# Prealgebra and Introductory Algebra with POWER Learning

## Messersmith/Perez/Feldman

Table of Contents

### Chapter 1Operations with Integers

1.1Place Value and Rounding

1.2Introduction to Integers

1.3Adding Integers

1.4Subtracting Integers

1.5Estimating a Sum or a Difference

1.6Multiplying Integers and Estimation

1.7Dividing Integers and Estimation PIAT

1.8Exponents and Order of Operations

### Chapter 2Variables and Solving Equations

2.1Introduction to Variables

2.2Simplifying Expressions

2.3Solving Equations Using the Addition Property of Equality

2.4Solving Equations Using the Division Property of Equality

2.5More on Solving Equations

2.6Applications Involving One Unknown

2.7Applications Involving Two Unknowns

### Chapter 3Operations with Signed Fractions

3.1Introduction to Signed Fractions

3.2Writing Fractions in Lowest Terms

3.3Multiplying and Dividing Signed Fractions

3.4Adding and Subtracting Like Fractions and Finding a Least Common Denominator

3.5Adding and Subtracting Unlike Fractions

3.6Operations with Mixed Numbers PIAT

3.7Order Relations and Order of Operations

3.8Solving Equations Containing Fractions

### Chapter 4Basic Geometry Concepts

4.1Introduction to Geometry

4.2Rectangles, Squares, Parallelograms, and Trapezoids

4.3Triangles

4.4Volume and Surface AreaPIAT

4.5Solving Geometry Applications Using Algebra

### Chapter 5Signed Decimals

5.1Reading and Writing Decimals

5.2Rounding Decimals

5.3Adding and Subtracting Signed Decimals

5.4Multiplying Signed Decimals

5.5Dividing Signed Decimals and Order of Operations PIAT

5.6Writing Fractions as Decimals

5.7Mean, Median, and Mode

5.8Solving Equations Containing Decimals

5.9Square Roots and the Pythagorean Theorem

5.1Circles, Spheres, Cylinders, and Cones

### Chapter 6Ratios and Proportions

6.1Ratios

6.2Rates

6.3Proportions

6.4Solve Applied Problems Involving Proportions

6.5Angles

6.6Solve Applied Problems Involving Congruent and Similar Triangles

### Chapter 7Measurement and Conversion

7.1Conversions Within the U.S. Measurement System

7.2The Metric System: Length

7.3The Metric System: Capacity and Weight (Mass)

7.4Solving Applied Problems Involving Metric Units

7.5Metric - U.S. Customary Conversions and Temperature

### Chapter 8Percents

8.1Percents, Fractions, and Decimals

8.2Compute Basic Percents Mentally

8.3Use an Equation to Solve Percent Problems

8.4Solve Applications Involving Percents PIAT

8.5More Applications with Percents

8.6Simple and Compound Interest

### Chapter 9Graphs

9.1Reading Tables, Pictographs, Bar Graphs, and Line Graphs

9.2Frequency Distributions and Histograms

9.3Using and Making Circle Graphs

Cumulative Review for Chapters 1-9

### Chapter 10Real Numbers, Equations, and Inequalities

10.1Real Numbers

10.2More on Solving Linear Equations

10.3Formulas and Solving for a Specific Variable

10.4Solving Linear Inequalities in One Variable

### Chapter 11Linear Equations in Two Variables

11.1Introduction to Linear Equations in Two Variables

11.2Graphing by Plotting Points and Finding Intercepts

11.3The Slope of a Line

11.4The Slope-Intercept Form of a Line

11.5Writing an Equation of a Line

### Chapter 12Solving Systems of Linear Equations

12.1Solving Systems by Graphing

12.2Solving Systems by Substitution

12.3Solving Systems by the Elimination Method PIAT

12.4Applications of Systems of Equations

12.5Linear Inequalities in Two Variables

### Chapter 13The Rules of Exponents and Polynomials

13.1The Product Rule and Power Rules

13.2Integer Exponents

13.3The Quotient Rule PIAT

13.4Scientific Notation

13.5Addition and Subtraction of Polynomials

13.6Multiplication of Polynomials

13.7Dividing a Polynomial by a Monomial

13.8Dividing a Polynomial by a Polynomial

### Chapter 14Factoring Polynomials

14.1The Greatest Common Factor and Factoring by Grouping

14.2Factoring Trinomials of the Form x^2 + bx + c

14.3Factoring Trinomials of the Form ax^2 + bx + c (a not 1)

14.4Factoring Special Trinomials and Binomials PIAT

14.5Solving Quadratic Equations by Factoring

14.6Applications of Quadratic Equations

### Chapter 15Rational Expressions

15.1Simplifying Rational Expressions

15.2Multiplying and Dividing Rational Expressions

15.3Finding the Least Common Denominator

15.4Adding and Subtracting Rational Expressions PIAT

15.5Simplifying Complex Fractions

15.6Solving Rational Equations

15.7Applications of Rational Equations and Variation

### Chapter 16Roots and Radicals

16.1Finding Roots

16.2Simplifying Radicals: The Product and Quotient Rules

16.3Adding and Subtracting Radicals

16.4Combining Operations on Radicals

16.5Dividing Radicals

16.6Solving Radical Equations

### Chapter 17Quadratic Equations

17.1Solving Quadratic Equations Using the Square Root Property

17.2Solving Quadratic Equations by Completing the Square

17.3Solving Quadratic Equations Using the Quadratic Formula PIAT

17.4Graphs of Quadratic Equations

17.5Introduction to Functions

### Appendix

A.1Adding Whole Numbers

A.2Subtracting Whole Numbers

A.3Multiplying Whole Numbers

A.4Introduction to Division and Short Division

A.5Long Division

B.1Sets of Numbers

B.2Graphing Inequalities

B.3Deriving the Area of a Parallelogram and the Area of a Trapezoid

B.4Inductive and Deductive Reasoning