Developmental Mathematics Prealgebra, Beginning, Intermediate Algebra

John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.

Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year award in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Massachusetts with his wife Shelley and his yellow lab Gracie.

Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.

Module 1: Whole Numbers and Introduction to Algebra

Topic 1: Understanding Whole Numbers

Topic 2: Adding Whole Number Expressions

Topic 3: Subtracting Whole Number Expressions

Topic 4: Multiplying Whole Number Expressions

Topic 5: Dividing Whole Number Expressions

Topic 6: Exponents and the Order of Operations

Topic 7: More on Algebraic Expressions

Topic 8: Introduction to Solving Linear Equations

Topic 9: Solving Applied Problems Using Several Operations

Module 2: Integers

Topic 1: Understanding Integers

Topic 2: Adding Integers

Topic 3: Subtracting Integers

Topic 4: Multiplying and Dividing Integers

Topic 5: The Order of Operations and Applications

Topic 6: Simplifying and Evaluating Algebraic Expressions

Module 3: Introduction to Equations

Topic 1: Equations of the form x + a = c and x – a = c

Topic 2: Equations of the form ax = c

Topic 3: Equations and Geometric Formulas

Topic 4: Performing Operations with Exponents

Module 4: Fractions, Ratios, and Proportions

Topic 1: Factoring Whole Numbers

Topic 2: Understanding Fractions

Topic 3: Simplifying Fractional Expressions

Topic 4: Simplifying Fractional Expressions with Exponents

Topic 5: Ratios and Rates

Topic 6: Proportions and Applications

Module 5: Operations on Fractional Expressions

Topic 1: Multiplying and Dividing Fractional Expressions

Topic 2: Least Common Multiples of Algebraic Expressions

Topic 3: Adding and Subtracting Fractional Expressions

Topic 4: Operations with Mixed Numbers

Topic 5: Order of Operations and Complex Fractions

Topic 6: Solve Applied Problems Involving Fractions

Topic 7: The Multiplication Principle of Equality

Module 6: Decimals and Percents

Topic 1: Understanding Decimal Fractions

Topic 2: Adding and Subtracting Decimal Expressions

Topic 3: Multiplying and Dividing Decimal Expressions

Topic 4: Estimating with Percents

Topic 5: Percents

Topic 6: Solving Percent Problems Using Equations

Topic 7: Solving Percent Problems Using Proportions

Topic 8: Solving Applied Problems Involving Percents

Module 7: Measurement and Geometric Figures

Topic 1: Using Unit Fractions with U.S. and Metric Units

Topic 2: Converting Between the U.S. and Metric Systems

Topic 3: Angles

Topic 4: The Circle

Topic 5: Volume

Topic 6: Similar Geometric Figures

Module 8: Introduction to Polynomials

Topic 1: Adding and Subtracting Polynomials

Topic 2: Multiplying Polynomials

Topic 3: Translate from English to AlgebraTopic 4: Factoring Using the Greatest Common Factor

Module 9: Equations, Inequalities, and Applications

Topic 1: Addition and Multiplication Principles of Equality

Topic 2: Using Both Principles of Equality Together

Topic 3: Solving Equations with Fractions

Topic 4: Formulas

Topic 5: Using Equations to Solve Word Problems

Topic 6: Solving Word Problems Involving Money and Percents

Topic 7: Solving Inequalities in One Variable

Module 10: Graphing and Functions

Topic 1: The Rectangular Coordinate System

Topic 2: Graphing Linear Equations

Topic 3: The Slope of a Line

Topic 4: Writing the Equation of a Line

Topic 5: Graphing Linear Inequalities

Topic 6: Functions

Module 11: Systems of Linear Equations and Inequalities

Topic 1: Systems of Linear Equations in Two Variables

Topic 2: Systems of Linear Equations in Three Variables

Topic 3: Applications of Systems of Linear Equations

Topic 4: Systems of Linear Inequalities

Module 12: Exponents and Polynomials

Topic 1: The Rules of Exponents

Topic 2: Negative Exponents and Scientific Notation

Topic 3: Fundamental Polynomial Operations

Topic 4: Multiplying Polynomials

Topic 5: Multiplication –Special Cases

Topic 6: Dividing Polynomials

Module 13: Factoring

Topic 1: Removing a Common Factor

Topic 2: Factoring by Grouping

Topic 3: Factoring Trinomials When a = 1

Topic 4: Factoring Trinomials When a ¹ 1

Topic 5: Special Cases of Factoring

Topic 6: A Brief Review of Factoring

Topic 7: Solving Quadratic Equations by Factoring

Module 14: Rational Expressions and Equations

Topic 1: Simplifying Rational Expressions

Topic 2: Multiplying and Dividing Rational Expressions

Topic 3: Adding and Subtracting Rational Expressions

Topic 4: Simplifying Complex Rational Expressions

Topic 5: Solving Equations Involving Rational Expressions

Topic 6: Ratio, Proportion, and Other Applied Problems

Module 15: Rational Exponents and Radicals

Topic 1: Rational Exponents

Topic 2: Radical Expressions and Functions

Topic 3: Simplifying, Adding, and Subtracting Radicals

Topic 4: Multiplying and Dividing Radicals

Topic 5: Radical Equations

Topic 6: Complex Numbers

Topic 7: Variation

Module 16: Quadratic Equations

Topic 1: Quadratic Equations

Topic 2: Solutions to Quadratic Equations—Quadratic Formula

Topic 3: Solving Equations That Are Quadratic in Form

Topic 4: Formulas and Applications

Module 17: The Conic Sections

Topic 1: The Distance Formula and the Circle

Topic 2: The Parabola

Topic 3: The Ellipse

Topic 4: The Hyperbola

Topic 5: Nonlinear Systems of Equations

Module 18: Additional Properties of Functions

Topic 1: Function Notation

Topic 2: General Graphing Procedures for Functions

Topic 3: Algebraic Operations on Functions

Topic 4: Inverse of a Function

Module 19: Logarithmic and Exponential Functions

Topic 1: The Exponential Function

Topic 2: The Logarithmic Function

Topic 3: Properties of Logarithms

Topic 4: Common and Natural Logarithms; Change of Base

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