Course Outline for a 14-year-old — AoPS + Rusczyk, Served Nigella-Style

Imagine mathematics laid out like a comforting, carefully arranged table: each chapter a dish, Alcumus the steady simmer, and enrichment projects sprinkled like a finishing zest. This plan is warm, deliberate and nourishing — intended to build rigorous problem solving while seasoning learning with economics, business thinking and practical financial literacy.

Overview & Flow

• Core textbooks (sequence): Prealgebra (Rusczyk, Patrick, Bopanna) → Introduction to Algebra (Rusczyk) → Introduction to Geometry (Rusczyk).
• Daily practice: Alcumus (Art of Problem Solving) used continuously to reinforce topics and develop contest-style problem solving.
• Enrichment themes: Economic reasoning, business applications, personal finance — each tied to the math you learn.
• Pacing idea: One school year (≈36 weeks). Roughly 6–8 hours/week: 3–4 hours Alcumus/problem practice, 2–3 hours reading/lessons, 1–2 hours projects or applied work.

Semester-by-Semester Roadmap

Term A (Weeks 1–12): Nourishing Foundations — Prealgebra + Alcumus

• Goals: arithmetic fluency, integers, fractions, percentages, basic ratios, introductory variables and simple equations, basic number theory and combinatorics.
• Reading: Prealgebra — aim to complete about 8–10 chapters in Term A (adjust to student level).
• Alcumus: daily practice focusing on Prealgebra topics; set weekly mastery goals (e.g., 20 targeted problems + 5 challenge problems/week).
• Economics tie-in: budgeting basics. Project: build a monthly personal budget, model savings with simple interest, and track spending for 4 weeks.

Term B (Weeks 13–24): Thickening the Broth — Introduction to Algebra + Alcumus

• Goals: linear equations & inequalities, systems, functions, polynomials basics, factoring, problem solving with algebraic thinking.
• Reading: Introduction to Algebra — aim to complete half to two-thirds here.
• Alcumus: shift to Algebra practice modules; weekly problem sets with increasing challenge.
• Business tie-in: cost, revenue, profit. Mini-project: use linear equations to model a small product: calculate break-even point, per-unit profit, and sensitivity to price changes.

Term C (Weeks 25–36): The Perfumed Finish — Introduction to Geometry + Synthesis

• Goals: Euclidean geometry basics — proofs, congruence, similarity, area/volume, circles, coordinate geometry.
• Reading: Introduction to Geometry — aim to complete major proof techniques and key chapters; integrate problems from prior algebra material.
• Alcumus: geometry topics + mixed-problem weeks to synthesize algebra and geometry skills.
• Finance tie-in: savings growth, compound interest, simple investing simulation. Capstone project: start a simulated small business or savings/investment portfolio and present results using algebra & geometry models (profit graphs, compound growth curves, break-even visuals).

Weekly Schedule (Sample 7–8 hour Week)

• Mon: 45–60 min — Read a book section, work example problems (concept focus).
• Tue: 60 min — Alcumus focused practice (build skill, aim for accuracy and time awareness).
• Wed: 45–60 min — Deeper problem solving / selected contest-style problems from AoPS community resources.
• Thu: 45 min — Applied math: business/finance exercise (spreadsheets, modeling a budget or product).
• Fri: 45–60 min — Review and consolidation: rework incorrect Alcumus problems, write short proof or explanation.
• Weekend: 60–90 min — Project work or a cumulative problem set. Optional: geometry drawing/Desmos exploration.

Assessments & Milestones

• Alcumus mastery: set milestones (e.g., 50% accuracy across 100 problems in a topic = mastery threshold) and track progress weekly.
• Monthly checkpoint: a 2-hour mixed problem set covering recently learned material plus a small applied task.
• Midyear exam (end of Term B): timed, mixed problems from Prealgebra & Algebra chapters covered; project submission (business mini-project).
• End-of-year capstone: formal write-up and presentation of the business/investment project and a collection of solved problems and proofs.

Enrichment & Applied Projects (Concrete Ideas)

1. Personal Budget and Savings Plan — Track real or simulated income & expenses for 4 weeks. Use percentages to categorize spending, calculate emergency fund targets, and model savings with simple & compound interest in a spreadsheet.
2. Mock Microbusiness — Choose a simple product or service. Use linear models for cost, revenue and profit. Find break-even, and explore pricing strategies. Present a one-page business plan and a profit graph.
3. Investing Simulation — Simulate investing small sums weekly into a few fictional assets. Track compounded returns, compare growth under different rates, and connect exponential functions to compound interest and inflation.
4. Data & Probability in Economics — Collect small datasets (prices, supply/demand instances), compute mean/median/variance, and model probability questions (e.g., chance a sale happens during a promotion). Use basic combinatorics to analyze inventory scenarios.
5. Geometry in Design & Cost — Use geometry to design packaging or a flyer; compute materials needed, area/volume costs, and optimize shape to reduce waste.

Tools & Resources

• Alcumus (AoPS): https://artofproblemsolving.com/alcumus — daily problem practice and adaptive review.
• Rusczyk textbooks: Prealgebra, Introduction to Algebra, Introduction to Geometry (use paperback or AoPS online resources).
• Desmos & GeoGebra — graphing, visual proofs, interactive exploration.
• Spreadsheets (Google Sheets / Excel) — budgets, break-even charts, compound interest tables.
• Personal finance primers: Khan Academy personal finance, Investopedia, Practical Money Skills — to support economic concepts.

How to Measure Success

• Alcumus completion and progress: consistent streaks, rising accuracy, and the ability to solve a set number of challenge problems per week.
• Textbook progress: completion of planned chapters by each term milestone, with written solutions to end-of-chapter problems.
• Project quality: clear spreadsheet models, correct math in business/investing tasks, and an explained write-up showing reasoning.
• Problem solving depth: ability to explain solutions in words or short proofs; transfer algebra to geometry and vice versa.

Study Tips — Nigella-Soft, Mathematically-Smart

• Be intentional: choose a small, realistic set of Alcumus problems daily rather than an enormous pile once a week.
• Savour mistakes: keep a "mistake journal" with the problem, your solution attempt, the correction, and a short note what the error taught you.
• Talk math aloud: explain a solution as if you were telling a friend about a recipe — why each step belongs and what it brings to the final dish.
• Make it real: whenever you learn a new technique, ask "how could someone in business or in daily life use this?" Then try to model it with a spreadsheet or graph.

Two Suggested Capstone Projects (with Rubrics)

1) Microbusiness Plan & Math Report

• Deliverables: short business plan (1–2 pages), cost/revenue/profit model in spreadsheet, break-even analysis (with algebra), and a 5-minute presentation (with graphs).
• Grading: correctness of math (40%), clarity of models/graphs (30%), realism & thoughtfulness (20%), presentation & write-up (10%).

2) Savings & Investing Study

• Deliverables: simulated portfolio over 6–12 months, compound interest calculations, sensitivity to rate changes, discussion of inflation impact, conclusions about long-term strategies.
• Grading: correct exponential modeling (40%), spreadsheet accuracy (30%), discussion of economic implications (20%), communication (10%).

Final Notes

This course outline invites you to a rhythm: steady daily problem practice, the satisfying turn of algebra into real-world numbers, and the elegant proofs of geometry. Keep curiosity as your spice — ask "why" about each step, and seek the small economic or business question that your math can answer. The combination of AoPS rigor and practical financial enrichment will equip you to think clearly, solve creatively, and manage real-world decisions with confidence.

If you like, I can now:

• Produce a week-by-week lesson plan for the full 36 weeks (with chapter-by-chapter breaks).
• Design the first monthly Alcumus problem set and a rubric for the first mini-project.
• Customize pacing if the student already knows parts of Prealgebra or Algebra.