📚 IGCSE Maths G-7 Teacher's Book Collection | IGCSE 数学 G-7 教师用书合集
This collection brings together the core teacher-support materials for the IGCSE Mathematics course, organised around the G-7 teaching sequence. It is designed to help teachers plan coherent lessons, identify key misconceptions, and prepare students for both Core and Extended assessment objectives. The resources follow a consistent structure: syllabus mapping, concept notes, guided practice, independent tasks, and assessment checks.
本合集汇集了 IGCSE 数学课程的核心教师支持材料，围绕 G-7 教学序列编排。它旨在帮助教师设计连贯的课堂、识别常见误区，并让学生为 Core 与 Extended 评估目标做好准备。所有资源遵循统一结构：大纲对应、概念讲解、引导练习、独立任务和评估检查。
1. Overview of the G-7 Collection | G-7 合集概览
The G-7 Teacher's Book Collection contains a lesson-by-lesson guide, editable worksheets, tiered practice sets, and assessment papers mapped to the Cambridge IGCSE Mathematics syllabus. Each unit opens with learning objectives, prior knowledge checks, and vocabulary support, so teachers can use the materials as a complete scheme of work or as a flexible supplement.
G-7 教师用书合集包含逐课指南、可编辑练习纸、分层练习套题和与 Cambridge IGCSE 数学大纲对应的评估试卷。每个单元都从学习目标、前备知识检查和词汇支持开始，因此教师可以将其作为完整教学方案或灵活补充材料使用。
- Teacher's guide: pacing, keywords, and teaching notes | 教师指南：进度、关键词与教学笔记
- Worksheets: Core and Extended versions | 练习纸：Core 与 Extended 版本
- Assessment pack: quizzes, exit tickets, and mock papers | 评估包：小测、退出票和模拟卷
The design follows three principles: spaced retrieval, worked examples, and low-stakes checking. Each topic reappears at intervals so students consolidate earlier skills while learning new content. Worked examples are annotated with step-by-step reasoning to model exam-quality solutions.
本合集设计遵循三个原则：间隔检索、示范例题和低风险检测。每个主题会间隔重现，使学生在学习新内容的同时巩固已有技能。示范例题配有逐步推理注释，为考试质量的解答提供范本。
2. Syllabus Mapping and Planning | 大纲对应与教学计划
Each G-7 unit is labelled with syllabus reference codes, such as N1, A2, G3 or S4, so teachers can quickly align lessons with assessment objectives. The planning grid distinguishes Core-only topics from Extended-only topics, helping departments build differentiated routes through the course.
每个 G-7 单元都标注了大纲参考编号，例如 N1、A2、G3 或 S4，便于教师将课堂与评估目标快速对齐。计划表区分 Core 专属主题与 Extended 专属主题，帮助学科组构建差异化教学路径。
| Core route | 核心路径 | Extended route | 扩展路径 |
| Number, basic algebra, descriptive statistics | 数、基础代数、描述性统计 | Surds, functions, conditional probability | 根式、函数、条件概率 |
The medium-term plan also suggests review weeks after major units and identifies which homework tasks can be self-marked. Teachers who have mixed-ability classes can use the grid to create two parallel threads without designing new resources from scratch.
中期教学计划还会在主要单元后安排复习周，并标明哪些家庭作业可以自行批改。教授混合能力班级的教师可以利用该计划表创建两条平行教学线，而无需从零设计新资源。
3. Number and Algebra Core Notes | 数与代数核心讲解
Number work in this collection emphasises mental strategies, written methods, and the correct use of the calculator, especially for standard form and bounds. Algebra notes develop from simplifying expressions to solving quadratic equations and interpreting graphs, with clear links between symbolic and graphical representations.
本合集中的数的运算强调心算策略、笔算方法以及正确使用计算器，尤其是在标准形式和上下界方面。代数讲解从化简表达式逐步发展到解二次方程和图解函数，并明确符号表示与图像表示之间的联系。
x = [-b ± √b² - 4ac] / 2a
minded to use the ×10ⁿ notation consistently and to link it with calculator display modes.
二次方程公式配有例题，展示判别式 b² - 4ac 如何决定实数根的个数。对于标准形式，教师用书提醒始终使用 ×10ⁿ 表示法，并与计算器显示模式联系起来。
Sequences receive particular attention in the G-7 notes because they bridge arithmetic and algebraic reasoning. Teachers are encouraged to move from term-to-term rules to position-to-term rules using tables, so that students can derive the nth term rather than memorise it.
数列在 G-7 讲解中受到特别关注，因为它是算术推理与代数推理之间的桥梁。教师用书鼓励教师利用表格从逐项规则过渡到位置-项规则，让学生推导第 n 项，而不是死记硬背。
4. Geometry and Measures Teaching Points | 几何与测量教学要点
Geometry sections in the G-7 collection build spatial reasoning through accurate construction, angle facts, and transformation geometry. Measurement topics link perimeter, area, and volume with unit conversion, while circle theorems and trigonometry are developed in the Extended units.
G-7 合集的几何部分通过精确作图、角的关系和变换几何培养空间推理能力。测量主题将周长、面积和体积与单位换算联系起来，而圆定理和三角学则在 Extended 单元中展开。
A = ½bh and C = 2πr and a² + b² = c²
Teachers are advised to model each formula with labelled diagrams before moving to worded problems. Constructing perpendicular bisectors and angle bisectors is taught with clear step-by-step diagrams, because accurate drawing supports later circle theorem work.
教师应先用带标注的图形示范每个公式，再进入文字应用题。垂直平分线和角平分线的作图通过清晰的分步图示进行教学，因为精确作图有助于后续圆定理的学习。
For Extended classes, the collection introduces sine and cosine rules with the ambiguous case carefully explained. Practise tasks include a mix of diagram-based and real-world problems, such as bearings and angles of elevation.
对于 Extended 班级，合集引入正弦定理和余弦定理，并仔细解释多解情况。练习任务混合了图形题和现实应用题，例如方位角和仰角问题。
5. Statistics and Probability Guidance | 统计与概率指导
Statistics units emphasise selecting the correct average, interpreting charts, and understanding the effect of outliers. Probability is introduced through experimental work and then formalised with sample space diagrams, tree diagrams, and rules for combined events.
统计单元强调选择正确的平均数、解读图表以及理解异常值的影响。概率通过实验活动引入，然后借助样本空间图、树状图以及组合事件的规则加以形式化。
P(A and B) = P(A) × P(B)
For independent events, this rule is practised alongside tree diagrams that show all possible outcomes. Extended students are challenged with conditional probability and Venn diagrams involving three sets, where notation such as A ∩ B and A ∪ B must be read fluently.
对于独立事件，该规则与展示所有可能结果的树状图一起练习。Extended 学生会学习条件概率和涉及三个集合的韦恩图，并需要熟练读出
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