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Review:This book was written to help students make the transition from arithmetic to algebra. To reach this goal, I introduce algebraic concepts early and repeat them as I treat traditional arithmetic topics, thus laying the groundwork for the next algebra course your students will take. A second goal was to show students the relevancy of the mathematics in everyday life and in the workplace.
In preparing this third edition, I considered the comments and suggestions of colleagues throughout the country and of the many users of previous editions. The numerous features that contributed to the success of the second edition have been retained. This updated revision includes new mathematical content and increased attention to geometric concepts, data interpretation, problem solving, and real-life applications. I have carefully chosen pedagogical features to help students understand and retain concepts. The AMATYC Crossroads in Mathematics document and the NCTM Standards (plus Addenda) also influenced the careful reexamination of every section of the text. The key content and pedagogical features are described on this and the following pages.
In addition, the supplements to this text have been enhanced and the range of supplements increased, offering a complete integrated teaching and learning package for maximum support and effectiveness. KEY PEDAGOGICAL FEATURES IN THE THIRD EDITION
Readability and Connections. Many reviewers of this edition as well as users of the previous editions have commented favorably on the readability and clear, organized presentation. I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. As new topics are presented, efforts have been made to relate the new ideas to those that the students may already know. Constant reinforcement and connections within problem-solving strategies, geometric concepts, pattern recognition, and situations from everyday life can help students gradually master both new and old information.
Accessible Real-World Applications. An abundance of new practical applications are found throughout the book in worked-out examples and exercise sets. The applications were carefully chosen to be accessible, to help motivate students, and to strengthen their understanding of mathematics in the real world. They help show connections to a wide range of fields such as agriculture, allied health, astronomy, automotive ownership and maintenance, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, cooking, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry, statistics, and probability. (See also the Index of Applications on page xx.) Many of the applications are based on recent and interesting real-life data. Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included.
Problem-Solving Process. This is formally introduced in Chapter 3 with a four-step process that is integrated throughout the text. The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' comfort level and confidence when solving problems.
Unique Exercise Sets. Each section ends with an Exercise Set, divided in parts. All parts contain graded exercises. Each exercise in the set, except those found in the parts labeled Review and Preview or Combining Concepts, is keyed to at least one of the objectives of the section. As appropriate, exercises are also keyed to one or more specific worked examples in the text. Exercises and examples marked with a video cassette icon have been worked out step-by-step by the author in the videos that accompany this text.
Throughout the exercise sets, there is an emphasis on Data and Graphical Interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. In addition, sections in Chapter 8 reinforce and extend these concepts. Similarly, throughout the text there is integration of Geometric Concepts, such as perimeter and area. Chapter 9 then provides a concise introduction and further coverage of geometry. A geometry icon o indicates exercises, examples or full sections involving geometric concepts.
In addition to the approximately 4400 exercises in end-of-section exercise sets, exercises may also be found in the Pretests, Integrated Reviews, Chapter Reviews, Chapter Tests, and Cumulative Reviews. Each exercise set contains one or more of the following features.
Mental Mathematics. These problems are found at the beginning of many exercise sets. They are mental warmups that reinforce concepts found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselve but also their number sense and estimation ability.
Review and Preview. Formerly called Review Exercises, these exercises occur in each exercise set (except for those in Chapter 1). These problems are keyed to earlier sections and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the links between earlier topics and later material.
NEW! Combining Concepts. These exercises are found at the end of each exercise set after the Review and Preview exercises. New to this edition, Combining Concepts exercises require students to combine several concepts from that section or to take the concepts of the section a step further by combining them with concepts learned in previous sections. For instance, sometimes students are required to combine the concepts of a section with the problem-solving process they learned in Chapter 3 to try their hand at solving an application problem. In addition, there are conceptual exercises that occur outside the Combining Concepts part of the exercise set, and these are keyed with an icon.
Writing Exercises. These exercises, found in almost every exercise set, are keyed with a pencil icon. They require students to show an understanding of a concept learned in the corresponding section. This is accomplished by asking students questions that require them to stop, think, and explain in their own words the concepts) used in the exercises they have just completed. Guidelines recommended by the American Mathematical Association of Two-Year Colleges (AMATYC Crossroads in Mathematics guidelines) and other professional groups suggest incorporating writing in mathematics courses to reinforce concepts.
NEW! Internet Excursions. New to this edition, these exercises occur once per chapter. Internet Excursions require students to use the internet as a source of information or a data-collection tool to complete the exercises, allowing students first-hand experience with manipulating and working with real data.
Practice Problems. Throughout the text, each worked example has a parallel problem called a Practice Problem, found in the margin. Practice Problems invite students to be actively involved in the learning process before beginning the section exercise set. Practice Problems immediately reinforce a skill or concept as it is being developed.
NEW! Concept Checks. These new margin exercises are appropriately placed in many sections of the text. They invite students to immediately check their conceptual understanding as material is developed, offering an additional way to actively involve students in the learning process.
NEW! Integrated Reviews. These "mid-chapter reviews" are appropriately placed once per chapter. The new Integrated Reviews allow students to review and assimilate the many different skills learned separately over several sections before moving on to related material in the chapter.
NEW! Helpful Hints. Helpful Hints, formerly Reminders, contain practical advice on applying mathematical concepts. These are found throughout the text and strategically placed where students are most likely to need immediate reinforcement. Helpful Hints are highlighted for quick reference.
Focus On. Appropriately placed throughout each chapter, these are divided into Focus on Study Skills, Focus on Mathematical Connections, Focus on Business and Career, Focus on the Real World, and Focus on History. They are new to this edition and written to help students develop effective habits for studying mathematics, engage in investigations of other branches of mathematics, and understand the importance of mathematics in various careers and in the world of business. They help show the relevance of mathematics in both the present and past through critical thinking exercises and group activities.
Calculator Explorations. These optional explorations offer point-of-use instruction, through examples and exercises, on the proper use of calculators as tools in the mathematical problem-solving process. Placed appropriately throughout the text, Calculator Explorations also reinforce concepts learned in the corresponding section.
Additional exercises building on the skill developed in the Explorations may be found in exercise sets throughout the text. Exercises requiring a calculator are marked with a calculator icon. The inside back cover of the text includes a brief description of selected keys on a scientific calculator for reference as desired.
Chapter Activity. These features, formerly Group Activity, occur once per chapter at the end of the chapter, often serving as a chapter wrap-up. For individual or group completion, the Chapter Activity, usually hands-on or data based, complements and extends the concepts of the chapter, allowing students to make decisions and interpretations and to think and write about mathematics.
Visual Reinforcement of Concepts. The text contains a wealth of graphics, models, photographs, and illustrations to visually clarify and reinforce concepts. These include bar graphs, line graphs, calculator screens, application illustrations, and geometric figures.
NEW! Pretests. New to this edition, each chapter begins with a pretest that is designed to help students identify areas where they need to pay special attention in the upcoming chapter.
Chapter Highlights. Found at the end of each chapter, these contain key definitions, concepts, and examples to help students understand and retain what they have learned.
Chapter Review and Test. The end of each chapter contains a review of topics introduced in the chapter. The Chapter Review offers exercises that are keyed to sections of the chapter. The Chapter Test is a practice test and is not keyed to sections of the chapter.
Cumulative Review. These are found at the end of each chapter (except Chapter 1). Each problem contained in the cumulative review is actually an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete worked-out solution, with explanation, can do so by turning to the appropriate example in the text.
Student Resource Icons. At the beginning of each section, videotape, software, study guide, and solutions manual icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to help them review concepts and skills at their own pace. These items have direct correlation to the text and emphasize the text's methods of solution.
NEW! Functional Use of Color and Design. Elements of the text are now highlighted with full color or design to make it easier for students to read and study. Color is also used to clarify the problem-solving process in worked examples. NEW KEY CONTENT FEATURES IN THE THIRD EDITION
Greater Emphasis on Geometry. There is increased emphasis and coverage of geometric concepts. This was accomplished by retaining the early introduction and integration of the concepts of perimeter and area (see Sections 1.2 and 1.5), strengthening the coverage of geometry within sections (see Sections 3.1 and 5.8), and providing a new chapter on Geometry and Measurement together with an Integrated Review dedicated to geometry concepts (see Chapter 9). A geometry icon indicates exercises, examples, or full sections involving geometric concepts.
Designed to be as flexible as possible, instructors may elect to use the new chapter as a convenient unit on geometry or use a section or sections in conjunction with earlier chapters. For instance, Section 9.3 on perimeter may be taught anytime after Section 3.5.
There is a geometry appendix containing a review of geometric figures and a new appendix contains coverage of surface area. The inside front cover of this text provides a summary of geometric formulas for easy reference. Formulas include perimeter, area, volume, circumference, and surface area.
The sections on geometry and measurement are written to help increase students' spatial sense, relate general geometric ideas to number and measurement ideas, and make and use estimates of measurement.
Expanded Coverage of Ratio and Proportion. The treatment of ratio and proportion now includes separate sections on rates (see Section 6.2) and proportions and problem solving (see Section 6.4).
The chapter on percent now offers full section coverage of solving percent problems with equations and solving percent problems with proportions (see Sections 7.2 and 7.3). The expanded coverage of ratio and proportion allows for an increased number of application problems, and increased flexibility in the amount and use of topics needed for students to succeed in both this course and future courses.
Increased Attention to Reading Graphs. The widely praised treatment of reading and interpreting graphs has been expanded to two sections (see Sections 8.1 and 8.2). In addition, there has been a significant increase in the number of examples and exercises throughout the text using a graph, table, or chart.
Probability. A new section on Counting and Introduction to Probability has been added to this edition (see Section 8.6). It provides for exploring concepts of chance and expanding students' number sense. The topic of probability is included in the AMATYC Crossroads in Mathematics content guidelines.
Solving Equations. Special emphasis is given to the addition property of equality and the multiplication property of equality (see Sections 3.2 and 3.3).
Increased Opportunities to Use Technology. Optional calculator explorations and exercises are integrated appropriately throughout the text.
New Examples. Additional detailed step-by-step examples were added where needed. Many of these reflect real-life situations. Examples are used in two ways—numbered, as formal examples, to check or increase understanding of a topic, and unnumbered, to introduce a topic or informally discuss the topic.
New Exercises. A significant amount of time was spent on the exercise sets. New exercises and additional examples help address a wide range of student learning styles and abilities. New
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