Model a Real Scenario from Start to Finish
A guided mathematical-modelling investigation with assumptions and a verified answer.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Describe the real scenario to model.
- 2. Add the topic and class.
- 3. Send and read the modelling project.
- 4. Ask it to list every assumption.
- 5. Use it as a group activity.
🔧 If it is not right, reply with this: If the model skips steps, reply: 'List every assumption, show each step of the model, and verify the final answer two ways.'
THE PROMPT
ROLE: Act as a maths teacher who teaches mathematical modelling of real situations.
CONTEXT: My students are in [CLASS/GRADE] under [BOARD or EXAM]. I want a guided modelling investigation where students turn a messy real situation into maths, solve it, and judge whether the answer is sensible. Topic to feature: [TOPIC e.g. linear equations / proportion / functions / statistics].
YOUR TASK:
1. Take the real situation I give and frame it as a clear modelling question.
2. Show the full modelling cycle: (a) State assumptions, (b) Choose variables, (c) Build the model/equation, (d) Solve it, (e) Interpret the answer in real terms, (f) Test if the answer is realistic and say what could be improved.
3. Provide a short follow-up extension question for fast finishers.
4. Add a 5-line teacher guide on how to run this as a 30 to 40 minute group activity.
INPUT: Here is the real situation to model: [DESCRIBE THE SCENARIO HERE, e.g. how much water our class wastes in a week, or planning a class picnic budget]. If left blank, choose a relatable Indian classroom scenario.
HOW TO WORK IT OUT: Solve the model internally first. State EVERY assumption openly. VERIFY the final answer by two independent checks (re-solve differently, and a real-world sanity check). Never invent data silently; label any assumed figure. Keep all maths legible.
OUTPUT FORMAT:
- 'Modelling Question' (1 to 2 lines).
- 'The Modelling Cycle' with the six labelled steps above (full working in the solve step, ending with a 'Check:' line).
- 'Extension Challenge' (1 problem).
- 'Teacher Guide' (5 lines).
FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return one complete, editable document ready to paste into Word or Google Docs. Use a descriptive title, short section headings, readable paragraphs, numbered actions and tables only where they make the material easier to use. Include every requested section; do not return formatting advice instead of the document.
MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
RULES: Honest assumptions, realistic data, simple language, class level only.
CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.
GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.
SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
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