“Do the Math” Video Notebook for Elementary & Intermediate Algebra

“Do the Math” Video Notebook for Elementary & Intermediate Algebra

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Table of Contents

  1. Operations on Real Numbers and Algebraic Expressions
    • 1.1. Success in Mathematics
    • 1.2. Fractions, Decimals, and Percents
    • 1.3. The Number Systems and the Real Number Line
    • 1.4. Adding, Subtracting, Multiplying, and Dividing Integers
    • 1.5. Adding, Subtracting, Multiplying, and Dividing Rational Numbers
      • Putting the Concepts Together (Sections 1.2 — 1.5)
    • 1.6. Properties of Real Numbers
    • 1.7. Exponents and the Order of Operations
    • 1.8. Simplifying Algebraic Expressions
    • Chapter 1 Activity: The Math Game
    • Chapter 1 Review
    • Chapter 1 Test
  2. Linear Equations and Inequalities in One Variable
    • 2.1. Linear Equations: The Addition and Multiplication Properties of Equality
    • 2.2. Linear Equations: Using the Properties Together
    • 2.3. Solving Linear Equations Involving Fractions and Decimals; Classifying Equations
    • 2.4. Evaluating Formulas and Solving Formulas for a Variable
      • Putting the Concepts Together (Sections 2.1 — 2.4)
    • 2.5. Problem Solving: Direct Translation
    • 2.6. Problem Solving: Problems Involving Percent
    • 2.7. Problem Solving: Geometry and Uniform Motion
    • 2.8. Solving Linear Inequalities in One Variable
    • Chapter 2 Activity: Pass to the Right
    • Chapter 2 Review
    • Chapter 2 Test
    • Cumulative Review Chapters 1 — 2
  3. Introduction to Graphing and Linear Equations in Two Variables
    • 3.1. The Rectangular Coordinate System and Linear Equations in Two Variables
    • 3.2. Graphing Linear Equations in Two Variables
    • 3.3. Slope
    • 3.4. Slope-Intercept Form of a Line
    • 3.5. Point-Slope Form of a Line
    • 3.6. Parallel and Perpendicular Lines
      • Putting the Concepts Together (Sections 3.1 — 3.6)
    • 3.7. Linear Inequalities in Two Variables
    • Chapter 3 Activity: Graphing Practice
    • Chapter 3 Review
    • Chapter 3 Test
    • Cumulative Review Chapters 1 — 3
  4. Systems of Linear Equations and Inequalities
    • 4.1. Solving Systems of Linear Equations by Graphing
    • 4.2. Solving Systems of Linear Equations Using Substitution
    • 4.3. Solving Systems of Linear Equations Using Elimination
      • Putting the Concepts Together (Sections 4.1 — 4.3)
    • 4.4. Solving Direct Translation, Geometry, and Uniform Motion Problems Using Systems of Linear Equations
    • 4.5. Solving Mixture Problems Using Systems of Linear Equations
    • 4.6. Systems of Linear Inequalities
    • Chapter 4 Activity: Find the Numbers
    • Chapter 4 Review
    • Chapter 4 Test
    • Cumulative Review Chapters 1 — 4
  5. Exponents and Polynomials
    • 5.1. Adding and Subtracting Polynomials
    • 5.2. Multiplying Monomials: The Product and Power Rules
    • 5.3. Multiplying Polynomials
    • 5.4. Dividing Monomials: The Quotient Rule and Integer Exponents
      • Putting the Concepts Together (Sections 5.1 — 5.4)
    • 5.5. Dividing Polynomials
    • 5.6. Applying the Exponent Rules: Scientific Notation
    • Chapter 5 Activity: What Is the Question?
    • Chapter 5 Review
    • Chapter 5 Test
    • Cumulative Review Chapters 1 — 5
  6. Factoring Polynomials
    • 6.1. Greatest Common Factor and Factoring by Grouping
    • 6.2. Factoring Trinomials of the Form x2 + bx + c
    • 6.3. Factoring Trinomials of the Form ax2 + bx + c, a ≠ 1
    • 6.4. Factoring Special Products
    • 6.5. Summary of Factoring Techniques
      • Putting the Concepts Together (Sections 6.1 — 6.5)
    • 6.6. Solving Polynomial Equations by Factoring
    • 6.7. Modeling and Solving Problems with Quadratic Equations
    • Chapter 6 Activity: Which One Does Not Belong?
    • Chapter 6 Review
    • Chapter 6 Test
    • Cumulative Review Chapters 1 — 6
    • Getting Ready for Intermediate Algebra: A Review of Chapters 1 — 6
  7. Rational Expressions and Equations
    • 7.1. Simplifying Rational Expressions
    • 7.2. Multiplying and Dividing Rational Expressions
    • 7.3. Adding and Subtracting Rational Expressions with a Common Denominator
    • 7.4. Finding the Least Common Denominator and Forming Equivalent Rational Expressions
    • 7.5. Adding and Subtracting Rational Expressions with Unlike Denominators
    • 7.6. Complex Rational Expressions
      • Putting the Concepts Together (Sections 7.1 — 7.6)
    • 7.7. Rational Equations
    • 7.8. Models Involving Rational Equations
    • Chapter 7 Activity: Correct the Quiz
    • Chapter 7 Review
    • Chapter 7 Test
    • Cumulative Review Chapters 1 — 7
    • Getting Ready for Intermediate Algebra: A Review of Chapters 1 — 7
    • Getting Ready for Chapter 8: Interval Notation
  8. Graphs, Relations, and Functions
    • 8.1. Graphs of Equations
    • 8.2. Relations
    • 8.3. An Introduction to Functions
    • 8.4. Functions and Their Graphs
      • Putting the Concepts Together (Sections 8.1 — 8.4)
    • 8.5. Linear Functions
    • 8.6. Compound Inequalities
    • 8.7. Absolute Value Equations and Inequalities
    • 8.8. Variation
    • Chapter 8 Activity: Shifting Discovery
    • Chapter 8 Review
    • Chapter 8 Test
    • Chapters 1 — 8 Cumulative Review
  9. Radicals and Rational Exponents
    • 9.1. Square Roots
    • 9.2. nth Roots and Rational Exponents
    • 9.3. Simplify Expressions Using the Laws of Exponents
    • 9.4. Simplifying Radical Expressions
    • 9.5. Adding, Subtracting, and Multiplying Radical Expressions
    • 9.6. Rationalizing Radical Expressions
      • Putting the Concepts Together (Sections 9.1 — 9.6)
    • 9.7. Functions Involving Radicals
    • 9.8. Radical Equations and Their Applications
    • 9.9. The Complex Number System
    • Chapter 9 Activity: Which One Does Not Belong?
    • Chapter 9 Review
    • Chapter 9 Test
    • Cumulative Review Chapters 1 — 9
  10. Quadratic Equations and Functions
    • 10.1. Solving Quadratic Equations by Completing the Square
    • 10.2. Solving Quadratic Equations by the Quadratic Formula
    • 10.3. Solving Equations Quadratic in Form
      • Putting the Concepts Together (Sections 10.1 — 10.3)
    • 10.4. Graphing Quadratic Functions Using Transformations
    • 10.5. Graphing Quadratic Functions Using Properties
    • 10.6. Polynomial Inequalities
    • 10.7. Rational Inequalities
    • Chapter 10 Activity: Presidential Decision Making
    • Chapter 10 Review
    • Chapter 10 Test
    • Cumulative Review Chapters 1 — 10
  11. Exponential and Logarithmic Functions
    • 11.1. Composite Functions and Inverse Functions
    • 11.2. Exponential Functions
    • 11.3. Logarithmic Functions
      • Putting the Concepts Together (Sections 11. 1 — 11.3)
    • 11.4. Properties of Logarithms
    • 11.5. Exponential and Logarithmic Equations
    • Chapter 11 Activity: Correct the Quiz
    • Chapter 11 Review
    • Chapter 11 Test
    • Cumulative Review Chapters 1 — 11
  12. Conics
    • 12.1. Distance and Midpoint Formulas
    • 12.2. Circles
    • 12.3. Parabolas
    • 12.4. Ellipses
    • 12.5. Hyperbolas
      • Putting the Concepts Together (Sections 12.1 — 12.5)
      • Nonlinear Systems of Equations
    • Chapter 12 Activity: How Do You Know That…?
    • Chapter 12 Review
    • Chapter 12 Test
    • Cumulative Review Chapters 1 — 12
  13. Sequences, Series, and the Binomial Theorem
    • 13.1. Sequences
    • 13.2. Arithmetic Sequences
    • 13.3. Geometric Sequences and Series
    • 13.4. The Binomial Theorem
    • Chapter 13 Activity: Pass to the Right
    • Chapter 13 Review
    • Chapter 13 Test
    • Cumulative Review Chapters 1 — 13

Appendix A: Synthetic Division

Appendix B: Geometry Review

Appendix C: More on Systems of Linear Equations

Appendix D: Table of Square Roots

Appendix E: Transformations

Answers to Selected Exercises

With training in mathematics, statistics, and economics, Michael Sullivan III has a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series, which he writes with his father, Michael Sullivan.

 

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series.When not in the classroom or writing, Michael enjoys spending time with his three children, Michael, Kevin, and Marissa, and playing golf. Now that his two sons are getting older, he has the opportunity to do both at the same time!

 

Kathy Struve has been a classroom teacher for nearly 35 years, first at the high school level and, for the past 27 years, at Columbus State Community College. Kathy embraces classroom diversity: diversity of students’ age, learning styles, and previous learning success. She is aware of the challenges of teaching mathematics at a large, urban community college, where students have varied mathematics backgrounds and may enter college with a high level of mathematics anxiety.

 

Kathy served as Lead Instructor of the Developmental Algebra sequence at Columbus State, where she developed curriculum, conducted workshops, and provided leadership to adjunct faculty in the mathematics department. She embraces the use of technology in instruction, and has taught web and hybrid classes in addition to traditional face-to-face emporium-style classes. She is always looking for ways to more fully involve students in the learning process. In her spare time Kathy enjoys spending time with her two adult daughters, her four granddaughters, and biking, hiking, and traveling with her husband.

 

Born and raised in San Diego county, Janet Mazzarella spent her career teaching in culturally and economically diverse high schools before taking a position at Southwestern College 25 years ago. Janet has taught a wide range of mathematics courses from arithmetic through calculus for math/science/engineering majors and has training in mathematics, education, engineering, and accounting.

 

Janet has worked to incorporate technology into the curriculum by participating in the development of Interactive Math and Math Pro. At Southwestern College, she helped develop the self-paced developmental mathematics program. In addition, Janet was the Dean of the School of Mathematics, Science, and Engineering, the Chair of the Mathematics Department, the faculty union president, and the faculty coordinator for Intermediate Algebra. In the past, free time consisted of racing motorcycles off-road in the Baja 500 and rock climbing, but recently she has given up the adrenaline rush of these activities for the thrill of traveling in Europe.

Jessica Bernards and Wendy Fresh of Portland Community College have worked extensively with the author team to create the How to exercises, new Geogebra applet exercises, and have made the assignments for the New MyMathLab courses.

About the Book

 

Extra Sullivan-level Student Support

  • Quick Response (QR) codes now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. They link students to the videos and applets that are available for that section, giving them resources at their fingertips.

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.

  • Video Program gives students just-in-time help at home, in the lab, or to go through a wealth of video resources in the MyMathLab course. Video resources include:
    • Author-in-Action videos feature author Mike Sullivan delivering in-class lectures and interacting with a live student audience. Students have access to a master teacher regardless of where and when they are studying.
    • Example-level solution clips
    • Chapter Test Prep videos help students during their most teachable moment–when they are preparing for a test with  step-by-step solutions for the exercises found in each Chapter Test.
  • How To exercises ask students to test their knowledge and are truly assignable in MyLab Math. These Guided Exercises walk students through each step of the problem-solving process, giving them a guided, step-by-step learning experience. These exercises were written and developed by Jessica Bernards and Wendy Fresh who are contributors to the author team.  Students are required to respond to questions as the steps to solving problems are developed.  This is similar to the Help Me Solve This feature in MyLab Math. They keep students engaged while developing their conceptual understanding.
  • GeoGebra applets have been developed by Jessica Bernards and Wendy Fresh along with discovery activities to allow students to develop understanding of mathematical concepts through experiential learning. These enable students to explore and manipulate math in a visual and tangible way. The Geogebra applets may be found in MyLab Math or directly at www.pearsonhighered.com/SullivanApplets.
  • Quick Response (QR) codes now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. Each code links students to the videos and applets that are available for that section, giving them resources at their fingertips.
  • Learning Catalytics™ 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.

The Video Notebook is an unbound, three-hole-punched workbook/note-taking guide that students use in conjunction with the Sullivan/Struve/Mazzarella “Author in Action” videos. The notebook helps them develop organized notes as they work along with the videos.

  • A Video Guide for each section is organized by learning objective. Typically, there is one Author in Action video per objective, and students are asked to write down important definitions and procedures and work through key examples as they watch the video.
  • The clean layout and ample space let students write out full definitions and show all work for the examples.
  • The unbound, loose-leaf format allows students to insert additional notes from class and/or homework–so they can build a course notebook and good study skills for future classes!

The Video Notebook is an unbound, three-hole-punched workbook/note-taking guide that students use in conjunction with the Sullivan/Struve/Mazzarella “Author in Action” videos. The notebook helps them develop organized notes as they work along with the videos.

  • A Video Guide for each section is organized by learning objective. Typically, there is one Author in Action video per objective, and students are asked to write down important definitions and procedures and work through key examples as they watch the video.
  • The clean layout and ample space let students write out full definitions and show all work for the examples.
  • The unbound, loose-leaf format allows students to insert additional notes from class and/or homework–so they can build a course notebook and good study skills for future classes!

About the Book

 

Unique Sullivan examples and exercise sets distinguish the text

  • Sullivan Examples are presented in a two-column, annotated format that explains what the authors are about to do in each step, just as a professor would. These examples read left to right, so that students understand what each step is accomplishing as they read through. (Often examples have annotations or pointers after each step, rather than before.)
  • Showcase Examples take the explanations one step further with a three column format that breaks the problem solving process down for students. The left column describes a step, the middle column provides a brief annotation, as needed, to explain the step, and the right column presents the algebra. These are now covered in MyLab™ Math as well, as Guided “How To” exercises,  giving students step-by-step support as they work through a problem.
  • The Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to “do the math”—at home or in the lab—through a full suite of resources that support a variety of learning environments.
  • Variety of exercise types throughout each section
    • Building Skills exercises develop students’ understanding of the procedures and skills in working with the methods presented in the section.
    • Mixed Practice exercises offer comprehensive skill assessment by asking students to relate multiple concepts or objectives.
    • Quick Check exercises exercises follow the examples, allowing students to apply what they have just learned. These are numbered as the first problems in each section’s exercise set, making them assignable as homework, and giving an easy way refer back to the relevant examples for extra help. Quick Checks include fill-in-the-blank and True/False questions to assess students’ understanding of vocabulary and formulas. Quick Checks are numbered as part of the homework set, and are assignable in MyLab Math for instructors.

 

Extra Sullivan-level Student Support

  • NEW! Quick Response (QR) codes now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. They link students to the videos and applets that are available for that section, giving them resources at their fingertips.
  • “Are You Prepared for this Section” problems test students’ grasp of the prerequisite material for each new section.
  • Explaining the Concepts problems ask students to explain concepts in their own words.
  • Various exercises to assist students’ understanding
    • Applying the Concepts exercises ask students to apply the mathematical concepts to real-world situations.
    • Extending the Concepts exercises go beyond the basics, using a variety of problems to sharpen students’ critical-thinking skills.
    • Synthesis Review exercises help students grasp the “big picture” of algebra—once they have a sufficient conceptual foundation to build upon from their work in Chapters R through 4. Synthesis Review exercises ask students to perform a single operation (adding, solving, and so on) on several objects (polynomials, rational expressions, and so on). The student is then asked to discuss the similarities and differences in performing the same operation on the different objects.
    • Technology exercises are included at the close of a section’s exercise set, allow for the use of graphing technology, such as graphing calculators, GeoGebra, or Demos to solve problems. These exercises are entirely optional.
  • Problem Icons flag selected problems to denote that:
    • Problems whose number is green have complete worked-out solutions in video found in MyLab Math.
    • Problems with a triangle icon focus on geometry concepts.
  • Section R.1: Success in Mathematics focuses the student on basic study skills, including what to do during the first week of the term; what to do before, during, and after class; how to use the text effectively; and how to prepare for an exam.
  • In Other Words helps to address the difficulty that students have in reading mathematically precise definitions and theorems by explaining them in easier to understand language.
  • Work Smart provides “tricks of the trade” hints, tips, reminders, and alerts. It also identifies some common errors to avoid and helps students work more efficiently.
  • Work Smart: Study Skills reminds students of study skills that will help them to succeed at various points in the course. Attention to these practices will help them to become better, more proficient learners.
  • Chapter Tests help students to make sure they understand the key topics in the chapter. The exercises in the Chapter Tests have been crafted to reflect the level and types of exercises a student is likely to see on a classroom test.

 

Helping Students Tie the Ideas Together

  • The Big Picture: Putting It Together (Chapter Opener) features are based on how we start each chapter in the classroom—with a quick sketch of what we plan to cover. These sections tie concepts and techniques together by summarizing material covered previously and then relate these ideas to upcoming material.
  • Putting the Concepts Together (Mid-Chapter Review) are groups of exercises in each chapter, at the appropriate point in the chapter, which serve as a review—synthesizing material introduced up to that point in the chapter. The exercises in these mid-chapter reviews are carefully chosen to assist students in seeing the “big picture.”
  • Cumulative Review Learning: Algebra is a building process, and building involves considerable reinforcement. The Cumulative Review exercises at the end of each odd-numbered chapter, starting with Chapter 1, help students reinforce and solidify their knowledge by revisiting concepts and using them in context. Cumulative Reviews for each even-numbered chapter can be found on the Instructor’s Resource Center. Answers to all cumulative review problems appear in the back of the text.

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.

  • MyLab Math course includes pre-made and preassigned homework assignments,based on the authors’ experience, helping students and instructors get the most of our their MyLab Math course.
    • Instructors have the ability to teach immediately with premade/assigned assignments, but also can edit or remove assignments as needed. The assignments for each section are comprised of two parts:

1) Learn, Explore, and Quick Check Exercises–these assignments are comprised of How-to exercises, applet exercises, video, and Quick Check problems.

2) Homework Exercises

The assignments are structured so that students will cover a typical course while employing the 2 to 3 hours outside of class for every credit hour of the class weekly.  This is based on data derived by the authors from the Third Editions.

 

  • EXPANDED! Video Program gives students just-in-time help at home, in the lab, or to go through a wealth of video resources in the MyLab Math course. Video resources include:
    • Author-in-Action videos feature author Mike Sullivan delivering in-class lectures and interacting with a live student audience. Students have access to a master teacher regardless of where and when they are studying.
    • Example-level solution clips
    • Chapter Test Prep videos help students during their most teachable moment–when they are preparing for a test with  step-by-step solutions for the exercises found in each Chapter Test.
  • NEW! How To exercises ask students to test their knowledge and are truly assignable in MyLab Math. These  Guided Exercises walk students through each step of the problem-solving process, giving them a guided, step-by-step learning experience. These exercises were written and developed by Jessica Bernards and Wendy Fresh who are contributors to the author team.  Students are required to respond to questions as the steps to solving problems are developed. This is similar to the Help Me Solve This feature in MyLab Math. They keep students engaged while developing their conceptual understanding.
  • NEW! GeoGebra applets have been developed by Jessica Bernards and Wendy Fresh along with discovery activities to allow students to develop understanding of mathematical concepts through experiential learning.  These enable students to explore and manipulate math in a visual and tangible way. The Geogebra applets may be found in MyLab Math or directly at www.pearsonhighered.com/SullivanApplets.
  • NEW! Quick Response (QR) codes now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. Each code links students to the videos and applets that are available for that section, giving them resources at their fingertips.
  • NEW! Learning Catalyticshelps 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.

Additional information

Dimensions 1.25 × 8.55 × 11.00 in
Imprint

Format

ISBN-13

ISBN-10

Author

, ,

Subjects

mathematics, higher education, Developmental Math, Combo: Elementary and Intermediate