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
