Picture a small courtroom of ideas — Ally McBeal’s aside meets math rigor. For a keen 15‑year‑old on an accelerated path, we finish AoPS Prealgebra swiftly (fractions, exponents, primes, ratios, percents, roots, introductory geometry, counting & probability), then fold into Introduction to Algebra while Introduction to Geometry simmers alongside.
Rhythm: Weeks 1–8 finish Prealgebra (2–4 sections/week, weekly mixed assessments); Weeks 9–20 begin Introduction to Algebra (linear equations, inequalities, functions, polynomials, quadratics, early number theory) with Geometry running concurrently (similarity, congruence, circles, power of a point, transformations, intro trig). Practice is daily Alcumus sets, AoPS video morsels, and weekly timed mixed-topic tests. Targets: 90%+ Alcumus accuracy; 80%+ on timed tests; comfortable AMC10-style problem solving.
ACARA v9 alignment: develops Number & Algebra, Measurement & Geometry, Statistics & Probability and mathematical reasoning through problem-first tasks, spaced practice and reflection. Pedagogy: savor problems before solutions, pair algebra topics with geometry applications, and use contest-style appetizers to build flexible thinking.
Weekly reflections, fortnightly problem sets modelled on contest problems, and monthly milestone reviews keep pace honest and joyful. The result: an accelerated, delightful year — technique, curiosity, and spatial fluency baked into a tasteful plan.