Imagine math like a rich, slow-baked pudding: patient heat, precise timing, and the right mix of ingredients. For a spirited 15-year-old ready to accelerate, we’ll finish Prealgebra, fold in Introduction to Algebra, and keep Introduction to Geometry simmering alongside — all with Alcumus practice and AoPS videos to taste.
Overall timeline & rhythm
- Length: approximately 6–9 months accelerated (flexible by readiness and time available).
- Weekly cadence: 5 days/week. Daily session: 60–90 minutes (lesson + problems + Alcumus). One longer weekly session (90–120 minutes) for the challenge set.
- Split: Stage 1 (finish Prealgebra) ~8–12 weeks. Stage 2 (Introduction to Algebra) ~16–20 weeks. Geometry: ongoing modules across the whole plan, one geometry topic per week or biweekly depending on intensity.
Daily structure — like following a recipe
- Warm-up (10–15 minutes): quick mental arithmetic, flash review of facts, or a 5-question Alcumus warm-up.
- Lesson (25–40 minutes): read a section from Prealgebra or Intro to Algebra / Geometry. Start each section by attempting the opening problems — AoPS style encourages trying before reading the solutions.
- Practice (20–30 minutes): work through textbook problems. Use the solutions manual only after 25–30 minutes of effort; treat solutions as gourmet notes to learn technique.
- Alcumus & videos (20–30 minutes): daily Alcumus practice tuned to current topic; watch 1–2 short AoPS videos weekly that align to the textbook section.
Stage specifics
- Finish Prealgebra: concentrate on fractions, exponents, ratios, percents, simple equations, basic number theory, counting, and introductory geometry. Aim to complete roughly 2–4 sections per week with regular problem sets and a weekly assessment.
- Begin Introduction to Algebra: once Prealgebra is complete, shift to algebraic manipulations, linear equations, ratios, quadratic introductions, functions, and graphing. Keep algebraic topics brisk but thorough.
- Geometry concurrent: each week, devote 1–2 sessions to geometry topics (similarity, congruence, areas, circles, power of a point, basic trig). This keeps spatial reasoning fresh and reinforces algebra through geometry problems.
Assessment & enrichment
- Weekly challenge: one curated hard problem from AoPS to stretch reasoning (use the solutions manual after serious effort).
- Monthly checkpoint: Alcumus diagnostics and a timed problem set to measure gains and adjust pacing.
- Emphasis: more than answers — cultivate strategies. AoPS texts teach by problems first; follow that delightful ritual.
Serve this plan with curiosity, a dash of patience, and regular reflection. The Alcumus system is your mise en place — immediate feedback, adaptive practice — and the free AoPS videos are the whispering tutor, guiding technique. Together, they turn a brisk curriculum into something quietly sumptuous.