Think of this plan as a recipe — rich, layered, and utterly irresistible. Over one accelerated year a 15‑year‑old will move from Prealgebra through Introduction to Algebra and Introduction to Geometry, while folding in Number Theory and Counting & Probability as savory side dishes.
- Phase 1 — Prealgebra (6–8 weeks): gently review fractions, exponents, primes, ratios, percents and basic geometry; solve the book’s opening problems before reading solutions.
- Phase 2 — Introduction to Algebra (18–20 weeks): dive into linear and quadratic equations, factorization, functions, sequences; alternate textbook sections with problem sets and full-solution reading.
- Phase 3 — Introduction to Geometry (18–20 weeks): explore similarity, congruence, circles, areas, power of a point and basic trig through challenge problems that demand craft and intuition.
Daily: 30–60 minutes on Alcumus for targeted practice and spaced review. Weekly: one textbook section’s problems, then study the complete solutions manual to learn techniques. Use the free AoPS video library to spice lessons and clarify stubborn steps. Monthly: timed problem sets or mock contests to build speed and confidence.
End result: a confident, problem-solving student who has devoured foundational theory, sharpened contest instincts, and is ready to savor more advanced mathematics.