Write a Maths Brief for a Sign-Language Interpreter

ROLE: Act as a teacher preparing a mathematics content brief for a qualified sign-language interpreter.

CONTEXT: Brief an interpreter for [LESSON CONTENT] in [CLASS] using [APPROVED TERMINOLOGY SOURCE].

INPUTS — FILL EVERY PLACEHOLDER:
- [LESSON CONTENT]
- [CLASS]
- [APPROVED TERMINOLOGY SOURCE]
- [DIAGRAMS OR VISUALS]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [NCERT_DIKSHA] Source-bound NCERT bookcodes: femh1 Class 6, gemh1 Class 7, hemh1 Class 8, iemh1 Class 9, jemh1 Class 10, lemh1/lemh2 Class 12 Parts I/II. Use https://ncert.nic.in/textbook.php?{BOOKCODE}={CHAPTER}-{TOTAL_CHAPTERS} only after the teacher confirms book, chapter and total. Never invent a DIKSHA dial code; relay only a code the teacher pasted.
- [CODECOGS] Whitelist: https://latex.codecogs.com/png.image?{PERCENT_ENCODED_LATEX}. CodeCogs renders one equation image, not a document. Start permanent classroom PNGs with the encoded form of \dpi{150}, keep the URL short, and tell the teacher to download rather than hotlink it.

DO THIS:
1. Lock placeholders, formulas, numbering, marks, units, and lesson sequence.
2. List each mathematical concept with a precise definition and example.
3. Identify spoken terms that are ambiguous in ordinary language.
4. Describe each diagram spatially without replacing the original visual.
5. Create questions for the qualified interpreter instead of inventing signs.
6. Provide optional equation-only CodeCogs references for exact notation.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Brief the exact distinction between angle and angle measure using theta.
Expected result or check target: The interpreter receives definitions, notation, context, and decision questions without fabricated signs.
check this yourself
CHECK → https://latex.codecogs.com/png.image?%5Ctheta%3D60%5E%5Ccirc
(paste-fallback: \theta=60^\circ)
Encoding note: Backslashes, equals, and caret decode to the exact angle notation fallback.

OUTPUT FORMAT:
1. Lesson Sequence — ordered concepts and transitions
2. Notation Lock — exact formulas and symbols
3. Interpreter Brief — definitions, context, and ambiguous terms
4. Visual Descriptions — diagrams and spatial relations
5. Decision Queue — terminology questions for the interpreter

QUALITY AND TOOL GUARDRAILS:
- Preserve every placeholder, notation token, number, mark, and sequence label exactly.
- Do not invent, prescribe, or claim authority for any sign-language sign.
- Use the qualified interpreter and [APPROVED TERMINOLOGY SOURCE] for final language decisions.
- CodeCogs is equation-only and cannot represent signing, prose, or a whole lesson.
- For multilingual Overleaf use free login, XeLaTeX, fontspec, and a font fallback without promises.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.