algebraic approach
		2. Solve an equation of the form x + a = b for x using an algebraic approach
		3. Use the four-step process to solve problems
		ACTIVITY 2.6 Leasing a Copier
		Solve an Equation Containing Two or More Operations
		Objectives: 1. Model contextual situations with symbolic rules of the form y = ax + b, a ≠ 0
		2. Solve equations of the form ax + b = c, a ≠ 0
		ACTIVITY 2.7 The Algebra of Weather
		Solve a Formula for a Specified Variable
		Objective: Solve a formula for a specified variable
		ACTIVITY 2.8 Four out of Five Dentists Prefer Crest
		Proportions
		Objectives: 1. Recognize that equivalent fractions lead to proportions
		2. Use proportions to solve problems involving ratios and rates
		What Have I Learned?
		How Can I Practice?
	CLUSTER 3 More Problem Solving Using Algebra
		ACTIVITY 2.9 Do It Two Ways
		Distributive Property, Greatest Common Factor, and Combining Like Terms
		Objectives: 1. Apply the distributive property
		2. Use areas of rectangles to interpret the distributive property geometrically
		3. Identify the greatest common factor in an expression
		4. Factor out the greatest common factor in an expression
		5. Recognize like terms
		6. Simplify an expression by combining like terms
		ACTIVITY 2.10 Decoding
		Simplifying Algebraic Expressions
		Objectives: 1. Recognize an algebraic expression as a code of instruction
		2. Simplify algebraic expressions
		ACTIVITY 2.11 Comparing Energy Costs
		Mathematical Models, General Strategy for Solving Linear Equations
		Objectives: 1. Develop mathematical models to solve problems
		2. Write and solve equations of the form ax + b = cx + d, where a ≠ 0 and c ≠ 0
		3. Use the distributive property to solve equations involving grouping symbols
		4. Solve formulas for a specified variable
		PROJECT 2.12 Summer Job Opportunities
		Problem Solving Using Linear Equations
		Objective: Use problem-solving skills to make decisions based on solutions of mathematical models
		What Have I Learned?
		How Can I Practice?
	Chapter 2 Summary
	Chapter 2 Gateway Review
CHAPTER 3 Function Sense and Linear Functions
	CLUSTER 1 Function Sense
		ACTIVITY 3.1 Summer Olympics
		Functions, Numerical and Graphical Representation of Functions
		Objectives: 1. Use the input-output concept to define a function
		2. Identify a function relationship between two variables
		3. Identify the independent and dependent variables
		4. Use function notation to express the input-output correspondence of a function
		5. Identify the domain and range of a function
		6. Expand the rectangular coordinate system to include all four quadrants in the plane
		7. Represent functions in tabular and graphical forms
		ACTIVITY 3.2 How Fast Did You Lose?
		Average Rate of Change
		Objective: Determine the average rate of change of an output variable with respect to the input variable
		PROJECT 3.3 Comparing Symbolically Defined Functions and Their Graphs
		Objectives: 1. Define functions by symbolic rules
		2. Recognize that an output value is determined by evaluating the symbolic rule
		3. Recognize that an input value is determined by solving an associated equation
		4. Understand the connection between the input-output pairs generated by the symbolic rule and the plotted points that form its graph
		5. Understand the connection between the average rates of change of a function and the shape of its graph
		6. Explore and compare the algebraic and graphical methods for evaluating a function
		7. Explore and compare the algebraic and graphical methods for solving an associated equation
		ACTIVITY 3.4 Course Grade
		Representing Functions Symbolically
		Objectives: 1. Determine the symbolic rule that defines a function
		2. Identify the practical domain and range of a function
		What Have I Learned?
		How Can I Practice?
	CLUSTER 2 Introduction to Linear Functions
		ACTIVITY 3.5 The Snowy Tree Cricket
		Slope and Intercepts of a Line
		Objectives: 1. Identify linear functions by a constant average rate of change of the output variable with respect to the input variable
		2. Interpret slope as an average rate of change
		3. Determine the slope of a nonvertical line drawn through two points
		4. Identify increasing and decreasing linear functions using slope
		5. Determine horizontal and vertical intercepts of a linear function from its graph
		6. Interpret the meaning of horizontal and vertical intercepts in a contextual situation
		ACTIVITY 3.6 Software Sales
		Slope-Intercept Equation of a Line
		Objectives: 1. Identify whether a situation can be represented by a linear function
		2. Write an equation of a line in slope-intercept form
		3. Use the y-intercept and the slope to graph a linear function
		4. Determine horizontal intercepts of linear functions using an algebraic approach
		5. Use intercepts to graph a linear function
		6. Identify parallel lines
		ACTIVITY 3.7 Predicting Population
		Problem Solving Using Slope-Intercept Equation of a Line
		Objectives: 1. Use the slope-intercept form of linear equations to solve problems
		2. Determine the relative error in a measurement or prediction using a linear model
		ACTIVITY 3.8 College Tuition
		Point-Slope Equation of a Line
		Objectives: 1. Determine the equation for a linear function when given two points, neither of which is the vertical intercept
		2. Use the point-slope form, y - y₁ = m(x - x₁), to write the equation of a nonvertical line
		3. Identify lines having zero or undefined slopes
		4. Determine the equation of horizontal and vertical lines
		What Have I Learned?
		How Can I Practice?
	CLUSTER 3 Linear Regression, Systems, and Inequalities
		ACTIVITY 3.9 Education Pays
		Line of Best Fit and Regression Equations
		Objectives: 1. Recognize when patterns of points in a scatterplot are approximately linear
		2. Estimate and draw a line of best fit through a set of points in a scatterplot
		3. Use technology to determine a line of best fit by the least-squares method
		4. Estimate the error of representing a set of data by a line of best fit
		LAB 3.10 Body Parts
		Problem Solving Using Regression Equations
		Objectives: 1. Collect and organize data in a table
		2. Recognize linear patterns in paired data
		ACTIVITY 3.11 Smartphone Plan Options
		Systems of Linear Equations in Two Variables
		Objectives: 1. Solve a system of two linear equations numerically
		2. Solve a system of two linear equations graphically
		3. Solve a system of two linear equations using the substitution method
		4. Recognize the connections between the three methods of solution
		5. Interpret the solution to a system of two linear equations in terms of the problem’s content
		ACTIVITY 3.12 Healthy Lifestyle
		Solving a System of Linear Equations in Two Variables Using the Addition Method
		Objectives: 1. Solve a system of two linear equations algebraically using the substitution method
		2. Solve a system of two linear equations algebraically using the addition (or elimination) method
		PROJECT 3.13 Modeling a Business
		Problem Solving Using Systems of Linear Equations in Two Variables
		Objectives: 1. Solve a system of two linear equations by any method
		2. Define and interpret the break-even point as the point at which the cost and revenue functions are equal
		3. Determine the break-even point of a linear cost and revenue system algebraically and graphically
		ACTIVITY 3.14 How Long Can You Live?
		Linear Inequalities
		Objective: Use properties of inequalities to solve linear inequalities in one variable algebraically
		What Have I Learned?
		How Can I Practice?
	Chapter 3 Summary
	Chapter 3 Gateway Review
CHAPTER 4 An Introduction to Nonlinear Problem Solving
	CLUSTER 1 Mathematical Modeling Involving Polynomials
		ACTIVITY 4.1 Fatal Crashes
		Polynomials
		Objectives: 1. Identify polynomials and polynomial functions
		2. Classify a polynomial as a monomial, binomial, or trinomial
		3. Determine the degree of a polynomial
		4. Simplify a polynomial by identifying and combining like terms
		5. Add and subtract polynomials
		6. Evaluate and interpret polynomials
		ACTIVITY 4.2 Volume of a Storage Box
		Properties of Exponents
		Objectives: 1. Use properties of exponents to simplify expressions and combine powers that have the same base
		2. Use the distributive property and properties of exponents to write expressions in expanded form
		ACTIVITY 4.3 Room for Work
		Operations with Polynomials
		Objectives: 1. Expand and simplify the product of two binomials
		2. Expand and simplify the product of any two polynomials
		3. Recognize and expand the product of conjugate binomials: difference of squares
		4. Recognize and expand the product of identical binomials: perfect-square trinomials
		What Have I Learned?
		How Can I Practice?
	CLUSTER 2 Problem Solving with Quadratic Equations and Functions
		ACTIVITY 4.4 The Amazing Property of Gravity
		Solving Quadratic Equations
		Objectives: 1. Evaluate quadratic functions of the form y = ax²
		2. Graph quadratic functions of the form y = ax²
		3. Interpret the coordinates of points on the graph of y = ax² in context
		4. Solve a quadratic equation of the form ax² = c graphically
		5. Solve a quadratic equation of the form ax² = c algebraically by taking square roots
		Note: a ≠ 0 in Objectives 1–5
		ACTIVITY 4.5 What Goes Up, Comes Down
		Quadratic Functions and Their Graphs
		Objectives: 1. Evaluate quadratic functions of the form y = ax² + bx, a ≠ 0
		2. Graph quadratic functions of the form y = ax² + bx, a ≠ 0
		3. Identify the x-intercepts of the graph of y = ax² + bx graphically and algebraically
		4. Interpret the x-intercepts of a quadratic function in context
		5. Factor a binomial of the form ax² + bx
		6. Solve an equation of the form ax² + bx = 0 using the zero-product property
		ACTIVITY 4.6 How High Did It Go?
		Solving Quadratic Equations by Factoring
		Objectives: 1. Recognize and write a quadratic equation in standard form, ax² + bx + c = 0, a ≠ 0
		2. Factor trinomials of the form x² + bx + c
		3. Solve a factorable quadratic equation of the form x² + bx + c = 0 using the zero-product property
		4. Identify a quadratic function from its algebraic form
		ACTIVITY 4.7 More Ups and Downs
		Solving Quadratic Equations Using the Quadratic Formula
		Objectives: 1. Use the quadratic formula to solve quadratic equations
		2. Identify the solutions of a quadratic equation with points on the corresponding graph
		What Have I Learned?
		How Can I Practice?
	CLUSTER 3 Other Nonlinear Functions
		ACTIVITY 4.8 Inflation
		Exponential Functions
		Objectives: 1. Recognize an exponential function as a rule for applying a growth factor or a decay factor
		2. Graph exponential functions from numerical data
		3. Recognize exponential functions from equations
		4. Graph exponential functions from equations
		ACTIVITY 4.9 A Thunderstorm
		Direct Variation
		Objectives: 1. Recognize the equivalent forms of the direct variation statement
		2. Determine the constant of proportionality in a direct variation problem
		3. Solve direct variation problems
		ACTIVITY 4.10 Diving under Pressure, or Don‘t Hold Your Breath
		Inverse Variation
		Objectives: 1. Recognize functions of the form y = k/x, x ≠ 0, as nonlinear
		2. Recognize equations of the form xy = k as inverse variation
		3. Graph an inverse variation relationship from symbolic rules
		4. Solve equations of the form a/x = b, x ≠ 0
		5. Identify functions of the form y = k/x² , x ≠ 0, as an inverse variation relationship
		ACTIVITY 4.11 Hang Time
		Square Root Functions
		Objectives: 1. Recognize functions of the form y = a√x as nonlinear
		2. Evaluate and solve equations that involve square roots
		3. Graph square root functions from numerical data
		4. Graph square root functions from symbolic rules
		What Have I Learned?
		How Can I Practice?
	Chapter 4 Summary
	Chapter 4 Gateway Review
APPENDICES
	Appendix A: Fractions
	Appendix B: Decimals
	Appendix C: Skills Checks
	Appendix D: Algebraic Extensions
	Appendix E: Getting Started with the TI-84 Plus Family of Calculators
Selected Answers
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