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John Squires has been teaching math for over 20 years. He was the architect of the nationally acclaimed “Do the Math” program at Cleveland State Community College and is now head of the math department at Chattanooga State Community College, where he is implementing course redesign throughout the department. John is the 2010 Cross Scholar for the League for Innovation and the author of the 13th Cross Paper which focuses on course redesign. As a redesign scholar for The National Center for Academic Transformation (NCAT), John speaks frequently on course redesign and has worked with both colleges and high schools on using technology to improve student learning.
Karen Wyrick is the current chair of the math department at Cleveland State Community College and has been teaching math there for over 18 years. She is an outstanding instructor, as students have selected her as the college’s best instructor more than once! Karen played an integral role in Cleveland State’s Bellwether Award-winning “Do the Math” redesign project, and she speaks frequently on course redesign at colleges throughout the nation and also serves as a redesign scholar for The National Center for Academic Transformation (NCAT).
Mini-Mod 1 Whole Numbers
Topic 1.1 Whole Numbers
Topic 1.2 Rounding
Topic 1.3 Adding Whole Numbers; Estimation
Topic 1.4 Subtracting Whole Numbers
Topic 1.5 Basic Problem Solving
Topic 1.6 Multiplying Whole Numbers
Topic 1.7 Dividing Whole Numbers
Topic 1.8 More with Multiplying and Dividing
Topic 1.9 Exponents
Topic 1.10 Order of Operations and Whole Numbers
Topic 1.11 More Problem Solving
Mini-Mod 2 Factors and Fractions
Topic 2.1 Factors
Topic 2.2 Prime Factorization
Topic 2.3 Understanding Fractions
Topic 2.4 Simplifying Fractions - GCF and Factors Method
Topic 2.5 Simplifying Fractions - Prime Factors Method
Topic 2.6 Multiplying Fractions
Topic 2.7 Dividing Fractions
Mini-Mod 3 LCM and Fractions
Topic 3.1 Finding the LCM - List Method
Topic 3.2 Finding the LCM - GCF Method
Topic 3.3 Finding the LCM - Prime Factor Method
Topic 3.4 Writing Fractions with an LCD
Topic 3.5 Adding and Subtracting Like Fractions
Topic 3.6 Adding and Subtracting Unlike Fractions
Topic 3.7 Order of Operations and Fractions
Mini-Mod 4 Mixed Numbers
Topic 4.1 Changing a Mixed Number to an Improper Fraction
Topic 4.2 Changing an Improper Fraction to a Mixed Number
Topic 4.3 Multiplying Mixed Numbers
Topic 4.4 Dividing Mixed Numbers
Topic 4.5 Adding Mixed Numbers
Topic 4.6 Subtracting Mixed Numbers
Topic 4.7 Adding and Subtracting Mixed Numbers - Improper Fractions
Mini-Mod 5 Operations with Decimals
Topic 5.1 Decimal Notation
Topic 5.2 Comparing Decimals
Topic 5.3 Rounding Decimals
Topic 5.4 Adding and Subtracting Decimals
Topic 5.5 Multiplying Decimals
Topic 5.6 Dividing Decimals
Topic 5.7 Order of Operations and Decimals
Topic 5.8 Converting Fractions to Decimals
Topic 5.9 Converting Decimals to Fractions
Mini-Mod 6 Ratios, Rates, and Percents
Topic 6.1 Ratios
Topic 6.2 Rates
Topic 6.3 Proportions
Topic 6.4 Percent Notation
Topic 6.5 Percent and Decimal Conversions
Topic 6.6 Percent and Fraction Conversions
Topic 6.7 The Percent Equation
Topic 6.8 The Percent Proportion
Topic 6.9 Percent Applications
Mini-Mod 7 U.S. and Metric Measurement
Topic 7.1 U.S. Length
Topic 7.2 U.S. Weight and Capacity
Topic 7.3 Metric Length
Topic 7.4 Metric Mass and Capacity
Topic 7.5 Converting between U.S. and Metric Units
Topic 7.6 Time and Temperature
Mini-Mod 8 Introduction to Geometry
Topic 8.1 Lines and Angles
Topic 8.2 Figures
Topic 8.3 Perimeter - Definitions and Units
Topic 8.4 Finding Perimeter
Topic 8.5 Area - Definitions and Units
Topic 8.6 Finding Area
Topic 8.7 Understanding Circles
Topic 8.8 Finding Circumference
Topic 8.9 Finding Area - Circles
Mini-Mod 9 More Geometry
Topic 9.1 Volume - Definitions and Units
Topic 9.2 Finding Volume
Topic 9.3 Square Roots
Topic 9.4 The Pythagorean Theorem
Topic 9.5 Similar Figures
Topic 9.6 Finding Missing Lengths
Mini-Mod 10 Statistics
Topic 10.1 Bar Graphs
Topic 10.2 Line Graphs
Topic 10.3 Circle Graphs
Topic 10.4 Mean
Topic 10.5 Median
Topic 10.6 Mode
Mini-Mod 11 Real Numbers and Variables
Topic 11.1 Introduction to Real Numbers
Topic 11.2 Graphing Rational Numbers Using a Number Line
Topic 11.3 Translating Phrases into Algebraic Inequalities
Topic 11.4 Finding the Absolute Value of a Real Number
Mini-Mod 12 Adding and Subtracting with Real Numbers
Topic 12.1 Adding Real Numbers with the Same Sign
Topic 12.2 Adding Real Numbers with Different Signs
Topic 12.3 Finding the Opposite of a Real Number
Topic 12.4 Subtracting Real Numbers
Topic 12.5 Addition Properties of Real Numbers
Mini-Mod 13 Multiplying and Dividing with Real Numbers
Topic 13.1 Multiplying Real Numbers
Topic 13.2 Finding the Reciprocal of a Real Number
Topic 13.3 Dividing Real Numbers
Topic 13.4 Exponents and the Order of Operations
Topic 13.5 The Distributive Property
Topic 13.6 Multiplication Properties of Real Numbers
Mini-Mod 14 Variables and Expressions
Topic 14.1 Introduction to Expressions
Topic 14.2 Evaluating Algebraic Expressions
Topic 14.3 Simplifying Expressions
Topic 14.4 Simplifying Expressions with Parentheses
Topic 14.5 Translating Words into Symbols
Mini-Mod 15 Introduction to Solving Linear Equations
Topic 15.1 Translating Words into Equations
Topic 15.2 Linear Equations and Solutions
Topic 15.3 Using the Addition Property of Equality
Topic 15.4 Using the Multiplication Property of Equality
Topic 15.5 Using the Addition and Multiplication Properties Together
Mini-Mod 16 Solving More Linear Equations and Inequalities
Topic 16.1 Solving Equations with Variables on Both Sides
Topic 16.2 Solving Equations with Parentheses
Topic 16.3 Solving Equations with Fractions
Topic 16.4 Solving a Variety of Equations
Topic 16.5 Solving Equations and Formulas for a Variable
Topic 16.6 Solving and Graphing Linear Inequalities
Mini- Mod 17 Introduction to Graphing Linear Equations
Topic 17.1 The Rectangular Coordinate System
Topic 17.2 Graphing Linear Equations by Plotting Points
Topic 17.3 Graphing Linear Equations Using Intercepts
Topic 17.4 Graphing Linear Equations of the Form x=a, y=b, and y=mx
Mini- Mod 18 Slope and the Equation of a Line
Topic 18.1 The Slope of a Line
Topic 18.2 Slope-Intercept Form
Topic 18.3 Graphing Lines Using the Slope and y-Intercept
Topic 18.4 Writing Equations of Lines Using a Point and Slope
Topic 18.5 Writing Equations of Lines Using Two Points
Mini-Mod 19 Introduction to Functions
Topic 19.1 Relations and Functions
Topic 19.2 The Vertical Line Test
Topic 19.3 Function Notation
Topic 19.4 Evaluating Functions
Topic 19.5 Piecewise Functions
Mini-Mod 20 Solving Systems of Linear Equations
Topic 20.1 Introduction to Systems of Linear Equations
Topic 20.2 Solving by the Graphing Method
Topic 20.3 Solving by the Substitution Method
Topic 20.4 Solving by the Elimination Method
Mini-Mod 21 Introduction to Polynomials and Exponent Rules
Topic 21.1 Introduction to Polynomials
Topic 21.2 Addition of Polynomials
Topic 21.3 Subtraction of Polynomials
Topic 21.4 Product Rule for Exponents
Topic 21.5 Power Rule for Exponents
Mini- Mod 22 Multiplying Polynomials
Topic 22.1 Multiplying by a Monomial
Topic 22.2 Multiplying Binomials
Topic 22.3 Multiplying Polynomials
Topic 22.4 Multiplying the Sum and Difference of Two Terms
Topic 22.5 Squaring Binomials
Mini-Mod 23 Dividing Polynomials and More Exponent Rules
Topic 23.1 The Quotient Rule
Topic 23.2 Integer Exponents
Topic 23.3 Scientific Notation
Topic 23.4 Dividing a Polynomial by a Monomial
Topic 23.5 Dividing a Polynomial by a Binomial
Mini-Mod 24 Factoring Polynomials
Topic 24.1 Greatest Common Factor
Topic 24.2 Factoring by Grouping
Topic 24.3 Factoring Trinomials of the Form
Topic 24.4 Factoring Trinomials of the Form
Topic 24.5 More Factoring of Trinomials
Mini-Mod 25 More Factoring and Quadratic Equations
Topic 25.1 Special Cases of Factoring
Topic 25.2 Factoring Polynomials
Topic 25.3 Solving Quadratic Equations by Factoring
Topic 25.4 Applications
Mini-Mod 26 Introduction to Rational Expressions
Topic 26.1 Undefined Rational Expressions
Topic 26.2 Simplifying Rational Expressions
Topic 26.3 Multiplying Rational Expressions
Topic 26.4 Dividing Rational Expressions
Mini-Mod 27 Adding and Subtracting Rational Expressions
Topic 27.1 Adding Like Rational Expressions
Topic 27.2 Subtracting Like Rational Expressions
Topic 27.3 Finding the Least Common Denominator for Rational Expressions
Topic 27.4 Adding and Subtracting Unlike Rational Expressions
Mini-Mod 28 Complex Rational Expressions and Rational Equations
Topic 28.1 Simplifying Complex Rational Expressions by Adding and Subtracting
Topic 28.2 Simplifying Complex Rational Expressions by Multiplying by the LCD
Topic 28.3 Solving Rational Equations
Topic 28.4 Direct Variation
Topic 28.5 Inverse Variation
Topic 28.6 Applications
Mini-Mod 29 Roots and Radicals
Topic 29.1 Square Roots
Topic 29.2 Higher-Order Roots
Topic 29.3 Simplifying Radical Expressions
Topic 29.4 Rational Exponents
Topic 29.5 The Pythagorean Theorem
Topic 29.6 The Distance Formula
Mini-Mod 30 Operations of Radical Expressions
Topic 30.1 Adding and Subtracting Radical Expressions
Topic 30.2 Multiplying Radical Expressions
Topic 30.3 Dividing Radical Expressions
Topic 30.4 Rationalizing the Denominator
Topic 30.5 Solving Radical Equations
Mini-Mod 31 Solving Quadratic Equations
Topic 31.1 Introduction to Solving Quadratic Equations
Topic 31.2 Solving Quadratic Equations by Factoring
Topic 31.3 Solving Quadratic Equations using the Square Root Property
Topic 31.4 Solving Quadratic Equations by Completing the Square
Topic 31.5 Solving Quadratic Equations using the Quadratic Formula
Mini-Mod 32 Graphing Quadratic Equations
Topic 32.1 Introduction to Graphing Quadratic Equations
Topic 32.2 Finding the Vertex of a Quadratic Equation
Topic 32.3 Finding the Intercepts of a Quadratic Equation
Topic 32.4 Graphing Quadratic Equations Summary
Mini-Mod 33 Compound and Quadratic Inequalities
Topic 33.1 Sets
Topic 33.2 Interval Notation
Topic 33.3 Graphing Compound Inequalities
Topic 33.4 Solving Compound Inequalities
Topic 33.5 Solving Quadratic Inequalities
Mini-Mod 34 Absolute Value Equations and Inequalities
Topic 34.1 Introduction to Absolute Value Equations
Topic 34.2 Solving Basic Absolute Value Equations
Topic 34.3 Solving Multiple Absolute Value Equations
Topic 34.4 Solving Absolute Value Inequalities
Appendix A Conic Sections
Topic A.1 The Circle
Topic A.2 The Parabola
Topic A.3 The Ellipse
Topic A.4 The Hyperbola
Appendix B Logarithmic and Exponential Functions
Topic B.1 Evaluating Exponential and Logarithmic Expressions
Topic B.2 Graphing Exponential Functions
Topic B.3 Solving Simple Exponential Equations and Applications
Topic B.4 Converting Between Exponential and Logarithmic Forms
Topic B.5 Solving Simple Logarithmic Equations
Topic B.6 Graphing Logarithmic Functions
Appendix C Solving Logarithmic and Exponential Equations
Topic C.1 Properties of Logarithms
Topic C.2 Common and Natural Logarithms
Topic C.3 Change of Base of Logarithms
Topic C.4 Solving Exponential Equations and Applications
Topic C.5 Solving Logarithmic Equations and Applications
Appendix D Additional Topics
Topic D.1 The Midpoint Formula
Topic D.2 Writing Equations of Parallel and Perpendicular Lines
Topic D.3 Graphing Linear Inequalities in Two Variables
Topic D.4 Systems of Linear Inequalities
Topic D.5 Synthetic Division
Topic D.6 Complex Numbers
Topic D.7 Matrices and Determinants
Topic D.8 Cramer’s Rule
Topic D.9 Solving Systems of Linear Equations Using Matrices
Topic D.10 Basic Probability and Statistics
Topic D.11 Applications of Systems of Linear Equations