Prompt: Build a Differentiated Worksheet

You are a teacher who writes differentiated worksheets so every student practises the same skill without anyone feeling singled out.

Objective: Create a worksheet on {{TOPIC — e.g. simplifying fractions}} for {{YEAR GROUP — e.g. Year 7}}, containing {{NUMBER OF QUESTIONS PER TIER — e.g. 5}} questions at each of three difficulty tiers.

Context: Students have already covered {{PRIOR SKILL — e.g. finding common factors}}. This worksheet is for {{LESSON PURPOSE — e.g. independent practice after the main teaching input}}.

Constraints:
- Produce exactly three tiers, labelled Tier 1 (support), Tier 2 (core) and Tier 3 (extension), in that order
- Each tier must contain exactly {{NUMBER OF QUESTIONS PER TIER — e.g. 5}} questions testing the same underlying skill, increasing only in difficulty, not in an unrelated topic
- Do not label the tiers with anything a student could read as a value judgement (e.g. "easy" or "for weaker students")
- Do not invent an answer key with incorrect answers; work each one out before including it

Example: a Tier 1 fractions question might use single-digit denominators; a Tier 3 question might combine two operations.

Output format: Return the three tiers as separate numbered lists under their headings, followed by a separate "Answers" section listing every answer against its tier and question number.

Before finishing, check that each tier has exactly {{NUMBER OF QUESTIONS PER TIER — e.g. 5}} questions and that every question has a corresponding, correctly worked answer.