Lesson Plan with Built-In Differentiation

ROLE: Act as a mathematics teacher skilled at differentiating one lesson for mixed ability.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM] in a single classroom with a wide ability range. I need one lesson on the topic below that runs three parallel tracks at once: Support (struggling), Core (on level), Challenge (advanced). Lesson length is [DURATION].

YOUR TASK:
1. State one shared learning goal that all three tracks work toward.
2. Teach a common core explanation that everyone hears together.
3. Then split into three tracks, each with its own worked examples and practice at the right difficulty.
4. Provide scaffolds for Support, standard work for Core, and extension for Challenge.
5. Give a single common exit check with three difficulty options and answers.

INPUT: Here is the topic: [PASTE THE TOPIC HERE].

HOW TO WORK IT OUT: Solve every example and check internally first. VERIFY each final answer two independent ways and never invent values or formulas. Keep maths legible in clean plain text or simple LaTeX. Make sure Support is clearly easier and Challenge is clearly harder than Core.

OUTPUT FORMAT (exact headings, in order):

OUTPUT FILE FORMAT: present the complete result as a clean, ready-to-use document I can paste straight into Microsoft Word or Google Docs - a clear bold title, section headings, neatly numbered items, comfortable spacing, and simple tables only where helpful (avoid heavy formatting that breaks on paste). It must also print cleanly to PDF on A4 (File > Print > Save as PDF). Keep all mathematics fully readable (fractions as a/b, powers as x^2, roots as sqrt(x)).

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.
1. TITLE BLOCK - topic, class, board, duration, 'Compiled by [YOUR NAME]'.
2. SHARED LEARNING GOAL - one line.
3. COMMON CORE EXPLANATION - the teaching everyone gets, with 1 worked example and two checks.
4. SUPPORT TRACK - scaffolded examples and practice with answers.
5. CORE TRACK - standard examples and practice with answers.
6. CHALLENGE TRACK - extension examples and practice with answers.
7. COMMON EXIT CHECK - 3 tiered questions with an answer key.
8. HOW TO MANAGE ALL THREE AT ONCE - a short logistics note.

RULES: All tracks aim at the same goal. Difficulty must clearly differ across tracks. Every answer verified.

At the very end add a footer line: 'Prepared by [YOUR NAME]', and put 'Compiled by [YOUR NAME]' in the title 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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Questions, feedback or appreciation are always welcome.
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