# Jump Start Your Teaching Career With Our GACE Math Test Prep Courses

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#### GACE Math Scope & Sequence

#### CHAPTER 1: WHOLE NUMBERS AND PROPERTIES

##### Unit 1: Place Value and Rounding

##### Unit 2: Exponents and Estimation

Estimating Sums and Differences

Estimating Products and Quotients

##### Unit 3: Variables and Properties

#### CHAPTER 2: INTEGERS AND EVALUATING EXPRESSIONS

##### Unit 1: Introduction to Integers

##### Unit 2: Operations with Integers

##### Unit 3: Order of Operations/Evaluation

#### CHAPTER 3: UNDERSTANDING FRACTIONS

##### Unit 1: Factors and Multiples

Multiples and Least Common Multiples

##### Unit 2: Fractions and Mixed Numbers

Equivalent Fractions (Part II)

Improper Fractions and Mixed Numbers

##### Unit 3: Comparing Fractions

##### Unit 4: Adding and Subtracting Fractions

Adding and Subtracting Like Fractions

Adding and Subtracting Unlike Fractions

##### Unit 5: Multiplying and Dividing Fractions

##### Unit 6: Operations with Rational Numbers

#### CHAPTER 4: DECIMALS

##### Unit 1: Decimal Concepts

Converting Decimals to Fractions

Converting Fractions to Decimals

##### Unit 2: Comparing and Rounding Decimals

##### Unit 3: Addition and Subtraction

Estimating Sums and Differences

##### Unit 4: Multiplication and Division

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Decimals

Dividing Decimals by Whole Numbers

##### Unit 5: Scientific Notation

Converting from Scientific to Standard Notation

Converting from Standard to Scientific Notation

##### Unit 6: Decimals and Rational Numbers

Terminating and Repeating Decimals

Determining if a Number is Rational or Irrational

#### CHAPTER 5: SIMPLIFYING EXPRESSIONS & SOLVING EQUATIONS

##### Unit 1: Simplifying Algebraic Expressions

##### Unit 2: Solving One- and Two-Step Equations

##### Unit 3: Solving Multi-Step Equations

Equations Involving Distributive

Variable on Both Sides / Distributive

##### Unit 4: Formulas

#### CHAPTER 6: RATIO, PROPORTION, & PERCENT

##### Unit 1: Ratios and Rates

##### Unit 2: Proportions

##### Unit 3: Percent, Decimals, and Fractions

##### Unit 4: Percent Problems

##### Unit 5: Applications of Percent

#### CHAPTER 7: WORD PROBLEMS

##### Unit 1: Beginning Word Problems

Translating English to Algebra

##### Unit 2: Value/Interest Problems

##### Unit 3: Mixture/Motion Problems

#### CHAPTER 8: INEQUALITIES AND ABSOLUTE VALUE

##### Unit 1: Linear Inequalities in One Variable

Solving and Graphing Inequalities

##### Unit 2: Absolute Value Equations & Inequalities

#### CHAPTER 9: GRAPHING AND TRANSFORMATIONS

##### Unit 1: The Rectangular Coordinate System

##### Unit 2: Transformations

##### Unit 3: Symmetry

#### CHAPTER 10: FUNCTIONS AND GRAPHING

##### Unit 1: Introduction to Functions

##### Unit 2: Graphing Functions

Graphing within a Given Domain

##### Unit 3: Linear Inequalities in Two Variables

Graphing Inequalities in Two Variables

#### CHAPTER 11: LINEAR EQUATIONS AND FUNCTIONS

##### Unit 1: Patterns and Table Building

Finding the nth Term in a Pattern

Word Problems and Table Building

##### Unit 2: Slope and Rate of Change

Using the Graph of a Line to Find Slope

Using Coordinates to Find Slope

##### Unit 3: Slope Intercept Form

Using Slope-Intercept Form to Graph a Line

Converting to Slope-Intercept Form and Graphing

##### Unit 4: Interpreting Graphs and Transformations

Linear Parent Graph and Transformations

##### Unit 5: Writing Equations in Slope-Intercept Form

Using Graphs and Slope-Intercept Form

Using Tables and Slope-Intercept Form

##### Unit 6: Writing Equations of Lines

#### CHAPTER 12: SYSTEMS OF LINEAR EQUATIONS

##### Unit 1: Solving Systems of Equations

##### Unit 2: Systems of Equations and Word Problems

#### CHAPTER 13: EXPONENTS AND POLYNOMIALS

##### Unit 1: Exponent Rules

##### Unit 2: Advanced Exponent Problems

Numerical Bases and Exponents of Zero

##### Unit 3: Multiplying Polynomials

#### CHAPTER 14: FACTORING

##### Unit 1: Greatest Common Factor

##### Unit 2: Factoring Special Polynomials

Special Trinomials with Positive Constant

Special Trinomials with Negative Constant

##### Unit 3: Factoring Trinomials

Coefficient on x^{2} Term, Positive Constant

Coefficient on x^{2} Term, Negative Constant

##### Unit 4: Advanced Factoring

Factoring Out G.C.F. as First Step

Factoring Difference of Two Squares as Last Step

##### Unit 5: Solving Polynomial Equations

#### CHAPTER 15: RATIONAL EXPRESSIONS AND EQUATIONS

##### Unit 1: Simplifying Rational Expressions

Simplifying Rational Expressions

Multiplying and Dividing Rational Expressions

##### Unit 2: Advanced Rational Expressions

Subtracting Rational Expressions

##### Unit 3: Rational Equations & Inverse Variation

#### CHAPTER 16: RADICAL EXPRESIONS AND EQUATIONS

##### Unit 1: Simplifying Radical Expressions

##### Unit 2: Multiplying and Dividing Radical Expressions

##### Unit 3: Advanced Radical Expressions

##### Unit 4: Radical Equations

#### CHAPTER 17: QUADRATIC EQUATIONS

##### Unit 1: Quadratic Graphs and Transformations

Graphs of Quadratic Functions and Beginning Transformations

Graphs of Quadratic Functions and Advanced Transformations

##### Unit 2: Completing the Square

Beginning Completing The Square

Advanced Completing The Square

##### Unit 3: The Quadratic Formula

#### CHAPTER 18: IMAGINARY AND COMPLEX NUMBERS

##### Unit 1: Imaginary Numbers

##### Unit 2: Complex Numbers

#### CHAPTER 19: QUADRATIC FUNCTIONS AND GRAPHING

##### Unit 1: Vertex Form

Understanding y - k = a(x - h)^{2} Form

Graphing Quadratic Equations in y - k = a(x - h)^{2} Form

Writing Quadratic Equations in y - k = a(x - h)^{2} Form

##### Unit 2: Quadratic Functions

#### CHAPTER 20: INTRODUCTION TO GEOMETRY

##### Unit 1: Segments and Length

Points, Lines, Planes, and Space

Segment Addition Postulate and Midpoint

##### Unit 2: Angles

Angle Addition Postulate and Angle Bisector

##### Unit 3: Reasoning

Inductive vs. Deductive Reasoning

##### Unit 4: Beginning Proofs

Algebra Proofs with Properties

Geometry Proofs with Midpoints and Angle Bisectors

#### CHAPTER 21: ANGLE PAIRS AND PERPENDICULAR LINES

##### Unit 1: Angle Pairs

Complementary and Supplementary Angles (Part 1)

Complementary and Supplementary Angles (Part 2)

##### Unit 2: Perpendicular Lines

Problems Involving Perpendicular Lines

Theorems Involving Perpendicular Lines

#### CHAPTER 22: PARALLEL LINES AND POLYGONS

##### Unit 1: Parallel Lines

##### Unit 2: Angles of a Triangle

Vocabulary and Triangle Sum Theorem

Word Problems and Exterior Angle Theorem

##### Unit 3: Polygons

Sum of Interior and Exterior Angles

#### CHAPTER 23: TRIANGLES AND CONGRUENCE

##### Unit 1: Beginning Concepts

Proving Triangles are Congruent by SSS, SAS, and ASA

##### Unit 2: Advanced Concepts

Proving Triangles are Congruent by AAS and HL

Medians, Altitudes, and Perpendicular Bisectors

#### CHAPTER 24: QUADRILATERALS

##### Unit 1: Parallelograms

Proving a Quadrilateral is a Parallelogram

##### Unit 2: More Quadrilaterals

Rectangles, Rhombuses, and Squares

#### CHAPTER 25: SIMILARITY

##### Unit 1: Proportion

##### Unit 2: Similar Polygons

Properties of Similar Polygons

Angle-Angle Similarity Postulate

##### Unit 3: Similarity Theorems

SSS and SAS Similarity Theorems

Triangle Proportionality and Triangle Angle-Bisector Theorems

#### CHAPTER 26: RIGHT TRIANGLES

##### Unit 1: Pythagorean Theorem

Converse of the Pythagorean Theorem

##### Unit 2: Special Right Triangles

30-60-90 and 45-45-90 degree Triangles (Part I)

##### Unit 3: Trigonometry

Sine, Cosine, and Tangent (Part I)

Sine, Cosine, and Tangent (Part II)

#### CHAPTER 27: CIRCLES

##### Unit 1: Vocabulary and Tangents

##### Unit 2: Arcs, Central Angles, and Chords

##### Unit 3: Angles and Segments

Angles Formed by Chords, Secants, and Tangents

##### Unit 4: Segment Lengths

Theorems and Beginning Problems

#### CHAPTER 28: MEASUREMENT AND AREA

##### Unit 1: Units of Measurement

##### Unit 2: Area of Rectangles, Squares, and Parallelograms

Area of Rectangles and Squares (Part I)

Area of Rectangles and Squares (Part II)

##### Unit 3: Area of Triangles, Rhombuses, and Trapezoids

##### Unit 4: Area of Polygons and Circles

Area and Circumference of Circles

##### Unit 5: Changing Dimensions

#### CHAPTER 29: VOLUME AND SURFACE AREA

##### Unit 1: Three-Dimensional Figures and Nets

Classifying 3-Dimensional Figures

##### Unit 2: Prisms

Vocabulary, Formulas, and Right Rectangular Prisms

##### Unit 3: Pyramids

Vocabulary, Formulas, and Regular Square Pyramids

##### Unit 4: Cylinders, Cones, and Spheres

#### CHAPTER 30: DATA AND STATISTICS

##### Unit 1: Common Graphs and Charts

##### Unit 2: Representing Data

Stem-and-Leaf Plots and Frequency Tables

##### Unit 3: Central Tendency

##### Unit 4: Probability

Probability of Independent Events

Probability of Dependent Events

##### Unit 5: Counting Methods

Tree Diagrams and the Counting Principle

#### CHAPTER 31: COORDINATE GEOMETRY

##### Unit 1: Segments in the Coordinate Plane

##### Unit 2: Circles in the Coordinate Plane

#### CHAPTER 32: NEGATIVE & RATIONAL EXPONENTS

##### Unit 1: Simplifying Expressions with Negative Exponents

Multiplying and Dividing with Negative Exponents

##### Unit 2: Operations with Scientific Notation

Multiplying and Dividing Scientific Notation

##### Unit 3: Rational Exponents and Radical Expressions

Writing Radicals in Exponential Form

##### Unit 4: Equations with Rational Exponents and Simplifying with Radical Exponents

Solving Equations with Rational Exponents

#### CHAPTER 33: COMPOSITE FUNCTIONS & INVERSES

##### Unit 1: Composite Functions

Composite Functions: f(g(x)) and g(f(x))

##### Unit 2: Inverses

#### CHAPTER 34: LOGARITHMS & EXPONENTIAL FUNCTIONS

##### Unit 1: Introduction to Logarithms

Logarithms and Logarithmic Functions

##### Unit 2: Properties of Logarithms

Logarithm Rules and Properties

Evaluating Logarithms by Condensing or Expanding

Solving Advanced Log Equations

##### Unit 3: Evaluating Logarithms with a Calculator

##### Unit 4: Exponential Equations and Logarithms

Exponential Equations and Change of Base Formula

Half Life Formula and Doubling Time Formula

##### Unit 5: The Natural Logarithm

#### CHAPTER 1: WHOLE NUMBERS

##### Unit 1: Addition and Subtraction

Estimating Sums and Differences

Addition and Subtraction Word Problems

##### Unit 2: Multiplication and Division

Estimating Products and Quotients

Multiplication and Division Word Problems

##### Unit 3: Order of Operations

##### Unit 4: Properties of Real Numbers

#### CHAPTER 2: INTEGERS

##### Unit 1: Integers and the Number Line

##### Unit 2: Integer Operations and Word Problems

#### CHAPTER 3: FRACTIONS

##### Unit 1: Factors and Multiples

Multiples and Least Common Multiples

##### Unit 2: Fractions and Mixed Numbers

Equivalent Fractions (Part II)

Improper Fractions and Mixed Numbers

##### Unit 3: Comparing Fractions

Comparing Mixed Numbers and Improper Fractions

##### Unit 4: Addition and Subtraction

Adding and Subtracting Like Fractions

Adding and Subtracting Unlike Fractions

##### Unit 5: Multiplication and Division

##### Unit 6: Operations on Rational Numbers

#### CHAPTER 4: DECIMALS

##### Unit 1: Decimal Concept

Converting Decimals to Fractions

Converting Fractions to Decimals

##### Unit 2: Addition and Subtraction

Estimating Sums and Differences

##### Unit 3: Multiplication and Division

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Decimals

Dividing Decimals by Whole Numbers

##### Unit 4: Scientific Notation

Converting from Scientific to Standard Notation

Converting from Standard to Scientific Notation

##### Unit 5: Rational and Irrational Numbers

Terminating and Repeating Decimals

Determining if a Number is Rational or Irrational

#### CHAPTER 5: ALGEBRAIC EXPRESSIONS

##### Unit 1: Patterns

Patterns with Fractions, Decimals, and Integers

##### Unit 2: Order of Operations/Evaluating Expressions

##### Unit 3: Simplifying and Modeling Expressions

#### CHAPTER 6: EQUATIONS & INEQUALITIES IN ONE VARIABLE

##### Unit 1: Beginning Equations

##### Unit 2: Multi-Step Equations

Equations Involving Distributive

Variable on Both Sides / Distributive

##### Unit 3: Formulas

##### Unit 4: Algebraic Proofs

Algebra Proofs with Properties

##### Unit 5: Inequalities in One Variable

Solving and Graphing Inequalities

#### CHAPTER 7: RATIO, PROPORTION, & PERCENT

##### Unit 1: Ratios and Rates

##### Unit 2: Proportion

##### Unit 3: Percent Concept

##### Unit 4: Percent Problems

##### Unit 5: Percent Applications

#### CHAPTER 8: WORD PROBLEMS

##### Unit 1: Modeling Equations & Beginning Word Problems

Translating English to Algebra

##### Unit 2: Value/Interest Problems

##### Unit 3: Motion Problems

#### CHAPTER 9: GEOMETRY

##### Unit 1: Lines and Angles

Points, Lines, Segments, and Rays

Complementary and Supplementary Angles (Part 1)

##### Unit 2: Triangles

##### Unit 3: Angles and Parallel Lines

##### Unit 4: Polygons and Angles

Sum of Interior and Exterior Angles

##### Unit 5: Circles

##### Unit 6: Three-Dimensional Figures

Classifying 3-Dimensional Figures

##### Unit 7: Congruent and Similar Figures

Problem Solving with Similar Figures

#### CHAPTER 10: GRAPHING, FUNCTIONS, AND TRANSFORMATIONS

##### Unit 1: Functions

##### Unit 2: Graphing Functions

Evaluating and Graphing Functions

Graphing within a Given Domain

##### Unit 3: Graphing Lines and Inequalities in Two Variables

Graphing Inequalities in Two Variables

##### Unit 4: Symmetry and Transformations

#### CHAPTER 11: LINEAR EQUATIONS

##### Unit 1: Patterns and Functions

Word Problems and Table Building

##### Unit 2: Slope

Using the Graph of a Line to Find Slope

Using Coordinates to Find Slope

##### Unit 3: Slope-Intercept Form

Using Slope-Intercept Form to Graph a Line

Converting to Slope-Intercept Form and Graphing

##### Unit 4: Equations of Lines

Using Graphs and Slope-Intercept Form

Using Tables and Slope-Intercept Form

##### Unit 5: Direct Variation

#### CHAPTER 12: SYSTEMS OF EQUATIONS

##### Unit 1: Solving Systems of Equations

##### Unit 2: Word Problems

#### CHAPTER 13: PROPERTIES OF EXPONENTS

##### Unit 1: Exponent Rules

##### Unit 2: Advanced Exponents

Numerical Bases and Exponents of Zero

#### CHAPTER 14: MEASUREMENT

##### Unit 1: Units of Measurement

##### Unit 2: Perimeter and Circumference

##### Unit 3: Area

Area of Squares and Rectangles

Area of Parallelograms and Trapezoids

##### Unit 4: Surface Area and Volume

Volume of Cylinders, Spheres, and Cones

#### CHAPTER 15: RIGHT TRIANGLES

##### Unit 1: Simplifying Radicals

##### Unit 2: Pythagorean Theorem

Using Square Roots to Solve Equations

##### Unit 3: Right Triangle Trigonometry

Sine, Cosine, and Tangent (Part I)

Sine, Cosine, and Tangent (Part II)

#### CHAPTER 16: STATISTICS AND PROBABILITY

##### Unit 1: Common Graphs and Charts

##### Unit 2: Representing Data

Stem-and-Leaf Plots and Frequency Tables

##### Unit 3: Central Tendency

##### Unit 4: Probability

Probability of Independent Events

Probability of Dependent Events

##### Unit 5: Counting Methods

Tree Diagrams and the Counting Principle

#### CHAPTER 17: NEGATIVE EXPONENTS

##### Unit 1: Simplifying Expressions with Negative Exponents

Multiplying and Dividing with Negative Exponents