Elementary Algebra Graphs and Authentic Applications

by Lehmann, Jay

• ISBN13: 9780134756998
• ISBN10: 0134756991
• Edition: 3rd
• Format: Hardcover
• Copyright: 2018-01-12
• Publisher: Pearson

Summary

For courses in Beginning Algebra.

Modeling authentic data through curve-fitting gives students new meaning to the math

Seeking the answer to students’ perennial question “But what is this good for?” the Lehmann Algebra Series uses authentic, real-life data sets to find models and derive equations that fit the scenario. The curve-fitting approach teaches the mathematical concepts within the context of data, getting students engaged from the start and building conceptual understanding. 

Updates in this revision keep the data sets authentic and current, and provide even more resources for students to practice, review, and explore the concepts. 

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Author Biography

Jay Lehmann has taught for the past 25 years at College of San Mateo, where he received the “shiny apple award” for excellence in teaching.  He has presented at over 80 conferences including AMATYC and ICTCM over the past 16 years. Jay is currently the newsletter editor for California Mathematics Council, Community Colleges (CMC3).  Still young at heart, he plays in a rock band appropriately named the Procrastinistas.  Jay has authored several algebra textbooks published by Pearson and is has also recently completed a Prestatistics textbook.

 

In the words of the author:

Before writing my algebra series, it was painfully apparent that my students couldn't relate to the applications in the course. I was plagued with the question, "What is this good for?" To try to bridge that gap, I wrote some labs, which facilitated my students in collecting data, finding models via curve fitting, and using the models to make estimates and predictions. My students really loved working with the current, compelling, and authentic data and experiencing how mathematics truly is useful.

My students' response was so strong that I decided to write an algebra series. Little did I know that to realize this goal, I would need to embark on a 15-year challenging journey, but the rewards of hearing such excitement from students and faculty across the country have made it all worthwhile! I'm proud to have played even a small role in raising people’s respect and enthusiasm for mathematics.

I have tried to honor my inspiration: by working with authentic data, students can experience the power of mathematics. A random-sample study at my college suggests that I am achieving this goal. The study concludes that students who used my series were more likely to feel that mathematics would be useful in their lives (P-value 0.0061) as well as their careers (P-value 0.024).

The series is excellent preparation for subsequent courses; in particular, because of the curve fitting and emphasis on interpreting the contextual meaning of parameters, it is an ideal primer for statistics. In addition to curve fitting, my approach includes other types of meaningful modeling, directed-discovery explorations, conceptual questions, 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.

Table of Contents

1. Introduction to Modeling

1.1  Variables and Constants

1.2  Scatterplots

1.3  Exact Linear Relationships

1.4  Approximate Linear Relationships

Taking It to the Lab: Climate Change Lab • Volume Lab • Linear Graphing Lab: Topic of Your Choice 

 

2. Operations and Expressions

2.1  Expressions

2.2  Operations with Fractions

2.3  Absolute Value and Adding Real Numbers

2.4  Change in a Quantity and Subtracting Real Numbers

2.5  Ratios, Percents, and Multiplying and Dividing Real Numbers

2.6  Exponents and Order of Operations

Taking It to the Lab: Climate Change Lab (continued from Chapter 1) • Stocks Lab

 

3. Using Slope To Graph Linear Equations

3.1  Graphing Equations of the Forms y = mx + b and x = a

3.2  Graphing Linear Models; Unit Analysis

3.3  Slope of a Line

3.4  Using Slope to Graph Linear Equations

3.5  Rate of Change

Taking It to the Lab: Climate Change Lab

 

4. Simplifying Expressions and Solving Equations

4.1  Simplifying Expressions

4.2   Simplifying More Expressions

4.3  Solving Linear Equations in One Variable

4.4  Solving More Linear Equations in One Variable

4.5  Comparing Expressions and Equations

4.6  Formulas

 

5. Linear Equations in Two Variables and Linear Inequalities in One Variable

5.1  Graphing Linear Equations in Two Variables

5.2  Finding Equations of Lines

5.3  Finding Equations of Linear Models

5.4  Using Equations of Linear Models to Make Estimates and Predictions

5.5  Solving Linear Inequalities in One Variable

Taking It to the Lab: Climate Change Lab (continued from Chapter 3) • Rope Lab • Shadow Lab • Linear Lab:  Topic of Your Choice

6. Systems of Linear Equations and Systems of Linear Inequalities

6.1  Using Graphs and Tables to Solve Systems

6.2  Using Substitution to Solve Systems

6.3  Using Elimination to Solve Systems

6.4  Using Systems to Model Data

6.5  Perimeter, Value, Interest, and Mixture Problems

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

Taking It to the Lab: Climate Change Lab (continued from Chapter 5)

 

7. Polynomials and Properties of Exponents

7.1  Graphing Quadratic Equations

7.2  Quadratic Models

7.3  Adding and Subtracting Polynomials

7.4  Multiplying Polynomials

7.5  Powers of Polynomials; Product of Binomial Conjugates

7.6  Properties of Exponents

7.7  Negative-Integer Exponents

7.8  Dividing Polynomials

Taking It to the Lab: Climate Change Lab (continued from Chapter 6) • Projectile Lab

 

8. Factoring Polynomials and Solving Polynomial Equations

8.1  Factoring Trinomials of the Form x ² + bx + c and Differences of Two Squares

8.2  Factoring Out the GCF; Factoring by Grouping

8.3  Factoring Trinomials of the Form ax ² + bx + c

8.4  Sums and Differences of Cubes; A Factoring Strategy

8.5  Using Factoring to Solve Polynomial Equations

8.6  Using Factoring to Make Predictions with Quadratic Models

 

9. Solving Quadratic Equations

9.1  Simplifying Radical Expressions

9.2  Simplifying More Radical Expressions

9.3  Solving Quadratic Equations by the Square Root Property; The Pythagorean Theorem

9.4  Solving Quadratic Equations by Completing the Square

9.5  Solving Quadratic Equations by the Quadratic Formula

9.6  More Quadratic Models

Taking It to the Lab: Climate Change Lab (continued from Chapter 7) • Projectile Lab (continued from Chapter 7)

 

10.  Rational Expressions and Equations

10.1  Simplifying Rational Expressions

10.2  Multiplying and Dividing Rational Expressions; Converting Units

10.3  Adding Rational Expressions

10.4  Subtracting Rational Expressions

10.5  Solving Rational Equations

10.6  Proportions; Similar Triangles

10.7  Variation

10.8  Simplifying Complex Rational Expressions

Taking It to the Lab: Climate Change Lab (continued from Chapter 9) • Estimating π Lab

 

11.  More Radical Expressions and Equations

11.1  Adding and Subtracting Radical Expressions

11.2  Multiplying Radical Expressions

11.3  Solving Square Root Equations

Appendix A: Using A TI-83 or TI-84 Graphing Calculator

Appendix B: Using StatCrunch