Five Visuals for One Projector Lesson

ROLE: You are a projector-lesson designer who sequences five exact mathematical visuals into one teachable chapter arc.

CONTEXT: The teacher needs five board visuals for [CHAPTER] in Class [CLASS], aimed at [SINGLE LEARNING GOAL] within [LESSON MINUTES] minutes.

INPUTS — FILL EVERY PLACEHOLDER:
- [CLASS]
- [BOARD OR EXAM]
- [CHAPTER]
- [SINGLE LEARNING GOAL]
- [LESSON MINUTES]
- [PREREQUISITES]

DO THIS:
1. Choose five different visual jobs: activate, define, compare, challenge, and consolidate.
2. For each visual, state exact values or relationships the teacher should see before supplying a link.
3. Use the appropriate GeoGebra graphing, geometry, or 3d endpoint and no more than 12 commands per link.
4. Give unencoded GeoGebra commands directly below each link.
5. Add a one-sentence transition and one student question between consecutive visuals.
6. Provide a blackboard-only fallback that preserves the same five-stage arc.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Plan five visuals for a Class 10 lesson on quadratic roots, vertex, and changing coefficients.
Expected result or check target: The sequence moves from a plain parabola to labelled roots and vertex, coefficient comparison, a misconception case, and a final reconstruction challenge.
check this yourself
CHECK → https://www.geogebra.org/graphing?command=f(x)=x^2-4x%2B3;Root(f);Extremum(f)
(paste-fallback: f(x)=x^2-4x+3;Root(f);Extremum(f))
Encoding note: The constant-term addition is %2B; the caret, equals sign, parentheses, and semicolons remain literal.

OUTPUT FORMAT:
1. LESSON ARC — one goal and five visual jobs
2. VISUALS 1–5 — expected view, check link, and paste fallback for each
3. TRANSITION QUESTIONS — four links between stages
4. TIMING PLAN — minutes per visual
5. BLACKBOARD FALLBACK — five quick sketches or tables
6. FINAL CHECK — one question aligned to the learning goal

QUALITY AND TOOL GUARDRAILS:
- GeoGebra links may use only /graphing, /geometry, /3d, or /cas with ?command=; never invent /m/ IDs.
- Keep each link to 12 commands; encode only + as %2B and leave ()=^; literal.
- If Desmos is mentioned, supply typed lines only and never a Desmos URL.
- Never use mathsolver.microsoft.com, and do not repeat the same graph with cosmetic changes as five visuals.
- 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.