Overview — You will work hard and get results

This is an accelerated, disciplined two-semester plan for a 13-year-old who wants fast, deep progress in problem solving. Semester 1 uses Beast Academy Level 5 (online). Semester 2 moves to AoPS Alcumus plus the AoPS texts Prealgebra and Introduction to Geometry. Expect steady daily practice, weekly checkpoints, and strict review. No skipping. No shortcuts.

Expectations and time commitment

• Daily: 45–90 minutes on weekdays; 90–150 minutes on two weekend days (total 8–12 hours/week accelerated).
• Weekly goals: complete assigned reading + practice problems, do Alcumus targets, write solutions for 6–10 challenging problems.
• Assessment cadence: weekly quizzes, biweekly problem set reviews, one midterm, one cumulative final each semester.
• Mastery definition: can explain solutions in writing and orally, solve similar problems without hints, and correct mistakes from an error log.

Semester 1 — Beast Academy Level 5 (16 weeks)

Main goals: fluent arithmetic with integers, fractions, decimals; mental calculation speed; strong problem‑solving habits; introduction to stronger reasoning and basic geometry/logic found in Level 5.

1. Weeks 1–2: Diagnostic & fundamentals
   • Take a timed diagnostic (45 min): mixed Beast Academy problems or similar. Identify weak areas.
   • Review place value, integer operations, factors & multiples. Daily speed drills (5–10 min).
2. Weeks 3–5: Fractions & decimals deep dive
   • Work through Beast Academy fraction/decimal units: equivalence, arithmetic, comparison, mixed numbers.
   • Weekly mastery quizzes and error log updates; 3 challenging written solutions per week.
3. Weeks 6–8: Ratios, proportions, percents, basic algebraic thinking
   • Ratio reasoning, solving proportions, percent change problems, simple equations and variables.
   • Introduce multi-step word problems; emphasize drawing pictures, setting equations.
4. Weeks 9–11: Number theory & combinatorics basics
   • Prime factors, GCF/LCM, divisibility rules, basic counting problems, permutations vs combinations intro.
   • 2 timed mini contests (25–40 min) to build speed.
5. Weeks 12–13: Geometry basics in Level 5
   • Angles, basic polygons, area/perimeter practice, coordinate basics when present in BA Level 5.
6. Weeks 14–15: Problem sets & review
   • Work mixed problem sets focusing on weakest topics. Build set of 20 problems to master.
7. Week 16: Final assessment & forward plan
   • Timed cumulative exam (60–90 min). Evaluate readiness for Semester 2. Set specific Alcumus targets for next semester.

Daily rule (Tiger cadence): You will complete your assigned Beast Academy lesson and 3 extra challenging problems. If you miss this, you must make it up on Saturday with additional timed practice.

Semester 2 — AoPS Alcumus + AoPS Prealgebra & Introduction to Geometry (16 weeks)

Main goals: rigorous prealgebra mastery and solid geometry foundations with proof practice and contest-style problem solving. Use Alcumus for targeted practice and tracking.

1. Weeks 1–2: Orientation & Alcumus baseline
   • Set up Alcumus profile, choose Prealgebra and Geometry tracks. Complete baseline Alcumus diagnostics.
   • Read first 2–3 chapters of Prealgebra: integers, arithmetic with negatives, absolute value, basic variable notation.
2. Weeks 3–6: Core Prealgebra topics
   • Chapters: factors & multiples, fractions (advanced), decimals & percents, ratios & proportional reasoning, exponents.
   • Weekly: 4 textbook sections, 6 Alcumus topics, one written solution set (4 problems) submitted to parent/tutor for review.
3. Weeks 7–9: Advanced Prealgebra & introduction to proofs
   • Chapters: integers/number theory, modular thinking, roots & radicals, introductory algebraic manipulations.
   • Introduce short, 3–5 step written proofs. Emphasize clear statements and logic.
4. Weeks 10–12: Start Introduction to Geometry
   • Text chapters: basics of geometry, points/lines/angles, triangle properties (including congruence), parallel lines.
   • Weekly geometry proof practice: 3 short proofs + 3 construction/diagram problems.
5. Weeks 13–14: Similarity, area, circles
   • Topics: similarity, similarity ratios, area and perimeter relations, circle basics (arcs, chords, inscribed angles).
   • Mix of AoPS textbook problems and Alcumus practice; begin timed geometry sets.
6. Weeks 15–16: Consolidation, contest practice & final
   • Mixed review, mock contest (60–90 min). Final cumulative exam covering Prealgebra and geometry foundations.
   • Assess readiness for next level (AoPS Intro Algebra / Geometry 1 or contest programs).

Weekly structure (example)

• Monday–Friday: 45–75 min — reading + worked examples (20–40 min), Alcumus practice or Beast Academy problems (20–30 min), write 1 solution to a hard problem (10–20 min).
• Saturday: 90–150 min — catch up, timed practice, review error log, work on 2 harder problems with full written solutions.
• Sunday: 60–90 min — light review, mental math drills, preview next week.

Assessments and milestones

• Weekly quiz (20–40 min) covering that week’s topics.
• Biweekly problem set (long-form written solutions) graded for correctness and clarity.
• Midterm (week 8) and final (week 16) each semester, timed and cumulative.
• Maintain an error log: record every mistake, why it happened, and the corrected solution. Review weekly.

How to study (concrete rules)

1. Read actively: before reading solution, try each problem for 10–15 minutes. Write all attempts.
2. Always write full solutions for harder problems — no mental shortcuts. A correct answer without reasoning is not mastery.
3. When you get stuck for 10 minutes, try a different representation (diagram, table, special cases), then consult hints. Document the hint and the moment you used it.
4. Do Alcumus problems until you reach at least 80% accuracy at the next-below target level, then raise difficulty.
5. Teach back: once a week, explain one solved problem out loud to a parent or peer. You must justify each step.

Parent / coach role (clear, strict)

• Check daily completion and weekly error log. Sign off on written solutions.
• Enforce the daily rule: assigned lesson + 3 extra hard problems, or makeup on Saturday.
• Provide focused feedback: correct reasoning errors, not just answers. If confusion persists after 2 review attempts, arrange short tutor help.

Resources & tools

• Beast Academy online (Level 5 lessons & problems).
• AoPS Alcumus — set to Prealgebra and Geometry tracks, track progress weekly.
• AoPS books: Prealgebra (Rusczyk et al., 2011) and Introduction to Geometry (Rusczyk, 2007) — follow chapter pacing above.
• Notebook for written solutions, error log, and index of favorite problem techniques.

Contests & stretch goals

• Short-term: aim for strong performance on AMC 8 or school math contests by semester end (use mock tests for practice).
• Longer-term: preparation for AMC 10 and MathCounts in subsequent year(s) if progress is strong.

Final notes — strict but fair

This plan is accelerated. If you follow it exactly — daily work, weekly solutions, error log, and parent checks — you will improve quickly. If you slack, progress stalls. There are no excuses: you will do the work, correct your mistakes, and show mastery. I will expect clear written solutions, faster mental math, and steady improvement in contest-style problems by the end of each semester.

If you want, I can now convert this into a printable week-by-week calendar (with exact Beast Academy unit assignments and AoPS chapters per week) — tell me how many weeks per semester you want and I will lay it out.