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Course Contents

Modeling Squares and Finding the Square Root of a Number

Course Contents at a Glance

Estimating and Approximating Square Roots

Learning Outcomes

Simplifying Expressions With Square Roots

Faculty Resources

Using Square Roots in Applications

Problem Sets

Summary: Simplifying and Using Square Roots

Module 1: Whole Numbers

Putting It Together: Applications With Decimals

Why It Matters: Whole Numbers

Module 7: Percents

Introduction to Whole Number Basics

Why It Matters: Percents

Writing Whole Numbers With Words

Introduction to Writing Percents Using Words, Ratios, and Fractions

Whole Numbers and Place Value

Writing Percents as Ratios

Rounding Whole Numbers

Writing Percents as Fractions and Decimals

Summary: Whole Number Basics

Writing Fractions and Decimals as Percents

Introduction to Adding Whole Numbers

Summary: Writing Percents Using Words, Ratios, and Fractions

Notation and Modeling Additions of Whole Numbers

Introduction to Solve General Applications of Percent

Adding Whole Numbers

Translating and Solving Basic Percent Equations

Adding Whole Numbers in Applications

Solving Applications With Percent

Summary: Adding Whole Numbers

Finding Percent Increase and Percent Decrease

Introduction to Subtracting Whole Numbers

Summary: Solve General Applications of Percent

Notation and Modeling Subtraction of Whole Numbers

Introduction to Solving Sales Tax, Commission, and Discount Applications

Subtracting Whole Numbers

Solving Sales Tax Applications

Subtracting Whole Numbers in Applications

Solving Commission Applications

Summary: Subtracting Whole Numbers

Solving Discount and Markup Applications

Introduction to Multiplying Whole Numbers

Summary: Solving Sales Tax, Commission, and Discount Applications

Notation and Modeling Multiplication of Whole Numbers

Introduction to Solving Simple Interest Applications

Multiplying Whole Numbers

Using the Simple Interest Formula to Calculate Interest Earned

Multiplying Whole Numbers in Applications

Applications With Simple Interest

Summary: Multiplying Whole Numbers

Summary: Solving Simple Interest Applications

Introduction to Dividing Whole Numbers

Introduction to Solving Proportions and their Applications

Notation and Modeling Division of Whole Numbers

Writing Proportions

Dividing Whole Numbers

Solving Proportions

Dividing Whole Numbers in Applications

Writing and Solving Percent Proportions

Summary: Dividing Whole Numbers

Summary: Solving Proportions and their Applications

Putting It Together: Whole Numbers

Putting It Together: Percents

Problem Set 1: Whole Numbers

Problem Set 7: Percents

Module 2: The Language of Algebra

Module 8: Real Numbers

Why It Matters: The Language of Algebra

Why It Matters: Real Numbers

Introduction to Using the Language of Algebra

Introduction to Classes of Real Numbers

Using Variables and Algebraic Notation

Identifying Rational and Irrational Numbers

Identifying Expressions and Equations

Classifying Real Numbers

Simplifying Expressions Using the Order of Operations

Summary: Classes of Real Numbers

Summary: Using the Language of Algebra

Introduction to Using the Commutative and Associative Properties

Introduction to Evaluating, Simplifying, and Translating Algebraic Expressions

Rewriting Expressions Using the Commutative and Associative Properties

Evaluating Algebraic Expressions

Evaluating and Simplifying Expressions Using the Commutative and Associative Properties

Simplifying Algebraic Expressions

Summary: Using the Commutative and Associative Properties

Translating Algebraic Expressions From Words

Introduction to Using the Distributive Property

Summary: Evaluating, Simplifying, and Translating Algebraic Expressions

Simplifying Expressions With Different Forms of the Distributive Property

Introduction to Solving One-Step Equations Using Whole Numbers

Simplifying and Evaluating Expressions Using the Distributive Property

Determining Whether a Whole Number is a Solution to an Equation

Summary: Using the Distributive Property

Solving Equations Using the Subtraction and Addition Properties of Equality

Introduction to Properties of Identity, Inverses, and Zero

Translating Words Into an Algebraic Equation and Solving

Using the Identity and Inverse Properties of Addition and Subtraction

Summary: Solving one-step Equations Using Whole Numbers

Using the Multiplication and Division Properties of Zero

Introduction to Finding Multiples and Factors

Simplifying Expressions Using the Properties of Identities, Inverses, and Zero

Identifying Multiples of Numbers

Summary: Properties of Identity, Inverses, and Zero

Finding All the Factors of a Number

Putting It Together: Real Numbers

Summary: Finding Multiples and Factors

Problem Set 8: Real Numbers

Introduction to Prime Factorization and the Least Common Multiple

Module 9: Multi-Step Linear Equations

Finding the Prime Factorization of a Composite Number

Why It Matters: Multi-Step Linear Equations

Finding the Least Common Multiple of Two Numbers

Introduction to Solving Equations Using the Subtraction and Addition Properties of Equality

Summary: Prime Factorization and the Least Common Multiple

Using the Subtraction and Addition Properties for Single-Step Equations

Putting It Together: The Language of Algebra

Using the Subtraction and Addition Properties for Multi-Step Equations

Problem Set 2: The Language of Algebra

Applications of the Subtraction and Addition Properties

Module 3: Integers

Summary: Solving Equations Using the Subtraction and Addition Properties of Equality

Why It Matters: Integers

Introduction to Solving Equations Using the Division and Multiplication Properties of Equality

Introduction to Identifying and Writing Integers

Using the Division and Multiplication Properties of Equality for Single-Step Equations

Locating and Ordering Integers on the Number Line

Using the Division and Multiplication Properties of Equality for Multi-Step Equations

Notation and Definition of the Set of Integers

Solving Equations With Variables on Both Sides

Simplifying Expressions With Absolute Value

Solving Equations By Clearing Fractions

Translating Word Phrases into Expressions With Integers

Summary: Solving Equations Using the Division and Multiplication Properties of Equality

Summary: Identifying and Writing Integers

Introduction to Using a Problem Solving Strategy

Introduction to Adding Integers

Solving Multi-Step Equations Using a General Strategy

Notation and Modeling Addition of Integers

Apply a Problem-Solving Strategy to Basic Word Problems

Simplifying and Evaluating Expressions With Integers

Using a Problem-Solving Strategy to Solve Number Problems

Applications With Adding Integers

Summary: Using a Problem Solving Strategy

Summary: Adding Integers

Introduction to Solving Word Problems That Have Decimals

Introduction to Subtracting Integers

Solving Word Problems Involving Tickets and Stamps

Notation and Modeling Subtraction of Integers

Solving Equations By Clearing Decimals

Simplifying and Evaluating Expressions With Integers

Solving Problems Involving Coins

Applications With Subtracting Integers

Summary: Solving Word Problems That Have Decimals

Summary: Subtracting Integers

Introduction to Using Formulas to Solve Word Problems

Introduction to Multiplying and Dividing Integers

Using the Distance, Rate, and Time Formula

Multiplying Integers

Solving a Formula for a Specific Variable

Dividing Integers

Summary: Using Formulas to Solve Word Problems

Simplifying and Evaluating Expressions With Integers That Use all Four Operations

Putting It Together: Multi-Step Linear Equations

Translating Word Phrases into Expressions With Integers Using Multiplication and Division

Problem Set: Multi-Step Linear Equations

Summary: Multiplying and Dividing Integers

Problem Set 9: Expressions and Equations with Fractions

Introduction to Solving One-step Equations Using Integers

Module 10: Polynomials

Determining Whether an Integer is a Solution to an Equation

Why It Matters: Polynomials

Solving Equations With Integers Using Properties of Equality

Introduction to Adding and Subtracting Polynomials

Summary: Solving one step Equations Using Integers

Identifying Characteristics of Polynomials

Putting It Together: Integers

Adding and Subtracting Polynomials

Problem Set 3: Integers

Evaluating a Polynomial for a Given Value

Module 4: Fractions

Summary: Adding and Subtracting Polynomials

Why It Matters: Fractions

Introduction to Simplifying Expressions With Exponents

Introduction to Representing Parts of a Whole as Fractions

Simplifying Real Numbers With Exponents

Using Models to Represent Fractions and Mixed Numbers

Simplifying Variable Expressions Using Exponent Properties

Converting Between Improper Fractions and Mixed Numbers

Multiplying Monomials

Modeling and Finding Equivalent Fractions

Summary: Simplifying Expressions With Exponents

Locating and Ordering Fractions and Mixed Numbers on the Number Line

Introduction to Multiplying Polynomials

Summary: Representing Parts of a Whole as Fractions

Multiplying a Polynomial by a Monomial

Introduction to Multiplying and Dividing Fractions

Multiplying Two Binomials Using the Distributive Property

Simplifying Fractions

Vertical and FOIL Methods for Multiplying Two Binomials

Multiplying Fractions

Multiplying a Trinomial By a Binomial

Finding the Reciprocal of a Number

Summary: Multiplying Polynomials

Dividing Fractions

Introduction to Dividing Monomials

Summary: Multiplying and Dividing Fractions

Using the Quotient Property

Introduction to Multiplying and Dividing Mixed Numbers and Complex Fractions

Combining Properties to Simplify Expressions

Multiplying and Dividing Mixed Numbers

Summary: Dividing Monomials

Simplifying Complex Fractions

Introduction to Simplifying Expressions With Negative Exponents

Simplifying an Expression With a Fraction Bar

Writing Negative Exponents as Positive Exponents

Summary: Multiplying and Dividing Mixed Numbers and Complex Fractions

Simplifying Expressions With Negative Exponents

Introduction to Adding and Subtracting Fractions With Common Denominators

Scientific Notation

Adding Fractions With Common Denominators

Summary: Simplifying Expressions With Negative Exponents

Subtracting Fractions With Common Denominators

Introduction to Factoring Polynomials

Summary: Adding and Subtracting Fractions With Common Denominators

Finding the Greatest Common Factor from Two Expressions

Introduction to Adding and Subtracting Fractions with Different Denominators

Finding the Greatest Common Factor of a Polynomial

Converting Fractions to Equivalent Fractions With the LCD

Summary: Factoring Polynomials

Adding and Subtracting Fractions With Different Denominators

Putting It Together: Polynomials

Simplifying and Evaluating Complex Fractions

Problem Set 10: Polynomials

Summary: Adding and Subtracting Fractions With Different Denominators

Module 11: Geometry

Introduction to Adding and Subtracting Mixed Numbers

Why It Matters: Geometry

Adding Mixed Numbers With Common Denominators

Introduction to Using Properties of Angles, Triangles, and The Pythagorean Theorem

Subtracting Mixed Numbers With a Common Denominator

Using Properties of Angles to Solve Problems

Adding and Subtracting Mixed Numbers With Different Denominators

Using the Properties of Triangles to Solve Problems

Summary: Adding and Subtracting Mixed Numbers

Using the Pythagorean Theorem to Solve Problems

Introduction to Solving Equations That Contain Fractions

Summary: Using the Properties of Angles, Triangles, and the Pythagorean Theorem

Translating Words to Equations and Solving

Introduction to Using Properties of Rectangles, Triangles, and Trapezoids

Solving Equations That Contain Fractions Using the Addition and Subtraction Properties of Equality

Using Linear, Square, and Cubic Measure Appropriately

Solving Equations That Contain Fractions Using the Multiplication Property of Equality

Using the Properties of Rectangles to Solve Problems

Summary: Solving Equations that Contain Fractions

Using the Properties of Triangles to Solve Problems

Putting It Together: Fractions

Using the Properties of Trapezoids to Solve Problems

Problem Set 4: Fractions

Summary: Using Properties of Rectangles, Triangles, and Trapezoids

Module 5: Decimals

Introduction to Solving Problems With Circles and Irregular Figures

Why It Matters: Decimals

Using the Properties of Circles to Solve Problems

Introduction to Writing and Identifying Characteristics of Decimals

Finding the Area of Irregular Figures

Writing and Naming Decimals

Summary: Solving Problems With Circles and Irregular Figures

Converting Decimals to Fractions or Mixed Numbers

Introduction to Solving Problems Using Volume and Surface Area

Locating and Ordering Decimals With a Number Line

Finding the Volume and Surface Area of Rectangular Solids

Rounding Decimals

Finding the Volume and Surface Area of a Cube

Summary: Writing and Identifying Decimals

Finding the Volume and Surface Area of a Sphere

Introduction to Operations on Decimals

Finding the Volume and Surface Area of a Cylinder

Adding and Subtracting Decimals

Finding the Volume of a Cone

Multiplying Decimals

Summary: Solving Problems Using Volume and Surface Area

Dividing Decimals

Introduction to Systems of Measurement

Using Decimals in Money Applications

Making Unit Conversions in the U.S. System of Measurement

Summary: Operations on Decimals

Making Unit Conversions in the Metric System of Measurement

Introduction to Exploring The Relationship Between Decimals and Fractions

Converting Between U.S. and Metric Systems of Measurement

Converting Fractions to Decimals

Summary: Systems of Measurement

Comparing Decimals and Fractions

Putting It Together: Geometry

Simplifying Expressions With Decimals

Problem Set 11: Geometry

Applications with Pi

Module 12: Graphs

Summary: Exploring the Relationship Between Decimals and Fractions

Why It Matters: Graphs

Introduction to Solving Equations with Decimals

Introduction to Plotting Points on the Rectangular Coordinate System

Using the Properties of Equality to Solve Equations With Decimals

Plotting Points on the Rectangular Coordinate System

Translating Words to Equations That Contain Decimals

Identifying Points on the Rectangular Coordinate System

Summary: Solving Equations With Decimals

Verifying Solutions to Equations in Two Variables

Putting It Together: Decimals

Creating a Table of Ordered Pair Solutions to a Linear Equation

Problem Set 5: Decimals

Summary: Plotting Points on the Rectangular Coordinate System

Module 6: Applications With Decimals

Introduction to Plotting Lines on the Rectangular Coordinate System

Why It Matters: Applications With Decimals

Identifying the Intercepts on the Graph of a Line

Introduction to Finding Averages and Basic Probabilities

Graphing Lines Using Points

Calculating the Mean of a Set of Numbers

Summary: Plotting Lines on the Rectangular Coordinate System

Finding the Median of a Set of Numbers

Introduction to Identifying and Using Slope

Identifying the Mode of a Set of Numbers

Using Models to Define Slope

Finding the Probability of an Event

Finding the Slope of a Line From Its Graph

Summary: Finding Averages and Basic Probabilities

Finding Slope Given Two Points on a Line

Introduction to Writing Ratios and Calculating Rates

Graphing a Line Given a Point and a Slope

Writing Ratios as Fractions

Summary: Identifying and Using Slope

Writing Rates and Calculating Unit Rates

Putting It Together: Graphs

Summary: Writing Ratios and Calculating Rates

Problem Set 12: Graphs

Introduction to Simplifying and Using Square Roots