Accelerated Math Course Outline for a 13-year-old — Semester 1: Beast Academy Level 5 (Online); Semester 2: AoPS Prealgebra + Introduction to Geometry

A warm, quick-start plan — with the cadence of Nigella:

Imagine mathematics like a favourite recipe: aromatic, layered, and surprising. We begin gently, stir in practice until the flavours develop, and finish with something confidently beautiful to serve. This accelerated two-semester course is built to move a bright 13-year-old from the joyful challenge of Beast Academy Level 5 into the structured elegance of AoPS Prealgebra and Introduction to Geometry, with Alcumus as the tasty, adaptive practice on the side.

Overall goals (by the end of the year)

• Solid mastery of Beast Academy Level 5 topics: confident number sense, puzzle-style reasoning, and flexible problem-solving.
• Strong foundations in prealgebra: integer arithmetic, fractions, exponents, algebraic expressions, linear equations, ratios, percent, basic counting and probability.
• Foundational geometry: reasoning about angles, triangles, polygons, circles, area, perimeter, and introductory coordinate methods.
• Regular practice habits: 3–5 focused sessions per week, with one extended problem-solving session weekly.
• Preparedness for contest-style problems (MathCounts level) and comfortable transition to AoPS contest training if desired.

Semester structure and pacing

Each semester: 16 weeks. Accelerated pacing assumes prior arithmetic fluency and motivation. Typical week:

• 3 shorter guided sessions (30–45 minutes) — new lessons, worked examples, video/comic reading.
• 1 longer session (60–90 minutes) — mixed practice, problems that require deeper thought, or a hands-on geometry task.
• Alcumus practice scattered across the week (15–30 minutes) for adaptive review and strengthening weak spots.

Semester 1: Beast Academy Level 5 (online) — 16 weeks

Approach the online modules like tasting courses: read the comic explanation, try the guided problems, then savour the harder practice problems.

1. Weeks 1–2: Diagnostic + foundations. Quick diagnostic to find gaps. Revisit place value, multi-digit arithmetic, and mental math strategies where needed.
2. Weeks 3–6: Core Level 5 units. Work steadily through each Beast Academy unit: number properties, factors and multiples, prime and composite, basic number theory topics and smart arithmetic tricks.
3. Weeks 7–9: Fractions, decimals, and percents as practiced in BA puzzles. Emphasize conversions, comparisons, and quirky fraction puzzles.
4. Weeks 10–12: Early algebraic thinking—patterns, simple expressions, and two-step reasoning puzzles.
5. Weeks 13–14: Problem sets and mixed reviews. Pull problems from earlier units for cumulative practice; focus on strategy and explanation.
6. Week 15: Assessment week — a mixed test of BA skills (timed and untimed problems) plus a reflection write-up: explain 3 favourite problems and the strategies used.
7. Week 16: Enrichment and transition. Introduce Alcumus and plan Semester 2 reading: skim Prealgebra chapters to see themes (fractions, exponents, algebra, geometry introductions).

Semester 1 assessments and projects

• Weekly short problem set from BA online (10–15 problems).
• Every fourth week: a 45-minute mixed quiz to check speed and accuracy.
• End-of-semester test and an explanatory portfolio: choose 6 problems, write clear solutions and reflections.

Semester 2: AoPS Prealgebra (Rusczyk) + Introduction to Geometry (Rusczyk) with Alcumus — 16 weeks

This semester balances two classic AoPS texts. Start with Prealgebra to build solid algebraic thinking, then move into Introduction to Geometry. Alcumus runs continuously for adaptive drills and topic reinforcement.

1. Weeks 1–6: AoPS Prealgebra focus
   • Week 1: Integers, absolute value, and order of operations with care and examples.
   • Week 2: Factors, multiples, primes, GCF, LCM, and number theory basics.
   • Week 3: Fractions, decimals, percents — conversions, comparisons, and word problems.
   • Week 4: Ratios, proportions, and mixture problems.
   • Week 5: Exponents, roots, scientific notation, and integer powers.
   • Week 6: Algebraic expressions, simple equations, two-step equations, and translating words to equations.
2. Weeks 7–10: Prealgebra continued + problem solving
   • Week 7: Inequalities, graphing simple linear relations, and problem strategies.
   • Week 8: Counting basics and introductory probability—fundamental counting principle, simple permutations and combinations.
   • Week 9: Word problems, rates, and work problems; mixture with AoPS-style proofs of reasoning.
   • Week 10: Midterm assessment and a creative problem project: design a 5-question puzzle set with solutions and difficulty notes.
3. Weeks 11–16: Introduction to Geometry focus
   • Week 11: Basics of geometry vocabulary, points, lines, planes, angles, and angle relationships.
   • Week 12: Triangles — classification, congruence ideas, triangle inequality, and problem tasks.
   • Week 13: Polygons and quadrilaterals — interior/exterior angles, special quadrilaterals, basic proofs.
   • Week 14: Circles — radius, diameter, chords, arcs, and inscribed angles (intro-level problems).
   • Week 15: Area and perimeter review across shapes, coordinate geometry basics (distance and midpoint), and simple locus problems.
   • Week 16: Final assessment — geometry packet and a capstone geometry art project (design a tiled pattern that uses area and symmetry calculations, and include a short write-up explaining the math).

Alcumus integration (continuous)

• Set Alcumus to focus on current reading topics; 15–30 minutes, 3x per week.
• Use Alcumus badges and strengths to guide review weeks; let Alcumus identify weak areas and schedule targeted practice.
• Record progress monthly and adjust topics if several Alcumus problems point to the same gap.

Assessments, projects, and milestones for Semester 2

• Biweekly problem sets drawn from AoPS texts (4–6 problems, with 2 challenging problems).
• Midterm project (end of Week 10): a 5-question original puzzle set with full solutions.
• Final assessment: mixed Prealgebra + Intro Geometry test and a geometry art project with explanation.
• Optional: attempt AMC 8 or MathCounts School-level practice if the student wants contest experience.

Study tips and rhythm

• Short, focused practice beats long, unfocused sessions: 30–45 minutes concentrated study is ideal.
• Keep a problem journal: write problems the student found interesting, the solution attempts, and the final, clean solution. This builds explanation skills and reflection.
• After every challenging problem, write a 2–3 sentence explanation of the key insight — this makes future recall easier.
• Use Alcumus as a gentle coach, not a judge. Encourage retries, and review the solution pages when stuck.
• Schedule one playful math session weekly: puzzles, games, or a math art project to keep curiosity alive.

How to measure success

• Monthly skill checks: 10–15 problems covering recent topics with 80%+ accuracy as a target.
• Portfolio growth: by year end, have 12 polished, written solutions the student can explain clearly aloud.
• Confidence with AoPS-style proofs and multi-step reasoning: can explain strategy choice for 3 medium-hard problems.

Resources and extras

• Beast Academy online: lessons, practice sets, and parental progress tracking.
• AoPS Prealgebra (Rusczyk et al., 2011) and Introduction to Geometry (Rusczyk, 2007) as primary texts.
• AoPS Alcumus for adaptive practice and topic tracking.
• Optional: AoPS online community, MathCounts Trainer, AMC practice tests, and engaging puzzle books.

Final note — a flourish to finish

Let every problem feel like a small dish you are tasting: sometimes surprising, sometimes familiar, always teaching you about balance. With Beast Academy to sharpen playful intuition, and AoPS texts to teach careful craft, this accelerated year should leave a 13-year-old hungry for the next course — confident, curious, and quietly delighted.