Open-Ended Investigation Task
A rich investigation with hints, expected findings and a reasoning rubric.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Type the topic and class in the brackets.
- 2. Paste the prompt into any AI chat.
- 3. Read the investigation and the hint ladder.
- 4. Hide the expected findings from students.
- 5. Grade using the reasoning rubric.
🔧 If it is not right, reply with this: If it gives away the answer too soon, reply: "Make the hints more gradual; the first hint must not reveal the pattern. Re-verify the expected findings."
THE PROMPT
ROLE: Act as a mathematics teacher who designs open-ended investigations that build reasoning and pattern-spotting.
CONTEXT: I teach [CLASS/GRADE] under [BOARD or EXAM e.g. CBSE / ICSE / State Board]. I want one INVESTIGATION TASK on [TOPIC or STARTING IDEA e.g. number patterns / areas of shapes on a grid / properties of digits]. Students should explore, find a pattern, make a conjecture, and justify it. It should suit [TIME e.g. one or two periods].
YOUR TASK:
1. Pose one intriguing starting question that invites exploration.
2. Give a few warm-up cases students can compute to get going.
3. Provide a ladder of 3 graded hints (gentle to strong) that guide without spoiling.
4. State the expected pattern, conjecture and a short justification (for the teacher only).
5. Suggest 2 extension questions for fast finishers.
6. Provide a rubric (15 marks) that rewards reasoning, not just the final answer.
INPUT: Here is my topic or starting idea: [PASTE TOPIC HERE]. If blank, choose a rich, age-appropriate investigation for the class and board above.
HOW TO WORK IT OUT: Work the investigation through internally to be sure a real pattern exists. VERIFY the pattern with at least three worked cases and a short proof or clear argument; show these checks in the teacher section. Never claim a pattern you have not verified. Keep all maths legible in clean plain text or simple LaTeX.
OUTPUT FORMAT (use these exact headings in this order):
1. INVESTIGATION TITLE
2. THE STARTING QUESTION (student-facing)
3. WARM-UP CASES (for students to try)
4. HINT LADDER (Hint 1 / Hint 2 / Hint 3)
5. EXPECTED FINDINGS - TEACHER ONLY (pattern + conjecture + justification + the three verification cases)
6. EXTENSIONS
7. RUBRIC (15 marks, criteria focused on reasoning)
RULES: Keep the student-facing part free of spoilers. Be precise. Short, plain sentences.
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.
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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