In Illinois, Algebra 1 begins with the assumption that students are familiar with the concepts of number systems, fractions, ratio, inequalities, and the very basics of graphing and solving one-variable equations. There is some conceptual review in beginning lessons, and the first significant topic in Algebra 1 is the study of linear equations in all of their various forms (namely: point-slope form, slope-intercept form and standard form).

Slope-intercept form (y=mx+b, where m is the slope and b is the y-intercept) is the most foundational of these and will follow a student of mathematics up through Calculus, linear algebra and graduate-level statistics (in generalized linear regression). Point-slope form ((y-y₁)=m(x-x₁)), if taught properly, introduces tools that can be used for translating and transforming equations that provide intuitive means of creating mathematical models of observed phenomena. Standard form (Ax+By=C) is most useful in learning how to apply rules of algebra to change an equation from one form to another.

An Algebra 1 class then generally progresses into the basics of polynomials and factoring. Being able to successfully and easily factor polynomials is one of the most important skills for students of algebra. If not learned early and learned well, Algebra 2 and Pre-Calculus will be enormously more difficult than they ever have to be. This is one of the skills that I spend the most time on. Algebra 1 students will see immediate applications of factoring when they learn how to simplify rational expressions.

Finally, an Algebra 1 class is likely to end with an introduction to some basic ideas in statistics and probability.

While I have not covered all of the topics generally covered in an Algebra 1 course (including linear inequalities, exponents and radical expressions), this gives a rough overview of some of the main points and what you or your son or daughter can expect from Algebra 1.

I provide supplementary instruction (tutoring) for Algebra 1 for $35 an hour. I provide more comprehensive homeschool instruction, including assigning homework and administering tests and quizzes for $50 an hour.