Guided Workbook for Developmental Mathematics with Applications and Visualization

Description

About this book                                   

Experiencing Math in Context: Rockswold/Krieger’s unique approach presents students with the math in context first, before explaining the abstract mathematical theory behind it. This gives students a familiar and concrete foundation to build the concepts on. Math in the context of the real world is emphasized throughout – both to engage students’ interest, and to help them grasp mathematical concepts through tangible applications.

• NEW! Connecting Concepts with Your Life reinforces students’ knowledge needed to understand a new concept. The new Connecting Concepts with Your Life feature gives meaning to mathematics by relating common life experiences that students already understand.
• NEW! Math in Context engages students by connecting mathematics to current and relevant topics. This new feature helps students recognize when and how math connects to everyday life.
• UPDATED! Applications engage students by connecting mathematics to current and relevant topics. Several new examples have been added that discuss the mathematics of the Internet, social networking, tablet computers, and other contemporary topics.
• NEW! Modeling Data in hundreds of exercises and examples offer students the chance to model real and relevant data with their own functions.
• NEW! Online Exploration exercises invite students to find their own data on the Internet and use mathematics to analyze it.            
• Chapter Openers start each chapter with a contemporary application that motivates students by offering insights into the relevance of that chapter’s mathematical concepts.

Understanding and Visualizing the Concepts: The Rockswold/Krieger approach excels at promoting conceptual understanding above procedural skills. Additionally, an emphasis on visualization provides opportunities for students with different learning styles to successfully absorb the information presented.

• NEW! See the Concept presents a concise, visual overview of topics that were previously written out as text. Visualizing the math makes it accessible to all students. Companion See the Concept videos in MyLab Math, presented by the authors, help bring the concept to life. Each See the Concept video also has accompanying MyLab Math assessment questions, making these videos truly assignable .
• Putting It All Together boxes at the end of each section summarize techniques and reinforce the mathematical concepts presented in the section and are also available to be assigned in MyLab Math.
• NEW! Comment Balloons appear next to steps and procedures to make them more (immediately) understandable.
• Learning the Math from Multiple Perspectives presents concepts by means of verbal, graphical, numerical, and symbolic representations to support multiple learning styles and problem-solving methods.
• New Vocabulary is listed at the start of every section, highlighting the math concepts that are introduced in that section. This gives students a glimpse of the big picture of the section and helps with test preparation.
• Reading Check questions appear alongside important concepts, ensuring that students understand the material they have just read. These are located throughout every section. Many Reading Checks are assignable in MyLab Math.
• Making Connections occur throughout the text and help students see how previous concepts are related to new concepts. Many Making Connections exercises are assignable in MyLab Math.
• Critical Thinking exercises are included in most sections, posing questions that can be used for class discussion, group work, or homework assignments. Selected Critical Thinking features are also available to be assigned in MyLab Math.
• NEW! Guided Workbook is keyed to the text by section and objective and leads students through the course, giving them the opportunity to record key information, work practice problems, and show and keep their work for reference—as well as taking conceptual understanding one step further by asking students to explain Why? after select questions.

Practicing and Mastering the Concepts: Ample opportunity for students to practice and review the concepts and skills ensures students retain what they’ve learned.                 

• Now Try exercises follow every example for immediate reinforcement of the skills and concepts.
• NEW! Objective Lists at the beginning of each section give a clear outline of the section contents, making it easier to customize the course.               
• Concepts and Vocabulary exercises appear in every section. 
• Checking Basic Concepts exercises appear after every other section and can be used for individual or group review. These exercises require 10–20 minutes to complete and are also appropriate for in-class work. 
• Thinking Generally encourage students to synthesize what they have just learned with open-ended conceptual questions that appear in most section exercise sets.                                           
• Writing about Mathematics exercises appear at the end of most sections. Students are asked to explain the concepts behind the mathematical procedures they just learned in their own words, encouraging true understanding instead of simple rote memorization.                             
• Group Activities appear once or twice per chapter and provide an opportunity for students to work collaboratively on a problem that involves real-world data. Most activities can be completed with limited use of class time.                         
• Using a Graphing Calculator                                                                                 
• Graphing Calculator Exercise icons denote an optional exercise that requires students to have access to a graphing calculator.
• Technology Notes throughout the text are optional notes that offer students guidance, suggestions, and caution.
• Study Tips offer just-in-time suggestions to help students stay organized and focused on the material at hand.
• Chapter Summary combines key terms, topics, and procedures with illuminating examples to assist students as they prepare for the test with a quick but thorough review.
• Chapter Review Exercises requires students to work exercises and gain confidence while mastering the material.
• Chapter Tests provide students with rehearsal for the real thing and help reduce math anxiety. 
• Chapter Test Prep Videos offer additional help by showing an instructor working through the step-by-step solutions to every exercise in each Chapter Test.
• Cumulative Review Exercises Starting with Chapter 2 and appearing in all subsequent chapters, Cumulative Review Exercises help students see the big picture of math by reviewing topics and skills they have already learned.                                                                                                            

Also available with MyLab Math.

MyLab^™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. The 2nd Edition continues to help students develop conceptual understanding and bring key concepts to life with content and assignments that reflect the authors’ approach, including new Section Introduction videos and See the Concept videos with assessment. New Skill Builder assignments offer adaptive practice to build students’ foundational skills, and new workspace assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path. 

NEW! Expanded assignable content brings the hallmark Rockswold/Krieger approach into the MyLab course 

• NEW! See the Concept videos, created entirely by the authors,bring key concepts to life by providing a visual overview of each See the Concept feature in the text. Visualizing the math makes the content accessible to all students.
• NEW! Section Introduction videos, also created entirely by the authors, are available for every section of the text. These videos introduce the section’s concepts in a contextual setting, giving students an engaging and concrete introduction to the topics they’ll explore.
• NEW! Video assessment questions are available for all See the Concept and Section Introduction videos. This allows instructors to assign the video and encourage students to watch them to reinforce conceptual understanding.

In addition to Section Introduction and See the Concept videos, the complete video program includes section lectures, objective-level videos, and example-level videos, along with Chapter Test Prep videos that cover complete solutions from the Chapter Tests.

• EXPANDED! In addition to end of section exercises, additional content from the text, including many of the Reading Checks, Making Connections, and Critical Thinking features, is available in MyLab Math for instructors to assign.
• NEW! Drag and Drop exercises allow students to manually select elements of the question, such as expressions, words, graphs, or images, and place them into a designated target area. This interactive, new exercise type assesses and reinforces students’ grasp of key concepts.
• NEW! A three step learning path in MyLab Math encourages students to first Connect with the Math, then Review, and then Practice. The learning path encourages students to take advantage of the resources in their course, such as the See the Concept videos, and to review the section, before going right to their assignments.
• NEW! Guided Workbook is keyed to the text by section and objective and leads students through the course, giving them the opportunity to record key information, work practice problems, and show and keep their work for reference—as well as taking conceptual understanding one step further by asking students to explain Why? after select questions.

NEW! Expanded functionality makes MyLab Math more personalized and targeted than ever

• NEW! Skill Builder offers adaptive practice to build students’ foundational skills as they complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.
• NEW! Workspace Assignments allow students to show their mathematical reasoning as they progress step-by-step, with specific feedback at each step in the problem-solving process that adjusts to their path. When accessed via a mobile device, workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.
• NEW! An Integrated Review MyLab Math course is an alternate version of the MyLab Math course that provides the full suite of supporting resources plus additional assignments and study aids for students who will benefit from remediation on prerequisite topics. Assignments for the integrated review content are preassigned in MyLab Math, making it easier than ever to create your course!

NEW! Foster student engagement and peer-to-peer learning 

• NEW! Learning Catalytics^™ is available through MyLab Math, and helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking. A library of premade developmental math questions are available in MyLab Math to give instructors a starting point for using this classroom engagement tool.

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. Not only has he taught at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his PhD in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing. He is currently an emeritus professor of mathematics at Minnesota State University–Mankato. He is an author for Pearson Education and has numerous textbooks at the developmental and precalculus levels. Making mathematics accessible to students and professing the power of mathematics are special passions for Gary. He frequently gives keynote and invited addresses at regional, national, and international math conferences. In his spare time he enjoys sailing, doing yoga, hiking, and spending time with his family.

Terry Krieger has taught mathematics for over 20 years at the middle school, high school, vocational, community college, and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University–Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia, and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry has been involved with various aspects of mathematics textbook publication throughout his career. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing.

1. Whole Numbers
1.1 Introduction to Whole Numbers
1.2 Adding and Subtracting Whole Numbers; Perimeter
1.3 Multiplying and Dividing Whole Numbers; Area
1.4 Exponents, Variables, and Algebraic Expressions
1.5 Rounding and Estimating; Square Roots
1.6 Order of Operations
1.7 More with Equations and Problem Solving
2. Integers
2.1 Integers and the Number Line
2.2 Adding Integers
2.3 Subtracting Integers
2.4 Multiplying and Dividing Integers
2.5 Order of Operations; Averages
2.6 Solving Equations That Have Integer Solutions
3. Algebraic Expressions and Linear Equations
3.1 Simplifying Algebraic Expressions
3.2 Translating Words to Expressions and Equations
3.3 Properties of Equality
3.4 Solving Linear Equations in One Variable
3.5 Applications and Problem Solving
4. Fractions
4.1 Introduction to Fractions and Mixed Numbers
4.2 Prime Factorization and Lowest Terms
4.3 Multiplying and Dividing Fractions
4.4 Adding and Subtracting Fractions–Like Denominators
4.5 Adding and Subtracting Fractions–Unlike Denominators
4.6 Operations on Mixed Numbers
4.7 Complex Fractions and Order of Operations
4.8 Solving Equations Involving Fractions
5. Decimals
5.1 Introduction to Decimals
5.2 Adding and Subtracting Decimals
5.3 Multiplying and Dividing Decimals
5.4 Real Numbers, Square Roots, and Order of Operations
5.5 Solving Equations Involving Decimals
5.6 Applications from Geometry and Statistics
6. Ratios, Proportions, and Measurement
6.1 Ratios and Rates
6.2 Proportions and Similar Figures
6.3 The U.S. System of Measurement
6.4 The Metric System of Measurement
6.5 U.S.-Metric Conversions; Temperature
6.6 Time and Speed
7. Percents
7.1 Introduction to Percent; Circle Graphs
7.2 Using Equations to Solve Percent Problems
7.3 Using Proportions to Solve Percent Problems
7.4 Applications: Sales Tax, Discounts, and Net Pay
7.5 Applications: Simple and Compound Interest
7.6 Probability and Percent Chance
8. Geometry
8.1 Plane Geometry: Points, Lines, and Angles
8.2 Triangles
8.3 Polygons and Circles
8.4 Perimeter and Circumference
8.5 Area, Volume, and Surface Area
9. Linear Equations and Inequalities in One Variable
9.1 Review of Linear Equations in One Variable
9.2 Further Problem Solving
9.3 Linear Inequalities in One Variable
10. Graphing Equations
10.1 Introduction to Graphing
10.2 Equations in Two Variables
10.3 Intercepts; Horizontal and Vertical Lines
10.4 Slope and Rates of Change
10.5 Slope-Intercept Form
10.6 Point-Slope Form
10.7 Introduction to Modeling

11. Systems of Linear Equations in Two Variables
11.1 Solving Systems of Linear Equations Graphically and Numerically
11.2 Solving Systems of Linear Equations by Substitution
11.3 Solving Systems of Linear Equations by Elimination
11.4 Systems of Linear Inequalities
12. Polynomials and Exponents
12.1 Rules for Exponents
12.2 Addition and Subtraction of Polynomials
12.3 Multiplication of Polynomials
12.4 Special Products
12.5 Integer Exponents and the Quotient Rule
12.6 Division of Polynomials
13. Factoring Polynomials and Solving Equations
13.1 Introduction to Factoring
13.2 Factoring Trinomials I (x2 + bx + c)
13.3 Factoring Trinomials II (ax2 + bx + c)
13.4 Special Types of Factoring
13.5 Summary of Factoring
13.6 Solving Equations by Factoring I (Quadratics)
13.7 Solving Equations by Factoring II (Higher Degree)
14. Rational Expressions
14.1 Introduction to Rational Expressions
14.2 Multiplication and Division of Rational Expressions
14.3 Addition and Subtraction with Like Denominators
14.4 Addition and Subtraction with Unlike Denominators
14.5 Complex Fractions
14.6 Rational Equations and Formulas
14.7 Proportions and Variation
15. Introduction to Functions
15.1 Functions and Their Representations
15.2 Linear Functions
15.3 Compound Inequalities and Piecewise-Defined Functions
15.4 Other Functions and Their Properties
15.5 Absolute Value Equations and Inequalities
16. Systems of Linear Equations
16.1 Systems of Linear Equations in Three Variables
16.2 Matrix Solutions of Linear Systems
16.3 Determinants
17. Radical Expressions and Functions
17.1 Radical Expressions and Functions
17.2 Rational Exponents
17.3 Simplifying Radical Expressions
17.4 Operations on Radical Expressions
17.5 More Radical Functions
17.6 Equations Involving Radical Expressions
17.7 Complex Numbers
18. Quadratic Functions and Equations
18.1 Quadratic Functions and Their Graphs
18.2 Transformations and Translations of Parabolas
18.3 Quadratic Equations
18.4 The Quadratic Formula
18.5 Quadratic Inequalities
18.6 Equations in Quadratic Form
19. Exponential and Logarithmic Functions
19.1 Composite and Inverse Functions
19.2 Exponential Functions
19.3 Logarithmic Functions
19.4 Properties of Logarithms
19.5 Exponential and Logarithmic Equations
20. Conic Sections
20.1 Parabolas and Circles
20.2 Ellipses and Hyperbolas
20.3 Nonlinear Systems of Equations and Inequalities
21. Sequences and Series
21.1 Sequences
21.2 Arithmetic and Geometric Sequences
21.3 Series
21.4 The Binomial Theorem
Appendix A: Using the Graphing Calculator
Appendix B: Sets
Appendix C: Linear Programming
Appendix D: Synthetic Division
Appendix E: Using a Calculator

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