Fallout-inspired Homeschool Plan for Ages 14–15 — AoPS Algebra & Geometry, STEM Labs, Medieval→1600s Crosslinks, and Futuristic Pathways

Style note and brief disclaimer: This plan is inspired by the imaginative, survivalist, world-building tone often found in post-apocalyptic fiction and roleplaying settings. It does not copy any specific living author or copyrighted text; instead it borrows a sense of practical resourcefulness, layered storytelling, and hands-on experimentation to make learning feel urgent, relevant, and exploratory.

Overview and goals (year-long; ages 14–15)

This plan blends rigorous math (AoPS Introduction to Algebra and Introduction to Geometry) with applied sciences and maker-style labs (kitchen chemistry, health & beauty formulations, safe food science), a humanities strand connecting the medieval period through the 1600s, and several forward-looking pathways (farming, marine science, life extension, textiles, maritime law, etc.). The aim is to build strong problem-solving math skills, scientific reasoning, interdisciplinary thinking, and practical project skills that lead to a portfolio and capstone.

Structure, pacing, and weekly schedule

Academic year: ~36 weeks. Daily routine modeled on a 5-day instructional week with flexible afternoons for labs, fieldwork, and pathway projects.

• Morning block (9:00–11:30): Math (AoPS) — warmups, problem sets, Socratic discussion, proof-writing practice. 4 days/week; geometry focus 2 days during the week when paired with algebra sections.
• Late morning (11:30–12:15): Medieval→1600s humanities rotations — primary-source study, map-reading, technology case studies, and cross-disciplinary problem sets linking history to math/science.
• Afternoon (1:30–4:00): Science labs, pathway workshops, field trips, fitness & nutrition sessions. Rotate intensive labs 2–3 days a week; lighter project time the other days.
• Evening / weekly creative time: astrology/tarot cultural study, fashion/textiles practice, reflective journals, and portfolio curation.

Math: AoPS Introduction to Algebra & Introduction to Geometry (core)

Goals: Develop deep algebraic reasoning, number theory intuition, problem-solving techniques, and rigorous geometric thinking (proofs, transformations, Euclidean constructions, coordinate geometry).

1. Pacing: Plan 36 weeks — 20 weeks focused primarily on Introduction to Algebra (foundational + contest-style problems), 16 weeks for Introduction to Geometry, and continual integration of algebraic geometry topics throughout the year.
2. Weekly routine: Two AoPS problem sets per week with one guided problem-solving seminar (student presents a solution), one timed reasoning exercise, and one written homework focused on proofs/explanations.
3. Assessment: Biweekly mini-exams testing techniques and reasoning, monthly take-home challenge problems, and a semester portfolio of solved and commented problems. Include math journals where students reflect on strategies used and mistakes made.
4. Enrichment: Encourage AoPS Alcumus practice, MathCounts-style team rounds, and occasional math modeling problems linked to pathway work (e.g., yield calculations for vertical farm prototype, geometry for textile patterning, trigonometry for astronomical observation).

Science, Health & Beauty, and Kitchen Labs

Principles: Hands-on, safe, reproducible experiments fostering chemistry literacy, microbiology awareness (safe/non-pathogenic), nutrition science, and practical formulation skills. All labs require supervision, written risk assessment, and attention to local laws.

• Kitchen chemistry labs: safe acid–base titrations using household indicators, fermentation (kimchi, sourdough) focusing on microbial ecology and food safety, caramelization and Maillard reaction experiments to explore chemistry of cooking.
• Health & beauty labs: pH testing of skin-care products, simple emulsions (basic lotions) using safe cosmetic-grade ingredients, study of UV protection (fabric shading tests and sunscreen theory rather than formulation of regulated products), ingredient reading and allergy testing protocols.
• General lab safety: goggles, gloves, lab notebook, proper ventilation, no culturing of unknown microbes. For microbiology, use safe, educational kits or model organisms (yeast, baker’s yeast, Spirulina) and avoid clinical or pathogenic strains.
• Kitchen-to-lab projects: nutritional analysis of recipes, macro- and micronutrient tracking, recipe reformulation to optimize protein, fiber, or calorie density for survival scenarios or long-duration fieldwork.

Medieval → 1600s Crosslinks (interdisciplinary unit)

Turn the medieval→early modern period into a thread that connects math, science, maritime exploration, economics, textiles, and law.

1. Quarter-long thematic units: 1) Feudal economies and resource management; 2) Ship design, navigation, and early maritime law; 3) Textiles, dyeing, and trade networks; 4) Scientific revolution beginnings — optics, astronomy, and methodology.
2. Projects: Reconstruct a simple waterwheel model (apply geometry and mechanical advantage), design a period-accurate navigation problem using latitude/longitude basics (pair with geometry/trigonometry), analyze the economics of a medieval market (supply, demand, coinage).
3. Primary sources: ship logs, navigation manuals, guild records, early scientific treatises. Pair reading with math tasks: compute distances, rates of travel, ballistics-style calculations of cannon range (theory only).

Futuristic Pathways (choose 2–4 in-depth; others remain elective)

Each pathway includes learning objectives, weekly activities, hands-on projects, community/field components, and assessments. Expect 3–6 weeks of focused work per pathway, plus ongoing maintenance projects.

1) Future Farming Methods & Horticulture

• Topics: hydroponics, aeroponics, vertical farming, soil science, pollinator gardens, seed saving, permaculture principles.
• Projects: Build a small hydroponic raft or Kratky system, run side-by-side trials comparing soil mixes, measure yield per square foot, document inputs and outputs.
• Math links: calculate nutrient concentrations, solution dilutions, yield forecasting using algebraic models.

2) Wildlife Stewardship & Marine Science

• Topics: population surveys, habitat restoration, intertidal ecology, sustainable fisheries science.
• Projects: Conduct bird or insect surveys, design a beach-intertidal species catalog, basic water quality testing (pH, salinity, turbidity) with safe kits, map local habitats using GIS-lite tools.
• Ethics & law: conservation ethics, introductions to marine protected areas and fisheries management.

3) Fitness, Nutrition & Life Extension

• Topics: exercise physiology basics, macronutrient planning, sleep science, aging theories at a high level (no human experimentation), and longevity lifestyle research evaluation.
• Projects: Create and run an evidence-based 8-week fitness & nutrition plan, log biometrics (resting HR, simple strength tests), critically review a peer-reviewed paper on aging interventions.

4) Astronomy, Astrology & Tarot (science + cultural studies)

• Distinguish astronomy as empirical science from astrology and tarot as historical/cultural systems. Teach sky mapping, phases, planetary motion, and telescope use alongside cultural history of astrological charts and tarot symbolism.
• Project: backyard observing log tied to geometric calculations of phases and angular separations; a separate creative project exploring symbolism in tarot and its use in historical worldviews.

5) Fashion & Textiles

• Topics: fiber science, pattern geometry, historical clothing tech (medieval to 1600s), sustainable textiles, dye chemistry (plant-based dyes, safety).
• Project: Draft a pattern using geometric constructions, weave a simple textile, experiment with safe natural dyestuffs (on swatches), and document material properties.

6) Seafood, Antarctica, Maritime Law & Economics

• Seafood science: sustainable sourcing, species identification, post-harvest handling, and economics of seafood trade.
• Antarctica unit: climate science overview, history of exploration, treaties and logistics (focus on non-sensitive content), and ecosystem stewardship.
• Maritime law & economics: basic principles of international maritime law, shipping economics, trade routes, and how law shapes resource access. Simulate a trade negotiation game linking economics and law.

Capstone and portfolio

Students complete one major capstone project integrating at least three domains (math, a pathway, and the medieval→1600s thread or maritime/economic study). Examples:

• Design and model a vertical farm sized for a coastal research station: math for yield estimates, marine science constraints, economics and supplies logistics, a protective textile design for harsh climates.
• Create a historically-informed navigational instrument model (non-hazardous), write a short policy brief on maritime law for resource sharing, and present statistical projections of resource use.

Capstone deliverables: written report, annotated lab notebook, a 12–20 minute presentation or recorded documentary, supporting models/prototypes, and a portfolio website or binder.

Assessment and rubrics

Blend formative assessment (weekly checks, math warmups, lab reflections) with summative assessment (biweekly math tests, pathway project rubrics, capstone evaluation). Rubrics should emphasize:

• Conceptual understanding (40%) — clear explanation of ideas and methods;
• Application & problem solving (30%) — correct solutions, creative methods, and real-world modeling;
• Communication & documentation (20%) — lab notebooks, citations, and presentation quality;
• Safety & ethics (10%) — proper safety procedures and ethical consideration in experiments and community work.

Resources and tools

• AoPS Introduction to Algebra and Introduction to Geometry textbooks and online class resources.
• Science kits: safe chemistry sets, hydroponics starter kits, water-quality test kits, telescope / binoculars for astronomy, sewing/loom kits.
• Books & references: accessible histories on medieval/early modern Europe, practical horticulture manuals, introductory marine biology texts, and economics primers (think-lite market simulations).
• Online: Khan Academy for background, NASA and NOAA education pages for astronomy/marine resources, JSTOR/Google Scholar for supervised article reading, local museum and university outreach programs.

Fieldwork, community, and real-world connections

Arrange periodic field trips: local farms or urban farms, aquaria or coastal tidepool walks, textile museums, maritime museums, community college labs, and court or port visits for maritime law overviews. Build relationships with local experts for guest lessons and portfolio mentorship.

Safety, supervision, and ethics notes

Always require adult supervision for labs. Avoid culturing unknown microbes or performing regulated formulations (like pharmaceuticals). Emphasize informed consent, environmental stewardship, and legal compliance for fieldwork. When discussing Antarctica, maritime law, or fisheries, keep focus on public-domain information and ethical frameworks rather than operational details that could be sensitive.

Sample 4-week micro-unit (example: Hydroponics + Algebra application)

1. Week 1: Intro to hydroponics — set up a Kratky system, measure baseline water parameters, begin AoPS chapter related problem set on ratios and proportional reasoning.
2. Week 2: Nutrient math — calculate concentration dilutions using algebra; run geometry task to optimize shelf layout for vertical racks; record plant health metrics daily.
3. Week 3: Data collection & statistics — plot growth curves, compute means and variance, connect to algebraic growth models; lab reflection on nutrient adjustments.
4. Week 4: Presentation & evaluation — prepare a poster explaining mathematical model used, present findings and next-step recommendations; AoPS challenge blending algebraic modeling and geometry for design constraints.

Final advice for implementation

Keep student choice central: let the student pick primary pathways and capstone focus. Balance rigor in math with creativity and practical application in labs and projects. Maintain careful records: lab notebooks, math journals, and a curated portfolio. Use the post-apocalyptic-inspired tone as flavor: frame problems as design challenges where resources, constraints, history, and law matter — but keep the learning safe, scholarly, and connected to contemporary science and ethics.

If you want, I can convert this into a week-by-week printable calendar, create rubrics for specific projects, or draft a detailed 36-week schedule aligned to AoPS chapter pacing and two chosen pathways.