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Solution Manual for Mathematics in Action: An Introduction to Algebraic, Graphical, and Numerical Problem Solving, 6th Edition

Solution Manual for Mathematics in Action: An Introduction to Algebraic, Graphical, and Numerical Problem Solving, 6th Edition simplifies complex textbook exercises with easy-to-understand solutions and step-by-step guides.

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    R ESOURCE M ANUAL WITH T ESTS M ATHEMATICS IN A CTION : AN INTRODUCTION TO ALGEBRAIC , GRAPHICAL , AND NUMERICAL PROBLEM SOLVING S IXTH E DITION The Consortium for Foundation Mathematics

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    iii C ONTENTS F OREWORD ............................................................................................................ vi S TUDENT O UTCOMES .......................................................................................................................... vii P ERFORMANCE O BJECTIVES ................................................................................................................ vii G ENERAL E DUCATION C OMPETENCIES .............................................................................................. viii S ECTION 1 O VERVIEW ............................................................................................................. 1 R ESOURCES IN THIS GUIDE ..................................................................................................................... 1 T EXTBOOK C ONTENT AND S TRUCTURE .................................................................................................. 1 T EXTBOOK S UPPLEMENTS ...................................................................................................................... 3 P EDAGOGY .............................................................................................................................................. 5 T ECHNOLOGY ......................................................................................................................................... 6 S UGGESTED S YLLABI .............................................................................................................................. 6 M ATHEMATICAL T OPICS C OVERED IN THE T EXT ………………………………………………… ........ 6 A NNOTATED L IST OF C ORE AND RECOMMENDED S UPPLEMENTAL A CTIVITIES ………………….......... 7 S AMPLE C OURSE O UTLINES …………………………………………………………………….......... 1 3 A SSESSMENT ......................................................................................................................................... 1 9 S ECTION 2 C HAPTER N OTES .................................................................................................. 21 C HAPTER 1: N UMBER S ENSE ................................................................................................................ 22 C LUSTER 1 I NTRODUCTION TO P ROBLEM S OLVING .......................................................................... 22 C LUSTER 2 P ROBLEM S OLVING WITH F RACTIONS & D ECIMALS (R ATIONAL N UMBERS ) ................. 23 C LUSTER 3 C OMPARISONS AND P ROPORTIONAL R EASONING ........................................................... 24 C LUSTER 4 P ROBLEM SOLVING WITH S IGNED N UMBERS …………………………… ...................... 25 C HAPTER 2: V ARIABLE S ENSE .............................................................................................................. 26 C LUSTER 1 S YMBOLIC R ULES AND E XPRESSIONS ............................................................................ 26 C LUSTER 2 S OLVING E QUATIONS ..................................................................................................... 28 C LUSTER 3 M ORE P ROBLEM S OLVING U SING A LGEBRA ……………………………… .................. 29 C HAPTER 3: F UNCTION S ENSE AND L INEAR F UNCTIONS .......................................................... 30 C LUSTER 1 F UNCTION S ENSE ............................................................................................................ 30 C LUSTER 2 I NTRODUCTION TO L INEAR FUNCTIONS ......................................................................... 31 C LUSTER 3 L INEAR REGRESSION , S YSTEMS , AND I NEQUALITIES ……………………. .................... 32 C HAPTER 4: A N I NTRODUCTION TO N ONLINEAR P ROBLEM S OLVING .................................................. 34 C LUSTER 1 M ATHEMATICAL M ODELING I NVOLVING P OLYNOMIALS ............................................... 34 C LUSTER 2 P ROBLEM S OLVING WITH QUADRATIC E QUATIONS AND F UNCTIONS ............................. 34 C LUSTER 3 O THER N ONLINEAR FUNCTIONS ........................................................................ 35 S ECTION 3 L EARNING IN G ROUPS .......................................................................................... 37 Q UESTIONS AND A NSWERS ABOUT L EARNING IN G ROUPS ......................................................... 38 What is collaborative learning? ......................................................................................................... 38 What skills do students gain through active learning in a collaborative environment? ..................... 38 What is our role as teachers in a collaborative learning environment? ............................................. 39 What if you have not used collaborative learning strategies before? ................................................ 39 How do we form groups? What size should they be?....................................................................... 39 How can we motivate students to learn in a collaborative setting? ................................................... 40 What can we do to ensure every student understands the major concepts? ....................................... 41 A student claims, "This is not how I learned it." How do you respond? ......................................... 41 How can time be used efficiently in a collaborative setting? ............................................................ 41 What can be done when a group falls behind or gets ahead? ............................................................ 42

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    iv What homework should you assign? ................................................................................................. 42 How is homework checked in a collaborative setting?...................................................................... 42 What can be done when a group member does not actively participate or contribute? ..................... 43 What can we do when a student is occasionally late to class?........................................................... 43 What can we do about absenteeism? ................................................................................................ 43 What can be done when two group members have a conflict? ......................................................... 44 How do we help students who lack the basic skills that are only reviewed in the course? ............... 44 How do we assess learning in groups? .............................................................................................. 44 S ECTION 4 T ECHNOLOGY ........................................................................................ 45 Q UESTIONS AND A NSWERS ABOUT T ECHNOLOGY ................................................................................ 45 How do scientific calculators assist students using this textbook? .................................................. 45 How do graphing calculators assist students using this textbook?......................... .......................... 46 Which type of calculator should your students use? ........................................................................ 46 Should students purchase their own calculators? ............................................................................. 46 Will students be totally dependent on the calculators in using this text? ......................................... 43 How should an instructor proceed when there are many different calculator models in the classroom? ......................................................................................................... 47 Are procedures for using the graphing calculator included in this text? .......................................... 47 What computer tutorial programs, graphing/computer algebra systems, or online resources are useful in connection with this textbook? ............................................ 47 How can graphing assignments be assessed?................................................................................... 48 S AMPLE A CTIVITIES USING THE G RAPHING C ALCULATOR OR C OMPUTER P ROGRAMS ........................ 48 S ECTION 5 WRITING T O L EARN ............................................................................... 65 H ELPING S TUDENTS K EEP A L EARNING L OG ........................................................................................ 65 J OURNAL A SSIGNMENTS ....................................................................................................................... 66 B RIEF E SSAY A SSIGNMENTS .................................................................................................................. 66 A SSESSMENT OF W RITING A SSIGNMENTS ............................................................................................. 66 C RITERIA FOR E VALUATION OF A SSIGNMENTS ..................................................................................... 67 K EEPING A J OURNAL IN M ATH ............................................................................................. 68 S AMPLE J OURNAL A SSIGNMENTS ......................................................................................... 72 S ECTION 6 B ASIC S KILLS P RACTICE ......................................................................... 89 P RACTICING AND A SSESSING B ASIC S KILLS ......................................................................................... 89 Calculator Usage ............................................................................................................................... 90 Percents, Decimals, and Fractions ..................................................................................................... 92 Order of Operations ........................................................................................................................... 94 Evaluating and Solving Linear Equations ......................................................................................... 96 Solving Literal Equations .................................................................................................................. 98 Proportions ...................................................................................................................................... 100 Functional Representations.............................................................................................................. 101 Slopes, Intercepts, and Equations of Lines ...................................................................................... 103 Systems of Equations ...................................................................................................................... 105 Properties of Exponents, Simplifying Algebraic Expressions ......................................................... 107 Factoring Algebraic Expressions ..................................................................................................... 109 Factoring Trinomials……………………………………………………………………. ............... 111

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    v S ECTION 7 A SSESSMENT ......................................................................................... 113 I NDIVIDUAL , G ROUP AND T AKE H OME E XAMS B Y C HAPTER .................................................... 113 Chapter 1 ........................................................................................................................................ 114 Chapter 2 ........................................................................................................................................ 136 Chapter 3 ........................................................................................................................................ 153 Chapter 4 ........................................................................................................................................ 195 I NDIVIDUAL AND G ROUP F INAL E XAMS ................................................................................ 213 P ORTFOLIOS AS A SSESSMENTS ............................................................................................ 229 S ECTION 8 A NSWERS TO B ASIC S KILLS P RACTICE WORKSHEETS ..................................... 231 S ECTION 9 A NSWERS TO A SSESSMENTS (S ECTIONS 4 AND 7) .............................................. 235

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    1 S ECTION 1 O VERVIEW RESOURCES IN THIS GUIDE We hope that the content and format of this Instructor’s Resource Manual with Tests will be of great help to you in teaching with Mathematics in Action . This section of the Manual is an annotated directory to the resources addressed at length in the other sections. What is available to you in this Guide is described under the following headings.  Textbook Content and Structure  Supplements available with the textbook  Pedagogy: Learning in Groups and Writing to Learn  Technology: Scientific Calculators, Graphing Calculators, and Computer Programs  Suggestions for Syllabi: Annotated List of the Major Mathematical Topics Covered in the Text  Sample Course Outlines  Assessment: Group Oral and Written Tests, Journals, Formal Writing Assignments, Traditional Testing, Basic Skills, Portfolios Mathematics in Action is adaptable to the various needs of courses at the introductory foundation level and we offer you an annotated list of the major mathematical topics covered in the text as the best guide to determining the content of your course. We also offer sample course syllabi, one for an elementary algebra course and one for an intermediate level algebra course. Please note that in planning your course, supplemental teaching and learning aids are available to you and your students. These supplements are listed in this Overview Section for your convenience. We organized and formatted this Instructor’s Resource Manual with Tests so, if you choose, you can use the sample graphing calculator experiments, journal assignments, writing assignments, skills worksheets, tests, and exams as presented. TEXTBOOK CONTENT AND STRUCTURE The text is divided into four chapters followed by appendices and a glossary.  Chapter 1: Number Sense  Chapter 2: Variable Sense  Chapter 3: Function Sense and Linear Functions  Chapter 4: An Introduction to Nonlinear Problem Solving Each chapter is subdivided into sections we call clusters. Each cluster focuses on a major mathematical topic within the context of a chapter. For example, Chapter 1 Cluster 3 focuses on comparisons and proportional reasoning and Chapter 4 Cluster 2 concentrates on problem solving using quadratic equations and functions. There are thirteen clusters in all; four in Chapter 1, three in Chapter 2, three in Chapter 3 and three in Chapter 4. The clusters are listed here to give you a convenient overview.

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    2 O VERVIEW Chapter 1 Number Sense  Cluster 1 Introduction to Problem Solving  Cluster 2 Problem Solving with Fractions and Decimals (Rational Numbers)  Cluster 3 Comparisons and Proportional Reasoning  Cluster 4 Problem Solving with Signed Numbers Chapter 2 Variable Sense  Cluster 1 Symbolic Rules and Expressions  Cluster 2 Solving Equations  Cluster 3 More Problem Solving using Algebra Chapter 3 Function Sense and Linear Functions  Cluster 1 Function Sense  Cluster 2 Introduction to Linear Functions  Cluster 3 Linear Regression, Systems, and Inequalities Chapter 4 An Introduction to Nonlinear Problem Solving  Cluster 1 Mathematical Modeling Involving Polynomials  Cluster 2 Problem Solving with Quadratic Equations and Functions  Cluster 3 Other Nonlinear Functions Each cluster is further divided into sections named  Activities (with Exercises)  What Have I Learned ?  How Can I Practice ? Activities are the essence of Mathematics in Action. They are where mathematical concepts and skills are introduced and developed in meaningful contextual problems and situations. We expect that students will see for themselves the need to master arithmetic and algebra skills, and be able to answer their own frequently asked questions, “Why do I need to learn this?” and “When will I ever use this outside this class?” In Activities , students respond to a series of structured prompts and questions that direct them to recall and apply mathematical knowledge they already have, and that lead them to acquire the other concepts and skills they must have to be successful problem solvers. Basic arithmetic and algebra skills are presented as they are needed in the contextual problems. Activities also include exercises that may be assigned as additional practice in class or for homework. A set of Activities in a cluster is followed by a section entitled What Have I Learned? As the name implies, students stop here to think about what they have learned before continuing to the next cluster. They have the opportunity to analyze and synthesize the ideas they studied in the cluster, and to test their knowledge by applying what they have learned to solve similar problems. You may want to use these sections to assess your students’ progress. Journal and writing assignments are good assessment tools for the questions in What Have I Learned? In addition, you will find suggestions for assessment in Sections

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    O VERVIEW 3 4, 5 and 7 of this guide. Students can also be encouraged to make these assignments part of their portfolios where they will have easy access to what they have learned when they are preparing for exams. How Can I Practice? sections follow What Have I Learned? sections to provide further opportunities for practice. Our textbook also addresses the need for plentiful skills practice and preparation for gateway exams that may be required in various programs. Appendix C includes two Skills Check sections specifically aimed to reinforce arithmetic skills. Each chapter concludes with  Chapter Summary  Gateway Review The Chapter Summary lists important concepts and skills from the chapter, together with a brief description and example of the concept or skill. The Chapter Summary provides reinforcement of what has been learned in the chapter and is helpful to students studying for exams . Following each Chapter Summary are Gateway Reviews, composed of exercises that test the fundamental concepts and skills in their respective chapters. Please note that some additional skills worksheets are provided in Section 6 of this Guide. You will also find several appendices in Mathematics in Action that provide just-in-time instruction on basic arithmetic and algebraic skills and the use of a graphing calculator.  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 Graphing Calculators The textbook also contains the following:  Answers to selected problems and gateway questions (the Instructor’s Edition contains answers to every problem within the text itself)  Glossary  Index TEXTBOOK SUPPLEMENTS A number of supplemental instructional and learning aids are available for users of Mathematics in Action and they are described here. Instructor Supplements Annotated Instructor’s Edition ISBN 10 – 0-13-498931-7 ISBN 13 – 978-0-13-498931-0 Contains all the content found in the student edition, plus answers to all exercises directly beneath each problem and Learning Catalytics instructor annotations.

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    4 O VERVIEW Instructor’s Resource Manual with Tests ISBN 10 – 0-13-498933-3 ISBN 13 – 978--0-13-498933-4 This valuable teaching resource includes the following materials:  Sample syllabi suggesting ways to structure the course around core and supplemental activities.  Sample course outlines containing timelines for covering topics.  Teaching notes for each chapter—ideal for using the text for the first time.  Extra skills practice worksheets for difficult topics.  Sample chapter tests and final exams.  Information about incorporating technology in the classroom, such as graphing calculators. TestGen® ISBN 10 – 0-13-516330-7 ISBN 13 – 978-0-13-516330-6 TestGen ® enables instructors to build, edit, print and administer tests using a computerized bank of questions developed to cover all the objectives of the text. TestGen is algorithmically based, allowing instructors to create multiple but equivalent versions of the same question or test with the click of a button. Instructors can also modify test bank questions or add new questions. Instructor’s Training Videos From author Ernie Danforth, the videos provide instructors with advice ranging from the Consortium teaching philosophy to tips for implementing group-work. New! PowerPoint Lectures These slides present key concepts and definitions from the text. These have been created to support instructors looking to implement this contextual approach in the classroom, and can also be used as a student study aid. Student Supplements Worksheets for Classroom or Lab Practice ISBN 10 – 0-13-516714-0 ISBN 13 – 978-0-13-516714-4  Provide extra practice to ensure that students have many opportunities to work problems related to the concepts learned in every activity.  Concept Connections, a feature unique to these worksheets, offer students an opportunity to show in words that they understand the mathematical concepts they have just practiced. Supplements for Instructors and Students MyLab Math® Online Course (access code required) MyLab Math from Pearson is the world’s leading online resource in mathematics, integrating interactive homework, assessment, and media in a flexible, easy to use format. It provides engaging experiences that

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    O VERVIEW 5 personalize, stimulate, and measure learning for each student. Moreover, it comes from an experienced partner with educational expertise and an eye on the future. MyLab Math is a complete online course that provides interactive, multimedia instruction correlated to this textbook content. A MyLab course provides the full eText with a multimedia library to provide additional support for students when they need it. For this revision, a new video series and PowerPoint series are available, in addition to MyLab's exercises with learning aids and feedback, a personalized study plan, and more. Instructor’s Training Video available in MyLab Math® (access code required) The Instructor’s Training Video discusses effective ways to implement the teaching pedagogy of the Mathematics in Action series, focusing on how to make collaborative learning, discovery learning, and alternative means of assessment work in the classroom. (Available in the Instructor Resources tab in MyLab Math®) PowerPoint Lectures are available in MyLab Math. These slides present key concepts and definitions from the text. These have been created to support instructors looking to implement this contextual approach in the classroom, and can also be used as a student study aid. To learn more about how MyLab Math combines proven learning applications with powerful assessment, visit www.MyLabMath.com or contact your Pearson representative. PEDAGOGY The pedagogical theme of Mathematics in Action is active learning, facilitated by emphasis on:  Writing to Learn Mathematics  Strategies for Problem Solving  Collaborative Learning in Groups  Whole-Class Interactive Discussions  Use of Technology Writing-to-learn strategies are built into the structure of the textbook, so students are consistently helped to think by writing, a time-honored way to learn mathematics. Section 5 of this Guide presents additional writing-to-learn techniques to share with your students. Students need to recognize and assimilate thinking strategies for problem solving. In Section 2, we describe our insights on the purposes and goals of individual activities, problems, and exercise sets, and the problem-solving strategies they elicit. In the classroom, we found, as many have, that the most active learning takes place in group settings where the teacher is a guide who helps students find their own correct understanding of concepts. Small groups promote attention to individual needs in learning, increase peer support for puzzling out solutions, and provide experience in teamwork. Whole-class interactive discussions allow an instructor to efficiently explain key concepts and clear up common misunderstandings, give students the opportunity to develop self-reliance in learning quantitative and algebraic skills for problem solving, and encourage the sharing and discussing of ideas in a large group setting. In Section 3, we share our experiences and offer

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    6 O VERVIEW suggestions for using collaborative learning and interactive discussion with the Activities and other components in the textbook. TECHNOLOGY Calculators and graphing programs are not only tools for doing mathematics and solving problems; they have fundamentally changed the way we teach and learn mathematics. We developed our textbook recognizing this modern pedagogical truth and you will find suggestions and ideas for using technology with the textbook in Section 4 of this Guide . Technology is an integral part of the textbook and a number of technical tools are compatible with the activities in the course.  Scientific Calculators  Graphing Calculators  Graphing Software  Tutorial Software for Skills Practice Scientific calculators are required and sufficient for the course, although graphing calculators are useful and are occasionally referenced for visual representation of functions in Chapters 3 and 4. Tutorial software can serve as an adjunct for practicing basic skills. You will find further discussion, suggestions, and examples regarding these tools in Section 4. SUGGESTIONS FOR SYLLABI Mathematics in Action : An Introduction to Algebraic, Graphical, and Numerical Problem Solving can be used as the text in a variety of foundation level courses. Among the authors, we have adopted all or part of the book for courses in arithmetic, elementary algebra, intermediate algebra, and introduction to functions. The number of contact hours for each of these courses varies considerably from three to six hours, with the latter often including a computer laboratory component. We compiled the following annotated list of the major mathematical topics covered in the textbook to serve as an effective guide for you to construct a syllabus that best suits your course. We have attempted to identify those activities that provide the essence of each major topic. In addition to these core activities, we have suggested other highly recommended activities that expand or reinforce the mathematical theme. We encourage you to use the many remaining activities for further exploration and practice. MATHEMATICAL TOPICS COVERED IN THE TEXTBOOK Below is a list of the major topics covered in Mathematics in Action. We then present an annotated list that indicates both the core activities and recommended supplemental activities that explore each of these topics.  Arithmetic Operations using Whole Numbers, Fractions (Rational Numbers) and Decimals  Numerical Literacy through Proportional Reasoning  Arithmetic Operations using Signed Numbers

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    O VERVIEW 7  Introduction to Variable Quantities; Numerical, Symbolic and Graphical Representations of Relationships Between Input and Output Variables  Symbolic Representation of Variable Quantities  Constructing, Evaluating, and Solving Single-Operation Algebraic Models  Constructing, Evaluating, and Solving Two-Operation Algebraic (Linear) Models  Equivalent Algebraic Expressions: Numerically, Graphically, and Algebraically  Solving More Complex (Linear) Equations  Function Definition and Notation  Rates of Change  Linear Functions: Numerical, Graphical, and Algebraic Features  Scatterplots and Linear Regression Equations  Problem Solving with Linear Functions  Systems of Linear Equations  Linear Inequalities  Polynomials and Properties of Exponents  Problem Solving with Quadratic Equations and Functions  A Brief Glimpse at Other Function Families ANNOTATED LIST OF CORE AND RECOMMENDED SUPPLEMENTAL ACTIVITIES Arithmetic Operations using Whole Numbers, Fractions and Decimals (Rational Numbers) Recommended: Activity 1.1 The Bookstore Steps in Problem Solving Develop communication skills and problem-solving skills; organize information. Recommended: Activity 1.2 The Classroom Problem-Solving Strategies Develop communication skills and problem-solving skills; organize information. Core: Activity 1.3 Properties of Arithmetic Properties and Vocabulary for Arithmetic Calculations Use the order of operations convention to evaluate arithmetic expressions containing positive integers; use the Distributive and Commutative Properties; exponential notation; use Scientific Notation for large numbers. Recommended: Appendix A Fractions Templates and skill practice. Recommended: Appendix B Decimals Templates and skill practice.

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    8 O VERVIEW Core: Activity 1.4 Top Chef Operations with Fractions and Mixed Numbers Add and subtract fractions; multiply and divide fractions. Core: Project 1.5 Course Grades and Your GPA Problem Solving Using Fractions and Decimals Solve problems with fractions and decimals. Numerical Literacy through Proportional Reasoning Core: Activity 1.6 Everything is Relative Ratios as Fractions, Decimals, and Percents Relative versus actual measures; express ratios as fractions, percents, and decimals; ratios as comparison. Core: Activity 1.7 The Opioid Epidemic Proportional Reasoning Proportional reasoning using ratios. Core: Activity 1.8 Who Really Did Better? Actual and Relative Change, Percent Increase and Decrease Investigate relative (percent) versus actual change – percent increase or percent decrease. Core: Activity 1.9 Going Shopping? Growth and Decay Factors Define and explore growth and decay factors. Core: Activity 1.10 Take an Additional 20% Off Consecutive Growth and Decay Factors Apply growth or decay factors consecutively. Core: Activity 1.11 Fuel Economy Rates and Unit Analysis Solve problems involving unit-of-measure conversions by Unit (Dimensional) Analysis. Arithmetic Operations using Signed Numbers Recommended: Activity 1.12 Celsius Thermometers Addition and Subtraction of Integers Add, subtract, and compare signed numbers; compute absolute values. Recommended: Activity 1.13 Shedding the Extra Pounds Multiplication and Division of Integers Multiply and divide signed numbers. Core: Activity 1.14 Order of Operations Revisited Negative Exponents and Scientific Notation Evaluate arithmetic expressions containing positive and negative numbers using the order of operations convention; evaluate expressions with negative exponents; Scientific Notation for very small numbers.

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    O VERVIEW 9 Introduction to Variable Quantities; Numerical, Graphical and Symbolic Representations of Relationships Between Input and Output Variables Core : Activity 2.1 Symbolizing Arithmetic Formulas and Algebraic Expressions Generalize from an arithmetic calculation to a symbolic representation by utilizing variables. Core: Activity 2.2 Blood Alcohol Levels Represent a Two-Variable Relationship Algebraically, Numerically, and Graphically Identify input and output in situations involving two variables; interpret relationships numerically and graphically. Recommended: Activity 2.3 College Expenses Symbolic Rules Identify input and output variables from a graph; write verbal rules and translate into symbolic rules. Symbolic Representation of Variable Quantities Core: Activity 2.4 Are they the Same? Equivalent Expressions and Grouping Symbols Identify equivalent algebraic expressions by examining their outputs and comparing the graphs. Constructing, Evaluating and Solving Single-Operation Algebraic Models Core: Activity 2.5 Let’s Go Shopping Solve an Equation Containing One Operation Construct, evaluate and solve equations of the form ax b  and x a b   . Constructing, Evaluating, and Solving Two-Operation (Linear) Algebraic Models Core: Activity 2.6 Leasing a Copier Solve an Equation Containing Two or More Operations Construct, evaluate and solve equations of the form ax + b = c, a ≠ 0. Core: Activity 2.7 The Algebra of Weather Solve a Formula for a Specified Variable Solve a formula (literal equation) for a specified variable. Core: Activity 2.8 Four Out of Five Dentists Prefer Crest Proportions Construct and solve proportion equations using equivalent fractions and cross multiplication. Equivalent Algebraic Expressions: Numerically, Graphically and Algebraically Core: Activity 2.9 Do It Two Ways Distributive Property, Greatest Common Factor, and Combining Like Terms Use the distributive property to transform one algebraic expression into an equivalent one. Expand and factor expressions; combine like terms.

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    10 O VERVIEW Recommended: Activity 2.10 Decoding Simplifying Algebraic Expressions Recognize an algebraic expression as a code of instruction; simplify algebraic expressions. Solving More Complex (Linear) Equations Core: Activity 2.11 Comparing Energy Costs Mathematical Models, General Strategy for Solving Linear Equations Model and solve equations of the form ax b cx d    . Recommended: Project Activity 2.12 Summer Job Opportunities Problem Solving Using Linear Equations Use critical thinking skills to make decisions based on solutions of systems of two linear equations. Function Definition and Notation Core: Activity 3.1 Summer Olympics Functions, Numerical and Graphical Representation of Functions Introduction to functions; function notation; graphical and numerical representations; expansion of rectangular coordinate system to include all 4 quadrants in the plane Core: Project 3.3 Comparing Symbolically Defined Functions and their Graphs Define functions by symbolic rules. Core: Activity 3.4 Course Grade Representing Functions Symbolically Determine symbolic rule that defines a function as well as practical domain and range of a function. Rates of Change Core: Activity 3.2 How Fast Did You Lose? Average Rate of Change Average rate of change—definition, contextual interpretations Linear Functions: Numerical, Graphical, and Algebraic Features Core: Activity 3.5 The Snowy Tree Cricket Slope and Intercepts of a Line Define linear functions by their constant rate of change and graph consisting of a single line; identify slope as the constant rate of change. Core: Activity 3.6 Software Sales Slope-Intercept Equation of a Line Write equation of line in slope intercept form; graph linear function using y-intercept and slope; use intercepts to graph linear equation. Recommended: Activity 3.7 Predicting Population Problem Solving Using Slope-Intercept Equation of a Line The slope-intercept form of a linear function; relative error in measurement using a linear model

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    O VERVIEW 11 Core: Activity 3.8 College Tuition Point-Slope Equation of a Line Determine equation for linear function when given two points. Identify lines having negative, zero or undefined slopes; equations of horizontal and vertical lines. Scatterplots and Regression Lines Recommended: Activity 3.9 Education Pays Line of Best Fit and Regression Equations Construct scatterplots from sets of data; use a scatterplot to estimate a line of best fit; generate linear regression models using technology. Recommended: Lab Activity 3.10 Body Parts Problem Solving Using Regression Equations Collect sets of data by measurement; use a scatterplot to estimate a line of best fit; generate linear regression models using technology. Systems of Linear Equations Core: Activity 3.11 Smartphone Plan Options Systems of Linear Equations in Two Variables Solve a system of two linear equations numerically, graphically and symbolically by the substitution method; interpret the solution. Recommended: Appendix D Addition Method for Solving a System of Two Linear Equations Core: Activity 3.12 Healthy Lifestyle Solving a System of Linear Equations in Two Variables Using the Addition Method Solve a system of two linear equations algebraically by the substitution method and by the addition method. Recommended: Project Activity 3.13 Modeling a Business Problem Solving Using Systems of Linear Equations in Two Variables Solve a system of two linear equations by any method; determine and interpret the break-even point; interpret break-even points in contextual situations. Linear Inequalities Recommended: Activity 3.14 How Long Can You Live? Linear Inequalities Solve linear inequalities in one variable algebraically and graphically. Polynomials and Properties of Exponents Core: Activity 4.1 Fatal Crashes Polynomials Identify, classify and simplify polynomials; add and subtract polynomials; evaluate and interpret polynomial models. Core: Activity 4.2 Volume of a Storage Box Properties of Exponents

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