📚 IGCSE Maths Teacher's Book 1000: Core Skills, Diagnostic Questions and Classroom Strategies | IGCSE 数学教师用书 1000：核心技能、诊断性题目与课堂策略
This teacher's book supports IGCSE Mathematics teachers who use a bank of 1000 diagnostic questions, drill exercises and exam-style items. It maps the questions to the Cambridge IGCSE 0580 syllabus and provides ready-to-use teaching notes for core and extended classes.
本书支持使用 1000 道诊断性题目、巩固练习与考试风格试题的 IGCSE 数学教师。题目对应剑桥 IGCSE 0580 大纲，并为核心和拓展课程提供即用型教学建议。
The question bank is designed to be flexible: a teacher can project a single starter question, print a set of 20 fluency drills, or build a full mixed-topic test in minutes. Each item is labelled by topic, tier, command word and diagnostic focus.
题库设计灵活：教师可以投影一道入门题，打印 20 道熟练度训练题，或在几分钟内组成一套混合主题测验。每道题均标注主题、层级、指令词和诊断重点。
1. Aims of Teacher's Book 1000 | 教师用书 1000 的目标
The main aim is to turn a large question bank into formative assessment, not just test practice. Teachers can identify gaps early, group learners by skill need, and adjust lesson pacing without writing new worksheets.
主要目标是将大型题库转化为形成性评价，而不仅是测试练习。教师可以尽早发现差距，按技能需求分组学生，并在无需重新编写讲义的情况下调整课堂节奏。
Each set of questions is tagged by topic, command word and difficulty. This allows teachers to build a short starter, a main-task fluency drill or a mixed revision quiz within minutes.
每组题目标注了主题、指令词和难度。这样教师可以在几分钟内组合出简短的入门题、主任务熟练度训练或混合复习测验。
The book also supports differentiation: support questions include scaffolding and visual hints, core questions target the standard syllabus, and extension questions require multi-step reasoning or unfamiliar contexts.
本书还支持分层教学：支持题包含支架和视觉提示，核心题针对标准大纲，拓展题要求多步骤推理或在陌生情境中应用。
- Use 10-minute starters to reveal misconceptions before teaching.
- Build retrieval practice by repeating question types after 1 week, 3 weeks and 6 weeks.
- Match question difficulty to observed student performance.
教师可在教学前使用 10 分钟入门题揭示误区；在 1 周、3 周和 6 周后重复同类题型以强化提取练习；根据观察到的学生表现匹配题目难度。
2. Curriculum Coverage and Skill Audit | 课程范围与技能清单
The 1000 questions cover the four IGCSE content areas: Number, Algebra, Shape and Space, and Statistics and Probability. Core-only content is separated from extended-only content so teachers can select the right tier.
1000 道题覆盖 IGCSE 四大内容领域：数、代数、图形与空间、统计与概率。核心内容与拓展内容分开标注，方便教师选择合适层级。
| Content area | Question count | Typical topics |
|---|---|---|
| Number | 280 | Fractions, ratios, percentages, standard form, bounds |
| Algebra | 320 | Linear equations, sequences, functions, graphs, quadratics |
| Shape and Space | 240 | Angles, trigonometry, vectors, transformations, mensuration |
| Statistics and Probability | 160 | Averages, cumulative frequency, probability trees, sets |
This audit helps departments check coverage and avoid over-testing the same learning objective while under-practising less familiar topics. It can also be used to create a paperless scheme of work for the year.
该清单有助于科组检查覆盖情况，避免过度测试同一学习目标而忽略较不熟悉主题的练习。它还可用于制定全年的无纸化教学计划。
3. Diagnostic Question Design | 诊断性题目设计
Each diagnostic question is written with three plausible distractors based on common IGCSE errors. For example, when expanding 3(x + 4), students often write 3x + 4, 7x or 3x + 12 incorrectly under time pressure.
每道诊断题都基于 IGCSE 常见错误设计了三个可能的干扰项。例如，在展开 3(x + 4) 时，学生在时间压力下常错写为 3x + 4、7x 或错误地得到 3x + 12。
Teachers are advised to use these distractors to promote discussion: ask learners to explain why each incorrect answer is attractive and what rule has been misapplied.
建议教师利用这些干扰项开展讨论：让学生解释每个错误答案为何具有迷惑性，以及误用了哪条规则。
Good distractors are never random. They are generated from actual student responses:
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