Elementary Algebra Graphs and Authentic Applications

by Lehmann, Jay

• ISBN13: 9780132201643
• ISBN10: 013220164X
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-04-19
• Publisher: Pearson

Summary

Jay Lehmann is passionate about answering the question so many math instructors hear their students ask: But what is this good for? He discovered that a curve fitting approach could enable students to see how math is used in all walks of life with current, compelling, and authentic situations. In addition to curve fitting, Lehmann's approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, labs, and of course, a large bank of skill problems. The curve fitting applications serve as a portal for students to see the usefulness of mathematics so that they become fully engaged in the class. Once involved, they are more receptive to all aspects of the course. Jayrs"s text is organized around aCurve Fitting Approach, withauthentic applicationstomodel. Jay provides animmediate introduction to modeling and authentic applications (chapter 1: Introduction to Modeling),unlike most elementary algebra texts in which the first chapter is primarily a review chapter. The use of the"Rule of Four" (graphical, numerical, algebraic and verbal solutions)is presented to provide students with a variety of methods to arrive at solutions and help them gain a better understanding of the concepts. This also helps addresses the different learning styles of the students taking the course. Chapters 1-6 focus onlinear models. In chapters 7-9, students model authentic situations withquadratic equationsin two variables. Rational Models and Radical modelsare used in Chapters 10 and 11 respectively. TI-83/TI-84 graphing calculators are relevant tools for curve fitting. After students solve symbolic problems by hand, the technology allows student to reinforce their numerical and graphical intuition.

Table of Contents

Note: Each chapter concludes with Chapter Summary, Key Points of the Chapter, Chapter Review Exercises, andChapter Practice Tests

Introduction to Modeling

Variables and Constants

Scattergrams

Exact Linear Relationships

Approximate Linear Relationships

Operations and Expressions

Expressions

Operations with Fractions

Adding Real Numbers

Change in a Quantity and Subtracting Real Numbers

Ratios, Percents, and Multiplying and Dividing Real Numbers

Exponents and Order of Operations

Using Slope to Graph Linear Equations

Graphing Equations of the Form y = mx + b

Graphing Linear Models; Unit Analysis

Slope of a Line

Using Slope to Graph Lines

Rate of Change

Simplifying Expressions and Solving Equations

Commutative, Associative, and Distributive Laws

Simplifying Expressions

Solving Linear Equations in One Variable

Solving More Linear Equations in One Variable

Comparing Expressions and Equations

Formulas

Linear Equations in Two Variables

Graphing Linear Equations

Finding Linear Equations

Finding Equations of Linear Models

Using Linear Equations to make Estimates and Predications

Solving Linear Inequalities in One Variable

Systems of Linear Equations

Using Graphs and Tables to Solve Systems

Using Substitution to Solve Systems

Using Elimination to Solve Systems

Using Systems to Model Data

Perimeter, Value, Interest, and Mixture Problems

Linear Inequalities in Two Variables; Systems of Linear Inequalities in 2 Variables

Polynomials

Graphing Quadratic Equations

Quadratic Models

Adding and Subtracting Polynomials

Multiplying Polynomials

Powers of Polynomials; Product of Binomial Conjugates

Properties of Exponents

Negative Exponents

Factoring Polynomials and Solving Polynomial Equations

Factoring Trinomials of the Form xsup2; + bx + c and Differences of Two Squares

Factoring Out the GCF; Factoring by Grouping

Factoring Trinomials of the Form axsup2; + bx + c

Sums and Differences of Cubes; A Factoring Strategy

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