Fill-in-the-Blank Derivation (Guided Proof Practice)
A derivation or proof with strategic blanks for students to complete, plus the filled key.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Name the formula or proof.
- 2. Add class and board.
- 3. Send the prompt.
- 4. Check the blanks make sense.
- 5. Print the guided derivation.
🔧 If it is not right, reply with this: If too many or too few blanks, reply: "Leave exactly 8 blanks at the key reasoning steps, not the trivial ones, and give the completed version below."
THE PROMPT
ROLE: Act as a mathematics teacher who turns derivations and proofs into guided fill-in-the-blank exercises.
CONTEXT: I teach [CLASS/GRADE] under [BOARD or EXAM e.g. CBSE / ICSE / JEE]. Students memorise derivations without understanding them. I want a derivation of [FORMULA OR THEOREM] written out with key steps blanked, so students must reconstruct the logic.
YOUR TASK:
1. Write the complete, correct derivation of [FORMULA OR THEOREM] as a clean numbered sequence of steps.
2. From that, produce a STUDENT VERSION where exactly 8 important steps or expressions are replaced with numbered blanks like (___1___), (___2___), etc. Blank the meaningful reasoning steps, not trivial copying.
3. Provide a short word-bank or hint list of what kinds of things go in the blanks (optional clue, not the answers).
4. Keep the logic flowing so a thinking student can fill each blank.
INPUT: Here is the exact formula/theorem and the level of rigour I want: [PASTE FORMULA/THEOREM AND NOTES HERE].
HOW TO WORK IT OUT: Construct the full derivation internally first and confirm it is mathematically valid. VERIFY the final result two independent ways (for example, check a special case and check units/limits). Never invent steps or skip logic. Keep all maths fully legible in clean LaTeX or clear plain text.
OUTPUT FORMAT (exact headings, in order):
- TITLE BLOCK: 'Guided Derivation', Formula/Theorem, Class, and 'Compiled by [YOUR NAME]'.
- STUDENT VERSION: the derivation with 8 numbered blanks.
- HINT BANK: short clues (no full answers).
- COMPLETED KEY: the full correct derivation with every blank filled, clearly separated at the end.
RULES: Exactly 8 blanks, all on meaningful steps. Logic must be airtight. Completed key must match the blanks. Clear, simple wording.
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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