Algebra I

About this course

This is a dedicated Algebra I course that spends the entire year on algebra and nothing else. It opens with the language of algebra — variables, terms, coefficients, order of operations, and the properties of real numbers — then covers integers and rational numbers on the number line, one-step through multi-step equations, equations with variables on both sides, literal equations solved for a chosen variable, and inequalities of every kind including compound and absolute value. Functions come next: domain and range, function notation, the vertical line test, direct variation, rate of change, slope, and the slope-intercept, point-slope, and standard forms of a line, along with parallel and perpendicular slopes, scatter plots and lines of best fit, and word problems on distance, mixture, age, and simple interest. The second half of the year covers systems solved by graphing, substitution, and elimination; exponent rules, scientific notation, and exponential growth and decay; polynomials, FOIL, and special products; a full unit on factoring that runs through grouping, trinomials with a leading coefficient, differences of squares, and the sum and difference of cubes; rational expressions and equations with attention to extraneous solutions; radicals, the Pythagorean theorem, and the distance and midpoint formulas; quadratic functions solved by graphing, square roots, completing the square, and the quadratic formula; and a closing statistics unit with box plots, histograms, correlation, probability, permutations, and combinations.

The course is 180 lessons in 15 units of 12, one lesson per school day at about 55 minutes, which is a full year. A lesson opens with prayer, states the day's idea in a short paragraph, defines the key vocabulary, and moves quickly into three to five fully worked examples with every step shown. A brief real-world application and a KJV verse tied to the day's math follow, along with the same closing notes on study habits and common mistakes that appear in every lesson. The instruction is compact and the worked examples carry most of the teaching, so a student who needs an idea explained several different ways will do better with you sitting nearby than working alone. Every lesson ends with a ten-question multiple-choice quiz that grades itself, and every unit closes with a review lesson. The final unit is cumulative review plus a few application lessons on algebra in science, finance, and geometry. Materials are pencil, graph paper, a Bible, and an optional calculator.

Algebra itself is taught from the ground up, so no prior algebra is needed, but your student does need a settled pre-algebra foundation: confident arithmetic with fractions, decimals, and percents, comfort with negative numbers, and familiarity with exponents, square roots, and the coordinate plane. Freedom Homeschool also offers a general Math course at ninth grade, and the two overlap heavily. That course is an integrated survey — algebra, proof-based geometry, and statistics through z-scores in the same year. This course sets the geometry aside and spends the year on algebra alone, which lets it go considerably deeper on functions, polynomials, factoring, rational expressions, and radicals. Each is a full 180-lesson year on its own, so assigning both would mean two math courses running at once. Most families will pick one: the general Math course for a broad year, or this one for a student who needs a full Algebra I on the transcript before moving on to Geometry.

What the course covers

• Variables, expressions, real number properties, and integer operations
• Multi-step, literal, and absolute value equations and inequalities
• Functions, function notation, domain and range, and direct variation
• Slope and the slope-intercept, point-slope, and standard forms of a line
• Systems of equations and systems of inequalities
• Exponent rules, scientific notation, and exponential growth and decay
• Polynomials, FOIL, special products, and every method of factoring
• Rational expressions and equations, and radical expressions
• Quadratic functions, completing the square, the quadratic formula, and the discriminant
• Statistics and probability: box plots, correlation, permutations, and combinations

What your student will be able to do

• Solve multi-step, literal, rational, radical, and absolute value equations
• Graph a line from any of its forms and write its equation from a graph or two points
• Solve a system of equations by graphing, substitution, or elimination
• Factor a polynomial completely and use factoring to solve quadratic equations
• Solve any quadratic by completing the square or the quadratic formula and read the discriminant
• Translate a word problem into an equation and check the answer in the original

Scope and sequence

All 15 units of Algebra I for Grade 9, in the order they are taught.

Every lesson, by title

All 180 lesson titles are listed here — nothing is withheld until you download. Open a unit to read its contents.

One whole lesson, exactly as it comes

This is a real lesson taken from the middle of the course — the teaching text, the practice, the homework, and the first three quiz questions with their answers. It is not a marketing excerpt.

What you will need

Drawn from the materials named across all 180 lessons of this course. Most families already own most of it.