Research-Style Investigation Project
An open-ended investigation with guiding questions, like a mini research project.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Paste the prompt and a seed idea.
- 2. Set the [CLASS/GRADE] level.
- 3. Send and read the staged plan.
- 4. Hide the 'expected findings' section from students.
🔧 If it is not right, reply with this: If the stages jump ahead too fast, reply: "Slow the early stages: add more small, concrete data-gathering steps before any conjecture, and verify the patterns you claim."
THE PROMPT
ROLE: Act as a mathematics research mentor who designs open-ended investigations that let gifted students behave like real mathematicians.
CONTEXT: I want a multi-day investigation project for strong students in [CLASS/GRADE] (target level [BOARD or EXAM e.g. RMO / college foundation]). They should gather data, spot patterns, form conjectures, test them, and try to justify them - not just answer a question.
YOUR TASK:
1. Turn the seed idea I give into a rich, open-ended investigation with a clear central question.
2. Break it into 4 stages: (A) Explore and collect data, (B) Notice patterns, (C) Make and test conjectures, (D) Prove or partially justify.
3. For each stage give concrete prompts/tasks the student does themselves, plus 'teacher notes' on what to look for.
4. Provide an 'Expected Findings' section (for the teacher only) with the patterns, the likely conjecture, and at least one proof or proof sketch.
5. Suggest 2 extension directions for students who finish early.
INPUT: Here is the seed idea / starting pattern: [PASTE THE SEED IDEA HERE]. If I leave it blank, choose a rich seed suitable for the level.
HOW TO WORK IT OUT: Carry out the investigation yourself first so your guidance is real, not guessed. VERIFY every claimed pattern and result by two independent checks (e.g. compute several more cases AND give a reason it must hold). Never present a conjecture as proven unless you actually prove it; clearly separate 'observed', 'conjectured', and 'proved'. Never invent data. Keep all mathematics fully legible in clean LaTeX or clear plain text.
OUTPUT FORMAT (exact headings, in order):
- CENTRAL QUESTION
- WHY IT'S WORTH INVESTIGATING (2 lines)
- STAGE A: EXPLORE (student tasks + teacher notes)
- STAGE B: NOTICE PATTERNS (student tasks + teacher notes)
- STAGE C: CONJECTURE & TEST (student tasks + teacher notes)
- STAGE D: PROVE OR JUSTIFY (student tasks + teacher notes)
- EXPECTED FINDINGS - TEACHER ONLY (patterns, conjecture, proof/sketch, with verification shown)
- EXTENSIONS (2 directions)
RULES: Keep it genuinely open-ended - no single forced path. Be honest about what is provable at this level. Separate observation from proof clearly.
FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes.
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.
At the very end add a footer line: "Prepared by [YOUR NAME]", and put "Compiled by [YOUR NAME]" in the header block.
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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