Interactive Algebra I: Learn By Doing

An Engaged Approach To Teach You Algebra I

What you'll learn

Solving multi-step algebraic equations

Graphing linear equations

Solving systems of linear equations

Learning to factor

Requirements

No algebra skills needed.

Description

This is an Algebra I course structured on the OpenStax textbook Elementary Algebra.  Each section begins with an original activity designed to show you the concepts in a way that brings deeper understanding.  Work the activity. And if you need help, watch the video where I walk through every question of the activity. A link to a full, traditional lecture is also available.  Use this course to learn Algebra I for the first time or use this course as a tutoring tool to help you with the course you are already taking.  Designed to mimic the engaged learning approach which I use in my college classrooms, you drive the learning, and I serve as the facilitator.  I also created this course to be an alternative to traditional tutoring.  Tutoring is fantastic, but it can be expensive and hard to find.  Here, my activities are the exact material and concepts which I would share with you in a tutoring session to bring the concepts home.  So, use the index of the textbook to find the topics you need, and search for the activity which you are working on in your traditional classroom.  The choice is yours.Section topics discussed are:Foundational SkillsSolving Linear Equations and InequalitiesLearning to Solve Word ProblemsGraphsSystems of Linear EquationsPolynomialsFactoringRational Expressions and EquationsRoots and RadicalsQuadratic Equations

Overview

Section 1: Course Introduction

Lecture 1 How To Use This Course For Learning All of Algebra I

Lecture 2 How To Use This Course As A Tutoring Resource

Section 2: Foundational Skills

Lecture 3 1.1a: The Place Value System, Naming Numbers, and Rounding

Lecture 4 1.1b: Prime vs Composite; Factor Trees; Prime Factorization

Lecture 5 1.2a: Exponents; Inequalities; Translating to Math Language

Lecture 6 1.2b: Order of Operations; Evaluating Expressions

Lecture 7 1.2c: Combining Like Terms; Identifying Coefficients and Terms

Lecture 8 1.3a: Negative Numbers; Absolute Values

Lecture 9 1.3b: Adding and Subtracting Positive and Negative Numbers

Lecture 10 1.4a: Multiplying positive and negative numbers

Lecture 11 1_4b: Translating into Math Language (Multiplication and Division)

Lecture 12 1.5a: Reducing, Multiplying and Dividing Basic Algebraic Fractions

Lecture 13 1.5b: Division of Fractions; Order of Operations with Fractions.

Lecture 14 1.6a: Adding and Subtracting Basic Algebraic Fractions

Lecture 15 1_6b: Complex Fractions; Evaluating Expressions with Two Variables

Lecture 16 1.7a: Naming, Rounding, Adding and Subtracting Decimals

Lecture 17 1_7b: Multiplying and Dividing Decimals

Lecture 18 1.7c: Converting Decimals to Fractions; Converting Fractions to Decimals

Lecture 19 1.8a: Classification of Numbers

Lecture 20 1.8b: Locating Decimals and Fractions on a Number Line

Lecture 21 1.9a: Basic Properties of Mathematics

Lecture 22 1_9b: The Distributive Property

Lecture 23 1.10a: Converting within the Standard System or the Metric System

Lecture 24 1.10b: Converting Between the Standard System and the Metric System

Section 3: Solving Linear Equations and Inequalities

Lecture 25 2.1a: Solving One-Step Equations Involving Addition and Subtraction

Lecture 26 2.1b: Basic Word Problems Involving One-Step Equations (Add/Subtract)

Lecture 27 2.2a: Solving One-Step Equations Involving Multiplication or Division

Lecture 28 2.2b: Basic Word Problems Involving One-Step Equations (Multiply/Divide)

Lecture 29 2.3a: Solving Two-Step Equations with Variables on Both Sides

Lecture 30 2.3b: Solving Equations Moving Variables and Constants on Both Sides

Lecture 31 2.4a: Solving Complex Multi-Step Equations

Lecture 32 2.4b: Equations with Solutions of All Real Numbers or No Solution

Lecture 33 2.5a: Clearing Fractions From Equations

Lecture 34 2.5b: Clearning Decimals from Equations

Lecture 35 2.6a: Using the Formula Distance Equals Rate Times Time

Lecture 36 2_6b: Solving Equations for a Variable

Lecture 37 2_7a: Solving Basic Equations Involving Inequalities

Lecture 38 2.7b: Solving More Complex Inequality Equations

Section 4: Learning to Solve Word Problems

Lecture 39 3.1a: Introduction to Word Problems

Lecture 40 3.1b: Number Problems

Lecture 41 3.2a: Introduction to Proportions

Lecture 42 3.2b: Percent Change; Simple Interest

Lecture 43 3.2c: Percent Mark-up; Percent Discount

Lecture 44 3.3a: Word Problems- Adjusting for Values

Lecture 45 3.3b: Word Problems Involving Mixtures

Lecture 46 3.4a: Word Problems Involving Triangles

Lecture 47 3.4b: Word Problems Involving the Pythagorean Theorem

Lecture 48 3.4c: Word Problems Involving the Perimeter and Area of a Rectangle

Lecture 49 3.5a: Word Problems Involving Distance, Rate and Time

Lecture 50 3.5b: Word Problems Involving Decimals in Distance, Rate, Time Problems

Lecture 51 3.6: Word Problems Involving Inequalites

Section 5: Graphs

Lecture 52 4.1a: Introduction to the Coordinate Plane

Lecture 53 4.1b: Graphing Lines by Plotting Points

Lecture 54 4.2a: Graphing Lines by Plotting Points (Fractional Slopes)

Lecture 55 4.2b: Graphing Vertical and Horizontal Lines

Lecture 56 4.3: Graphing Lines Using the Intercepts

Lecture 57 4.4a: Introduction to Slope

Lecture 58 4.4b: Graphing a Line Using the Slope and a Point

Lecture 59 4.5a: Graphing Lines Using the Slope-Intercept Form

Lecture 60 4.5b: Reviewing Methods for Graphing Lines

Lecture 61 4.5c: Determining if Lines are Parallel or Perpendicular

Lecture 62 4.6a: The Point-Slope Equation

Lecture 63 4.6b: Parallel or Perpendicular to a Given Line

Lecture 64 4.7: Graphing Linear Inequalities

Section 6: Systems of Linear Equations

Lecture 65 5.1: Graphing Systems of Linear Equations

Lecture 66 5.2: Solving Systems of Linear Equations by Substitution

Lecture 67 5.3: Solving Systems of Linear Equations by Elimination (Addition)

Lecture 68 5.4a: Word Problems Involving Systems of Linear Equations

Lecture 69 5.4b: Solving Distance, Rate and Time Problems Using A System of Equations

Lecture 70 5.5a: Systems Word Problems Accounting for Value

Lecture 71 5.5b: Investment Problems Using a System of Linear Equations

Lecture 72 5.6a: Systems of Linear Inequalities

Lecture 73 5.6b: Word Problems Involving Systems of Linear Inequalities

Section 7: Polynomials

Lecture 74 6.1a: Introduction to Polynomials; Adding and Subtracting Polynomials

Lecture 75 6.1b: Evaluating Polynomials

Lecture 76 6.2a: Exponents Rules for Monomials

Lecture 77 6_2b: Multiplying a Polynomial by a Monomial

Lecture 78 6.3: Multiplying Binomials

Lecture 79 6.4a: Multiplying Two of the Same Binomials

Lecture 80 6.4b: Multiplying Conjugate Binomials

Lecture 81 6.5a: Exponent Rules for Fractions

Lecture 82 6.5b: Exponent Rules for Algebraic Fractions

Lecture 83 6.5c: Dividing Monomials

Lecture 84 6.6a: Diving a Polynomial by a Monomial

Lecture 85 6.6b: Dividing Polynomials

Lecture 86 6.7a: Negative Exponents

Lecture 87 6.7b: Multiplying and Dividing Monomials Involving Negative Exponents

Lecture 88 6.7c: Scientific Notation

Section 8: Factoring

Lecture 89 7.1a: The Greatest Common Factor

Lecture 90 7.1b: Factoring by Grouping

Lecture 91 7.2a: Factoring Basic Trinomials

Lecture 92 7.2b: Factoring Basic Trinomials with Two Variables

Lecture 93 7.3a: The Trial and Error Method for Factoring Trinomials

Lecture 94 7.3b: The A/C Method of Factoring Trinomials

Lecture 95 7.4a: Factoring Perfect Square Trinomials

Lecture 96 7.4b: Factoring the Difference of Squares

Lecture 97 7.4c: Factoring the Difference of Cubes

Lecture 98 7.5: General Strategy for Factoring

Lecture 99 7.6a: Solving Equations Using the Zero-Product Property

Lecture 100 7.6b: Word Problems Using the Zero-Product Property

Section 9: Rational Expressions and Equations

Lecture 101 8.1a: Introduction to Rational Expressions; Evaluating Rational Expressions

Lecture 102 8.1b: Simplifying Rational Expressions

Lecture 103 8.1c: Simplifying Rational Expressions (The -1 Trick)

Lecture 104 8.2a: Multiplying Rational Expressions

Lecture 105 8.2b: Dividing Rational Expressions

Lecture 106 8.3a: Adding/Subtracting Rational Expressions with a Common Denominator

Lecture 107 8.3b: Adding/Subtracing Rational Expressions Using the -1 Trick

Lecture 108 8.4a: Adding Rational Expressions Without a Common Denominator

Lecture 109 8.4b: Subtracting Rational Expressions Without a Common Denominator

Lecture 110 8.5a: Simplifying Complex Rational Expressions

Lecture 111 8.5b: Using the LCD Approach to Simplify Complex Rational Expressions

Lecture 112 8.6a: Solving Equations Involving Rational Expressions

Lecture 113 8.6b: Solving for a Variable Using the GCF Trick

Lecture 114 8.7a: Solving Rational Expressions Set Up as a Proportion

Lecture 115 8.7b: Solving Proportion Word Problems

Lecture 116 8.7c: Solving Proportion Word Problems Involving Similar Figures

Lecture 117 8.8a: Solving Distance, Rate, Time Problems Involving Rational Expressions

Lecture 118 8.8b: Solving Rate of Work Problems

Lecture 119 8.9a: Direct Variation Problems

Lecture 120 8.9b: Indirect Variation Problems

Section 10: Roots and Radicals

Lecture 121 9.1a: Introduction to Roots

Lecture 122 9.1b: Roots Involving Variables

Lecture 123 9.2a: Roots that Don't Completely Simplify

Lecture 124 9.2b: Fractions Beneath Roots

Lecture 125 9.3a: Adding and Subtracting Roots

Lecture 126 9.3b: Simplifying and Adding and Subtracting Roots with Variables

Lecture 127 9.4a: Multiplying Roots

Lecture 128 9.4b: Multiplying Roots which are Binomials

Lecture 129 9.5a: Simplifying Square Roots over a Fraction Bar

Lecture 130 9.5b: Rationalizing Denominators

Lecture 131 9.5c: Rationalizing Denominators Using Conjugates

Lecture 132 9.6a: Solving Equations Involving Roots

Lecture 133 9.6b: Using Formulas which Involve Roots

Lecture 134 9.7a: Simplifying Higher Order Roots

Lecture 135 9.7b: Higher Order Roots Which Don't Completely Simplify

Lecture 136 9.7c: Higher Order Roots with Fractions

Lecture 137 9.7d: Adding and Subtracting Higher Order Roots

Lecture 138 9.8a: Fractional Exponents and Roots

Lecture 139 9.8b: Exponent Rules for Fractional Exponents

Section 11: Quadratic Equations

Lecture 140 10.1a: Solving Equations with the Square Root Property

Lecture 141 10.1b: Solving Equations with the Square Root Property (No Perfect Square)

Lecture 142 10.2a: Introduction to Completing the Square

Lecture 143 10.2b: Solving Equations by Completing the Square

Lecture 144 10.2c: Solving Equations by Completing the Square (Coefficient not 1)

Lecture 145 10.3a: Introduction to the Quadratic Formula

Lecture 146 10.3b: The Discriminant

Lecture 147 10.4: Word Problems Requiring the Quadratic Formula

Lecture 148 10.5a: Finding the Vertex of a Quadratic Function

Lecture 149 10.5b: Graphing Quadratic Functions

Lecture 150 10.5c: Word Problems Involving Parabolas

Students needing help with Elementary Algebra who want an interactive approach to learning.