Pre-Algebra

Pre-algebra pulls together everything a student knows about numbers and starts pointing it at algebra. Core topics include integer operations (including negatives), full fluency with fractions and decimals, exponents and order of operations, square roots, ratios and proportions, percent and percent change, solving one- and two-step equations and inequalities, the coordinate plane, basic functions, and a survey of geometry (angles, triangles, area, volume, the Pythagorean theorem).

It's usually taught in 7th grade for students on a standard track or 8th grade for those a year behind, though some accelerated students take it in 6th. It follows 6th grade math and leads directly into algebra I. The course is intentionally broad and a bit repetitive — it's the last chance to fill in arithmetic gaps before the curriculum assumes mastery and moves on.

Pre-algebra exposes every gap a student has carried forward. If fractions were shaky in 5th grade, they will be a daily problem in pre-algebra, because almost every topic uses them. Don't let a student bluff through with a calculator. Insist on at least some daily work with fractions, percents, and integer operations by hand, even if it feels slow.

For most homeschool families, a structured spine works best at this level — AoPS Pre-Algebra (challenging, depth-first), Saxon Pre-Algebra or Algebra 1/2 (incremental, lots of review), Math Mammoth 7 (clear and affordable), or Lial's Basic College Math (text-heavy and thorough). Khan Academy is a reliable backup for any concept that doesn't land. Word problems are non-negotiable; this is the year students learn to translate English into equations, and the only way to learn it is to do a lot of them. If your student can explain why dividing both sides of an equation by -2 flips the inequality, they're getting it.