Algebra 1 – Homeschool

Course Description

Algebra 1 lays the essential foundation for all high school mathematics. It serves as the bridge from concrete arithmetic to the abstract thinking required in higher-level math. The course integrates real-world applications throughout, including optional use of a graphing calculator. See the Table of Contents below for a full list of sections and subsections included in the course.


How the Course Works

  1. The student begins by watching a video lesson (typically 30–50 minutes long), followed by a corresponding textbook assignment.
  2. The student stops working at the end of their scheduled math time.
  3. On the next day, the student continues the assignment. A third day may be needed to finish the work—and that's perfectly fine.
  4. After completing a chapter (or in some cases, mid-chapter), the student takes a practice test for review, followed by the actual test the next day. (Both should be administered by a parent.)
  5. The process continues with the next section and progresses through the full course.

When Help Is Needed

If students or parents encounter difficulties, support is available through multiple methods:

  1. Re-watch the video lesson.
  2. Review similar examples in the textbook.
  3. Consult the solutions manual for step-by-step guidance.
  4. Submit a question through the Cool Math Guy website. Replies typically arrive within 24 hours.

Sample Videos from this Course


Table of Contents

1.1  Real Numbers: Order and Absolute Value 26 min.

  • Sets and Real Numbers
  • The Real Number Line
  • Ordering Real Numbers
  • Absolute Value

1.2  Adding and Subtracting Integers 15 min.

  • Adding Integers Using a Number Line
  • Adding Integers Algebraically
  • Subtracting Integers Algebraically
  • Informal (simple) Rules for Collecting Integers

1.3  Multiplying and Dividing Integers 35 min.

  • Multiplying Integers
  • Dividing Integers
  • Informal (simple) Rules for Multiplying and Dividing Integers
  • Factors and Prime Numbers

1.4  Operations with Rational Numbers 36 min.

  • Rewriting Fractions (rules for signs, simplifying fractions, and building up fractions)
  • Adding and Subtracting Fractions
  • Multiplying and Dividing Fractions
  • Operations with Decimals

1.5  Exponents, Order of Operations,

and Properties of Real Numbers 33 min.

  • Exponents (structure and manipulations)
  • Order of Operations
  • Properties of Real Numbers

2.1  Writing and Evaluating Algebraic Expressions 15 min.

  • Variables
  • Algebraic Expressions
  • Evaluating Algebraic Expressions

2.2  Simplifying Algebraic Expressions 25 min.

  • Properties of Algebra
  • Combining Like Terms
  • Simplifying Algebraic Expressions
  • Symbols of Grouping

2.3  Algebra and Problem Solving 23 min.

  • Constructing Verbal Models
  • Translating Phrases and Sentences into Expressions and Equations
  • Verbal Models with Hidden Operations
  • Additional Problem-Solving Strategies

2.4  Introduction to Equations 19 min.

    • A General Discussion about Equations
    • Checking Solutions of Equations
    • Forming Equivalent Equations
    • Constructing Equations

3.1  Solving Linear Equations 30 min.

  • Linear Equations in the Standard Form ax + b = c
  • Solving a Linear Equation in Nonstandard Form
  • Applications

3.2  Equations that Reduce to Linear Form 20 min.

  • Equations Containing Symbols of Grouping
  • Equations Involving Fractions
  • Equations Involving Decimals

3.3  Problem Solving with Percents 41 min.

  • Percents and Converting Among Fractions, Decimals, and Percents
  • The Percent Equation
  • Markup and Discount

3.4  Ratios and Proportions 39 min.

  • Setting Up Ratios
  • Unit Prices
  • Solving Proportions

3.5  Geometric and Scientific Applications 87 min.

  • Using Formulas
  • Solving Mixture Problems
  • Solving Work-Rate Problems

3.6  Linear Inequalities 49 min.

    • Inequalities and Their Graphs on a Number Line
    • Compound Inequalities
    • Properties of Inequalities
    • Solving Inequalities

4.1  Ordered Pairs and Graphs 11 min.

  • The Rectangular Coordinate System
  • Ordered Pairs as Solutions of Equations
  • Constructing a Table of Values

4.2  Graphs of Equations in Two Variables 16 min.

  • Constructing the Graph of an Equation in Two Variables
  • X-Intercepts and Y-Intercepts

4.3  Slope and Graphs of Linear Equations 23 min.

  • The Slope of a Line
  • Slope as a Graphing Aid (The Slope-Intercept Form of a Linear Equation)
  • Parallel and Perpendicular Lines

4.4  Equations of Lines 26 min.

  • The Point-Slope Form of the Equation of a Line
  • Equations of Horizontal and Vertical Lines

4.5  Graphs of Linear Inequalities 14 min.

    • Linear Inequalities in Two Variables
    • The Graph of a Linear Inequality in Two Variables

5.1  Negative Exponents and Scientific Notation 33 min.

  • Rules of Exponents
  • Negative Exponents
  • Scientific Notation

5.2  Adding and Subtracting Polynomials 16 min.

  • Basic Definitions
  • Adding Polynomials
  • Subtracting Polynomials

5.3  Multiplying Polynomials: Special Products 27 min.

  • Monomial Multipliers
  • Multiplying Binomials
  • Multiplying Polynomials
  • Special Products

5.4  Dividing Polynomials 21 min.

  • Dividing a Polynomial by a Monomial
  • Dividing a Polynomial by a Binomial

6.1  Factoring Polynomials with Common Factors 17 min.

  • Greatest Common Factor
  • Common Monomial Factors
  • Factoring by Grouping

6.2  Factoring Trinomials 23 min.

  • Factoring Trinomials of the Form x2 + bx + c
  • Factoring Trinomials in Two Variables
  • Factoring Completely

6.3  More About Factoring Trinomials 17 min.

  • Factoring Trinomials of the form ax2 + bx + c
  • Factoring Completely

6.4  Factoring Polynomials with Special Forms 29 min.

  • Difference of Two Squares
  • Repeated Factorization
  • Perfect Square Trinomials
  • Sum or Difference of Two Cubes

6.5  Solving Quadratic Equations by Factoring24 min.

  • The Zero-Factor Property
  • Solving Quadratic Equations by Factoring

7.1  Simplifying Rational Expressions 18 min.

  • Rational Expressions and Their Domains
  • Simplifying Rational Expressions

7.2  Multiplying and Dividing Rational Expressions 15 min.

  • Multiplying Rational Expressions
  • Dividing Rational Expressions

7.3  Adding and Subtracting Rational Expressions 25 min.

  • Rational Expressions with Like Denominators
  • Least Common Multiple
  • Rational Expressions with Unlike Denominators

7.4  Complex Fractions 16 min.

  • Complex Fractions
  • Complex Fractions with Sums or Differences

7.5  Rational Equations and Applications 25 min.

  • Equations Containing Constant Denominators
  • Equations Containing Variable Denominators
  • Applications

8.1  Solving Systems of Equations by Graphing 11 min.

  • Systems of Linear Equations
  • Solving a System of Linear Equations by Graphing
  • The No-Solution and Many-Solution Cases

8.2  Solving Systems of Equations by Substitution 15 min.

  • The Method of Substitution
  • The No-Solution and Many-Solution Cases

8.3  Solving Systems of Equations by Elimination 25 min.

  • The Method of Elimination
  • The No-Solution and Many-Solution Cases

8.4  Applications of Systems of Linear Equations 14 min.

  • Constructing Systems of Equations
  • Applications of Systems of Linear Equations

8.5  Systems of Linear Inequalities 16 min.

  • Systems of Linear Inequalities in Two Variables
  • Finding Boundaries and Identifying the Solution Region

9.1  Roots and Radicals 22 min.

  • Equal Factors and Roots
  • Radicals
  • Radicals and Calculators

9.2  Simplifying Radicals 37 min.

  • Simplifying Radicals with Constant Factors
  • Simplifying Radicals with Variable Factors
  • Rationalizing Denominators

9.3  Operations with Radical Expressions 26 min.

  • Adding and Subtracting Radical Expressions
  • Multiplying Radical Expressions
  • Conjugates
  • Simplifying Quotients Involving Radicals

9.4  Radical Equations and Applications 29 min.

  • Solving Equations Involving One Radical
  • Solving Equations Involving Two Radicals
  • Applications Involving Radicals

10.1  Solution by the Square Root Property 11 min.

  • Solving Quadratic Equations by Factoring
  • Solving Quadratic Equations by the Square Root Property

10.2  Solution by Completing the Square 24 min.

  • Constructing Perfect Square Trinomials
  • Completing the Square

10.3  Solution by the Quadratic Formula 23 min.

  • Deriving the Quadratic Formula
  • Solving Equations by the Quadratic Formula

10.4  Graphing Quadratic Equations 36 min.

  • Quadratic Equations in Two Variables
  • Sketching the Graph of a Quadratic Equation

10.5  Applications of Quadratic Equations 23 min.

  • Applications of Quadratic Equations

10.6  Complex Numbers 28 min.

  • The Imaginary Unit i
  • Complex Numbers
  • Operations with Complex Numbers
  • Complex Conjugates
  • Quadratic Equations with Complex Solutions

10.7  Relations, Functions, and Graphs 32 min.

  • Relations
  • Functions
  • Function Notation
  • Finding the Domain of a Function

Supporting Parents

We understand that questions can come up, especially in the beginning. Personal support is available via text, email, or phone. We’re here to help both parents and students every step of the way.


Course Materials

Textbook Recommendations
New textbooks can be expensive, so we recommend purchasing used copies online. The following two textbooks are directly correlated with our video instruction and include ISBN numbers and vendor links for convenience:

Option 1
Elementary Algebra, 5th Edition by Larson

Option 2
Elementary Algebra Within Reach, 6th Edition by Larson


Practice Tests, Tests, and Answer Keys

All assignments and testing materials are available to subscribers through a password-protected link.


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Annual Flat Rate: $150 for One Year of Access

Start your Algebra 1 journey today with easy-to-follow instruction, responsive support, and a proven method trusted by homeschool families and educators nationwide.

$150.00 for 1 year