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Introductory Algebra: Everyday Explorations, 5th Edition

Alice Kaseberg, Greg Cripe, Peter Wildman

  • Copyright 2013
  • {{checkPublicationMessage('Published', '2012-02-03T00:00:00+0000')}}
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Introductory Algebra: Everyday Explorations 5th Edition by Alice Kaseberg/Greg Cripe/Peter Wildman
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Overview

Kaseberg/Cripe/Wildman's respected INTRODUCTORY ALGEBRA is known for an informal, interactive style that makes algebra more accessible to students while maintaining a high level of mathematical accuracy. This new edition introduces two new co-authors, Greg Cripe and Peter Wildman. The three authors have created a new textbook that introduces new pedagogy to teach students how to be better prepared to succeed in math and then life by strengthening their ability to solve critical-thinking problems. This text's popularity is attributable to the author's use of guided discovery, explorations, and problem solving, all of which help students learn new concepts and strengthen their skill retention.

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Meet the Authors

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Alice Kaseberg

Alice Kaseberg combines 30 years of secondary school and community college teaching experience with an avid mathematical curiosity, constantly seeking to answer the commonly asked question, "What is mathematics good for?" Her BA in Business Administration, MA in Mathematics, and MS in Engineering Science reflect her keen interest in academics and mathematics applications. She began her career as a teacher in Australia. Then, as a junior high teacher, she class-tested materials from the Mathematics Resource Project, Lane County Math Project, School Mathematics Project (of Great Britain), and Bob Wirtz's Drill and Practice at the Problem Solving Level. Her mentors were early advocates of the discovery approach, laboratory activities, and membership/involvement in professional organizations. Kaseberg has always reached out to mathematics students in a variety of situations. She was a high school teacher for the hearing impaired, where she taught contrasting classes such as Advanced Placement Calculus and remedial mathematics. Always eager to take on new projects, she organized weekly problem-solving activities for the entire department. As a community college teacher (15 years), she has taught a range of courses from Beginning Algebra through Calculus, as well as Strength of Materials and Statics in Engineering. While on sabbatical from teaching, she worked 15 months for the EQUALS Project, Berkeley, CA, writing Odds-on-You and coauthoring the EQUALS Handbook. In addition to her teaching at the school and community college level, she has developed and presented numerous workshops on mathematics applications, content strategies, problem solving, art and math, and teaching strategies. Group work and intense participation by attendees characterize her workshops and her classroom. Her goal in writing textbooks is to help students succeed in mathematics, learn how to learn, and become actively aware of the mathematics in their daily lives.

Greg Cripe

Greg Cripe has been an instructor of mathematics for 10 years at Spokane Falls Community College in Spokane, WA. He has a wide variety of interests and teaching experiences. He has a performance degree in music and a B.S. in mathematics from Indiana University. While there, he also taught music lessons and set painting techniques. He taught high school mathematics while serving as a Peace Corps Volunteer in Swaziland. He then received an M.S. in mathematics from Eastern Washington University. He later went on to receive an M.A. in computer science and a Ph.D. in applied mathematics from the University of Montana. He was a visiting professor at Montana before taking his current position in Spokane.

Peter Wildman

Peter Wildman is an instructor of mathematics at Spokane Falls Community College in Spokane, WA. Prior to teaching at Spokane Falls, he taught at Casper College in Casper, WY for 16 years. He has been actively involved with mathematics at a national level. He is an active member of AMATYC, where he has served as Central Region Vice-President and as editor of the AMATYC journal MATHAMATYC EDUCATOR. He has also been active in a number of mathematics reform initiatives at a regional and national level. Wildman has a great interest in finding and adopting authentic applications of mathematics to the classroom. He has worked as an author for a number of projects that focus on generating real-life applications, such as the Wyoming Real Life Mathematics Project, NASA--AMATYC--NSF Year I and II, and the math works project. Wildman has been fortunate to win a number of local and national teaching awards including the Phi Theta Kappa Teacher of the Year, The Rosenthal Outstanding Educator Award at Casper College, the AMATYC Teaching Excellence Award, and the NISOD Excellence Award. In his spare time Wildman writes and performs math songs and plays that are usually centered on mathematical history. Some of his recent plays include C.F. GAUSS EXPLAINS IT ALL TO YOU, Leonhard Euler--mathematical idol, and SIMONE POISSON'S EXCELLENT MATHEMATICAL DAY.

What's New

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  • In order to preserve alignment of the content with the AMATYC standards but also to reflect the evolution of these standards over the years, content has been rethought and rearranged to focus on linear functions.
  • A chapter on Statistics, Chapter 10, has been added and is available online.
  • In Chapter 2, the more familiar exponent and order of operations topics are now placed before number properties.
  • In Chapter 3, solving equations with tables and graphs is now before solving with algebraic notation.
  • Solving formulas has been moved from Chapter 4 to Chapter 3
  • Chapters 4 and 5 have been exchanged, placing Ratios, Rates, and Proportional Reasoning before Functions, Linear Equations, and Linear Inequalities.

Features

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  • A list of Objectives is included at the beginning of the section. They serve as a summary for both students and instructors and coordinate with the titles of the Examples.
  • The Warm-Up at the beginning of each section is designed to serve as a class opener, reviewing important concepts, beginning exploration, and linking prior and upcoming topics. Warm-Ups tend to be skill-oriented; they generally connect to the algebra needed to solve text examples. The answers to the Warm-Up appear in the Answer Box at the end of the section.
  • Each Example begins with a title, which states the purpose of the Example. Usually these titles relate back to the objectives for the section. Several Examples link with others elsewhere in the book.
  • Included throughout the text, Explorations are another type of Example that is intended to be used in class for individual or group exploration.
  • Answers to the Warm-Up and some Examples, as well as the Practice questions, are placed in the Answer Box at the end of each section. By providing answers as feedback, the Answer Box permits the text to be used in class or as a laboratory manual for group work or independent study.

Table of Contents

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1. ALGEBRAIC REPRESENTATIONS.
Problem-Solving Steps and Strategies. Numeric Representations. Symbolic & Verbal Representations, Part 1. Symbolic & Verbal Representations, Part 2. Visual Representations: Rectangular Coordinate Graphs. Chapter Summary. Review Exercises. Chapter Test.
2. OPERATIONS WITH REAL NUMBERS AND EXPRESSIONS.
Addition and Subtraction with Integers. Multiplication and Division with Positive and Negative Numbers. Fractions, Exponents, and Order of Operations. Properties of Real Numbers Applied to Simplifying Expressions and Adding Like Terms. Unit Analysis and Formulas. Inequalities, Intervals, and Line Graphs. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review of Chapters 1 and 2.
3. SOLVING EQUATIONS AND INEQUALITIES IN ONE VARIABLE.
Linear Equations in One and Two Variables. Solving Equations with Tables and Graphs. Solving Equations with Algebraic Notation, Part 1. Solving Equations with Algebraic Notation, Part 2. Solving Linear Inequalities in One Variable. Solving Formulas. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review of Chapters 1 to 3.
4. RATIOS, RATES, AND PROPORTIONAL REASONING.
Ratios and Rates. Proportions and Proportional Reasoning. Percents. Proportions in Similar Figures and Similar Triangles. (Optional) Right Triangle Trigonometry. Writing Equations from Word Problems with Quantity-Rate Tables. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review of Chapters 1 to 4.
5. FUNCTIONS, LINEAR EQUATIONS, AND INEQUALITIES IN TWO VARIABLES.
Functions and Graphs. Linear Functions: Slope and Rate of Change. Linear Functions: Intercepts and Slope. Linear Equations in Two Variables. Inequalities in Two Variables. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review of Chapters 1 to 5.
6. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Solving Systems of Equations with Graphs and Tables. Setting Up Systems of Equations. Solving Systems of Equations by Substitution. Solving Systems of Equations by Elimination. Solving Systems of Linear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review for Chapters 1 to 6.
7. POLYNOMIAL EXPRESSIONS AND INTEGER EXPONENTS.
Operations on Polynomials. Multiplication of Binomials and Special Products. Factoring Trinomials. Factoring Special Products and Greatest Common Factors. Exponents. Scientific Notation. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review of Chapters 1 to 7.
8. SQUARES AND SQUARE ROOTS: EXPRESSIONS AND EQUATIONS.
Pythagorean Theorem. Square Root Expressions and Properties and the Distance Formula. Simplifying Expressions and Solving Square Root Equations. Graphing and Solving Quadratic Equations. Solving Quadratic Equations by Taking the Square Root or Factoring. Solving Quadratic Equations with the Quadratic Formula. Chapter Summary. Review Exercises. Chapter Test. Cumulative Review of Chapters 1 to 8.
9. RATIONAL EXPRESSIONS AND EQUATIONS.
Rational Functions: Graphs and Applications. Simplifying Rational Expressions. Multiplication and Division of Rational Expressions. Finding the Common Denominator and Addition and Subtraction of Rational Expressions. Solving Rational Equations. Chapter Summary. Review Exercises. Chapter Test. Final Exam Review.
10. STATISTICS (ONLINE).
What is Statistics. Descriptive Statistics: Averages. Descriptive Statistics: Summary and Spreads. Display of Data. Linear Regression. Chapter Summary. Review Exercises. Chapter Test

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Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

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This guide helps students navigate Enhanced WebAssign. It includes instructions on how to use the Assignment page and its Summary, tips on using MathPad for providing easy input of math notation and symbols, an overview of the Graphing Utility's drawing tools for completing graphing assignments, and information on how to access grades and scores summary.

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This guide helps students navigate Enhanced WebAssign. It includes instructions on how to use the Assignment page and its Summary, tips on using MathPad for providing easy input of math notation and symbols, an overview of the Graphing Utility's drawing tools for completing graphing assignments, and information on how to access grades and scores summary.

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WebAssign for Introductory Algebra: Everyday Explorations is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of instructors, enabling you to deploy assignments, instantly assess individual student and class performance and help your students master the course concepts. Enrich the teaching and learning experience with the superior content within the powerful digital platform of WebAssign. Tailor your course with a wide range of assignment settings, the ability to add your own questions and content, analytics at the individual and course level and student/teacher communication tools.