Algebra 1 Course Description
In this course, I strive to provide all students with a dynamic mathematics education that balances a solid foundation of basic algebraic skills with a constructed understanding of concepts that challenges, supports, and instills an excitement for math. My goal is to help students develop as curious and flexible thinkers who are confident in their individual mathematical abilities, allowing them to feel prepared to meet the challenges of higher mathematics. Topics mastered include number sense, graphing and solving linear and quadratic equations, solving systems of equations and inequalities, exponent rules, radical and rational expressions and equations, parabolas and real-life applications through word problems. It is a rich curriculm which is designed to challenge each student while at the same time help him/her begin to enjoy the world of mathematics. Homework pdfs are included, as well as short videos to review the homework solutions. Each homework has a few problems from previous lessons so that students practice recalling and implementing previously learned skills.
This course includes:
- 12 Chapters
- 132 Homework Worksheets
- 272 Videos Total
- 138 Lesson Videos
- 134 Homework Solutions Videos (I work out on the board the solutions to each problem step by step)
- 4 Final Exam Review Lessons
- 1 FINAL EXAM
- Over 75 Hours of Video Instruction!
COURSE TOPICS
Chapter 1: Foundations of Algebra
Lessons:
Introduction to Course
Classification of Real Numbers
Adding & Subtracting Positive and Negative Numbers (Part 1)
Adding & Subtracting Positive and Negative Numbers (Part 2)
Multiplying & Dividing Positive and Negative Numbers
Evaluating Algebraic Expressions
Order of Operations
Some Key Properties in Algebra
Chapter 2: Linear Equations
Lessons:
Solving One-Step Equations
Solving Two-Step Equations
Solving Multi-Step Equations
Equations with Infinite and Zero Solutions
Solving Equations with Fractions (Same Denominators)
Solving Equations with Fractions (Different Denominators)
Solving Proportions
Solving Equations with Decimals
Solving Absolute Value Equations
Solving Literal Equations
Solving Percent Equations
Percent Increase or Decrease
Chapter 3: Introduction to Word Problems
Lessons:
Translating English into Math
Number Word Problems
Consecutive Integer Word Problems (Part 1)
Consecutive Integer Word Problems (Part 2)
Geometry Word Problems
Age Word Problems
Ratio Word Problems
Percent Word Problems
Simple Interest Word Problems
Distance / Motion Word Problems (Parts 1,2 &3)
Chapter 4: Linear Inequalities
Lessons:
Graphing and Writing Single-Variable Inequalities
Solving Single-Variable Inequalities
More Practice solving Inequalites; Examples of Zero and Infinite Solutions
Solving and Graphing Compound Inequalities with “AND” Statements
Solving and Graphing Compound Inequalities with “OR” Statements
Absolute Value Inequalities
Chapter 5: Graphing and Writing Functions
Lessons:
Introduction to Equations with Two Variables
Relations vs. Functions
Graphing on a Cartesian Plane with T-charts
Graphing Equations in Slope Intercept Form (Using Shortcut)
Graphing Equations in Point-Slope Form
Graphing Equations in Standard Form
Graphing Practice
Finding the Slope Using The Slope Formula
Writing Equations With Given Data
Converting Equations From One Form to Another
Parallel and Perpendicular Lines
Scatter Plots and Trend Lines
Direct Variation
Graphing Absolute Value Functions
Graphing One-Variable Inequalities on Cartesian Plane
Graphing Two-Variable Inequalities on Cartesian Plane
Chapter 6: Systems of Equations and Inequalities
Lessons:
Solving Systems of Equations by Graphing
Solving Systems of Equations by Substitution (Parts 1-2)
Solving Systems of Equations by Elimination (Parts 1-4)
Systems with No Solutions or Infinite Solutions
Systems of Equations Word Problems (5 Types)
Graphing Systems of Inequalities with Parallel Boundary Lines
Systems of Inequalities Word Problems
Chapter 7: Exponents and Exponential Functions
Lessons:
Introduction to Exponents; Rules for Zero and Negative Exponents
Multiplication Properties of Exponents
Division Properties of Exponents
Division Property: A Cool Little Trick
Scientific Notation
Exponential Functions and Their Graphs
Exponential Growth and Decay
Compound Interest
Chapter 8: Radicals and Radical Functions
Lessons:
Introduction to Radicals; Simplifying Radicals with Numbers
Simplifying Radicals with Variables
Adding and Subtracting Radicals
Multiplying Radicals (Parts 1 & 2)
Dividing Radicals and Rationalizing the Denominator
Practicing with Radicals
Solving Radical Equations (Parts 1 & 2)
Graphing Radical Equations
Chapter 9: Polynomials: Combining, Multiplying and Factoring
Lessons:
Introduction to Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Multiplying Binomials using FOIL
Special Products of Binomials
Factoring Polynomials: Finding Factors, Tree Factorization, Greatest Common Factor
Factoring Out the Greatest Common Factor
Factoring Out the “Blobs” (…or Binomials)
Factoring by Grouping
Factoring Quadratic Trinomials: a = 1
Factoring Quadratic Trinomials: ”a” is Not 1
Gary’s Terrific Trick
Factoring the Difference of Two Squares
Factoring Practice
Chapter 10: Quadratic Functions and Equations
Lessons:
Understanding and Solving Quadratic Equations (Parts 1 & 2)
Using Square Roots to Solve Quadratic Equations
Vertical Motion Model Word Problems
Completing the Square
Deriving the Quadratic Formula
Using the Quadratic Formula
Understanding the Discriminant
Quadratic Word Problems – Rectangles
Finding the Axis of Symmetry and Vertex
More Quadratic Word Problems
Anatomy of a Quadratic Equation
Graphing Quadratics with “Standard Parabola Guy”
Reviewing Different Types of Graphs
Functions, Set Notation, Domain and Range
Chapter 11: Rational Expressions and Equations
Lessons:
Rational Expressions: Finding the Excluded Value
Simplifying Rational Expressions
Simplifying Rational Expressions with Opposite Binomials
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions (Parts 1 & 2)
Dividing Polynomials Using Long Division
Solving Rational Equations: Proportions
Solving Rational Equations: Multiplying by LCD
Solving Rational Equations: Extraneous Solutions
Understanding and Graphing Inverse Variation
Direct Variation vs. Inverse Variation
Graphing Rational Functions Using Asymptotes & T-charts
Work Word Problems
Inverse Variation Word Problems and Other Rational Word Problems
Chapter 12: End-of-Course Review
Lessons:
Final Exam Prep #1
Final Exam Prep #2
Final Exam Prep #3
Final Exam Prep #4
FINAL EXAM
