📚 Year 7 CAIE Maths: Intensive Winter Break Revision Plan | Year 7 CAIE 数学：寒假强化复习计划
Winter break is the perfect time to consolidate Year 7 maths knowledge and fill in any gaps before the next term. A structured revision plan can transform a few weeks of holiday into a powerful learning boost. Use this guide to organise your time, revisit key topics, and practise smart.
寒假是巩固Year 7数学知识、弥补漏洞的理想时机。一份有条理的复习计划能把几周假期变成一次强势的学习提升。利用本指南来安排时间、重温重点主题并智慧地练习。
1. Setting Your Winter Study Timetable | 制定你的寒假学习时间表
Map out all the days of your winter break on a calendar. Block out time for family, rest and hobbies first, then assign 30-minute revision slots for maths. 在日历上标出寒假的所有日子。先留出家庭、休息和爱好的时间，然后安排每次30分钟的数学复习时段。
Aim for five to six sessions per week rather than long marathons. Consistency beats cramming, and short bursts keep your brain fresh. 每周安排五到六次学习，而不是长时间突击。持续学习优于填鸭式，短时冲刺能让大脑保持清醒。
Rotate topics each day so you revisit number work, algebra, geometry and data regularly. This spaced practice helps long-term memory. 每天轮换主题，定期重温数的运算、代数、几何和数据。这种分散练习有助于长期记忆。
2. Reviewing Whole Numbers and Place Value | 复习整数与位值
Begin with place value up to billions and down to thousandths. Write numbers in expanded form, identifying the value of each digit. 从位值开始，上至十亿、下至千分位。把数字写成展开式，辨别每位数字的数值。
Recap formal written methods for addition, subtraction, multiplication and division. Practise column addition with carrying and long multiplication with two-digit numbers. 重温加、减、乘、除的正式竖式方法。练习进位加法和两位数的长乘法。
Work on mental arithmetic: times tables up to 12 × 12, doubles and halves, and partitioning strategies. Speed and accuracy here make harder topics much easier. 练习心算：12×12以内的乘法表、加倍与折半和拆分策略。这里的速度与准确度会让更难的主题变得轻松许多。
3. Strengthening Fractions and Decimals | 强化分数与小数
Convert fluently between mixed numbers and improper fractions. Use diagrams or number lines to visualise equivalents. 熟练转换带分数和假分数。用图形或数轴直观显示等值关系。
Add and subtract fractions with different denominators by finding the lowest common multiple. For 1/4 + 1/6, the LCM of 4 and 6 is 12, giving 3/12 + 2/12 = 5/12. 通过找出最小公倍数来加减异分母分数。例如 1/4 + 1/6，4和6的最小公倍数是12，得到 3/12 + 2/12 = 5/12。
Multiply fractions simply as numerator × numerator and denominator × denominator; for division, flip the second fraction and multiply. Simplify answers whenever possible. 分数相乘，分子乘分子、分母乘分母；分数相除则将第二个分数颠倒再相乘。答案务必化简。
Decimals: add zeros when aligning columns, multiply by ignoring the point then putting it back based on total decimal places, and relate fractions to decimals (e.g. 3/8 = 0.375). 小数：列竖式时对齐小数点补零，乘法先忽略小数点计算再根据小数位数点回小数点，并将分数与小数关联（如 3/8 = 0.375）。
4. Building Percentage Skills | 构建百分比技能
Understand that ‘per cent’ means ‘out of 100’. Convert between fractions, decimals and percentages confidently. 理解百分数表示“每一百中的”，在分数、小数和百分数之间自信地转换。
Find percentages of amounts: 10% by dividing by 10, 5% by halving 10%, 1% by dividing by 100, then build any percentage using these building blocks. 求某个数的百分之几：10%即除以10，5%是10%的一半，1%即除以100，然后用这些基本单位组合出任意百分比。
Apply percentage increase and decrease in simple contexts, such as ‘a £40 jacket with a 15% discount costs £40 − £6 = £34’. 在简单情境中应用百分比增减，例如“一件40英镑的夹克打15%折扣，价格为 40 − 6 = 34 英镑”。
5. Exploring Algebra Foundations | 探索代数基础
Use letters to represent unknown numbers. Write expressions like 2n + 3 or 5(y − 2) from word descriptions. 用字母表示未知数。根据文字描述写出表达式，如 2n + 3 或 5(y − 2)。
Substitute positive and negative values into simple formulae. For example, if y = 4, evaluate 3y + 7 = 3×4 + 7 = 19. 将正数和负数代入简单公式。例如，若 y = 4，计算 3y + 7 = 3×4 + 7 = 19。
Simplify expressions by collecting like terms: 3a + 2b + 5a − b = 8a + b. Always keep the sign with its term. 通过合并同类项化简表达式：3a + 2b + 5a − b = 8a + b。始终让符号紧跟该项。
Solve one-step equations using inverse operations: if x + 6 = 13, then x = 7. Check your answer by substituting back into the original equation. 用逆运算解一步方程：若 x + 6 = 13，则 x = 7。将答案代回原方程检验。
6. Geometry: Lines, Angles and Shapes | 几何：线、角与形状
Identify and draw acute, obtuse, right and reflex angles. Measure angles with a protractor to the nearest degree. 识别并画出锐角、钝角、直角和优角。使用量角器测量角度，精确到度。
Know angle facts: angles on a straight line sum to 180°, angles around a point sum to 360°, and vertically opposite angles are equal. 掌握角度事实：平角之和为180°，绕点一周的角之和为360°，对顶角相等。
Classify triangles by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Recognise properties of quadrilaterals including squares, rectangles, parallelograms, rhombuses and trapeziums. 按边（等边、等腰、不等边）和角（锐角、直角、钝角）对三角形分类。识别四边形包括正方形、矩形、平行四边形、菱形和梯形的性质。
Calculate missing angles in triangles (sum to 180°) and in quadrilaterals (sum to 360°). 计算三角形（内角和180°）和四边形（内角和360°）中的未知角度。
7. Mastering Measurement and Units | 掌握度量衡与单位
Convert between metric units: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm. For mass, 1 kg = 1000 g; for capacity, 1 L = 1000 mL. 进行公制单位换算：1 千米 = 1000 米，1 米 = 100 厘米，1 厘米 = 10 毫米。质量单位：1 千克 = 1000 克；容量单位：1 升 = 1000 毫升。
Find perimeters of rectilinear shapes and compound figures by adding all side lengths. Remember to convert to the same unit first. 通过加总所有边长计算直线图形和组合图形的周长。记得先统一单位。
Calculate area of rectangles and squares using length × width; find area of right-angled triangles as half the base × height. Use appropriate units such as cm² or m². 用长 × 宽计算长方形和正方形的面积；直角三角形的面积为½ × 底 × 高。使用合适的单位，如厘米² 或 米²。
Work with time intervals: add and subtract hours and minutes, and interpret 24‑hour clock times. 进行时间间隔运算：加减小时和分钟，并识别24小时制时间。
8. Developing Data Handling Skills | 培养数据处理技能
Collect data using tally charts and frequency tables. Organise raw data into groups when dealing with large sets. 使用划记表和频率表收集数据。当数据量较大时，将原始数据分组整理。
Draw and interpret bar charts, pictograms and line graphs. Always label axes, give a title and use a consistent scale. 绘制和解读条形图、象形图和折线图。务必标注坐标轴、添加标题并使用统一刻度。
Calculate the mean (sum of values divided by number of values), and find the mode and median for small data sets. 计算平均数（数值之和除以数值个数），并求小数据集的众数和中位数。
Use pie charts to show proportions. Practise reading and drawing simple pie charts with given sectors. 用饼图表示比例。练习阅读和绘制给定扇区的简单饼图。
9. Tackling Word Problems | 攻克应用题
Read each problem twice. Underline key numbers and words, and decide what mathematical operation is needed. 每道题读两遍。圈出关键数字和词语，决定需要哪种数学运算。
Translate word problems into equations or diagrams. For instance, ‘Tom has three times as many stickers as Liam, and they have 48 in total’ becomes L + 3L = 48. 将文字题转化为方程或图表。例如，“Tom的贴纸是Liam的三倍，他们共有48张”转化为 L + 3L = 48。
Check if your answer makes sense in the real context. A length cannot be negative, and a discount price should be lower than the original. 检查答案在实际情况中是否合理。长度不能为负数，折扣价应低于原价。
10. Targeted Practice Strategies | 针对性练习策略
Identify weak areas by reviewing marked tests and classwork. Make a list of topics where you lost marks. 通过回顾批改过的试卷和课堂作业找出薄弱环节。列出丢分的主题清单。
Use a diagnostic quiz for each weak topic: try 5 questions without help, then mark and note mistakes. Create a ‘mistake diary’ to avoid repeating errors. 针对每个薄弱主题进行一次诊断小测：独立完成5道题，然后批改并记录错误。建立“错题日记”避免重复犯错。
Practise ‘interleaving’ – mix different question types in one session rather than blocking the same type. This builds flexible thinking. 练习“交错学习”——在同一时段混合不同题型，而不是集中练同一类型。这能培养灵活的思维。
Gradually increase difficulty from basic fluency to reasoning and problem‑solving questions. Celebrate small improvements to build confidence. 逐步增加难度，从基础熟练题过渡到推理和应用题。庆祝小进步以建立信心。
11. Using Digital Tools and Resources | 运用数字工具与资源
Explore interactive websites such as Mathigon, Transum or BBC Bitesize for animated explanations and games. Always choose activities linked to the CAIE Year 7 framework. 探索互动网站如Mathigon、Transum或BBC Bitesize，获取动画讲解和游戏。优先选择与CAIE Year 7框架相关的活动。
Watch short tutorial videos on challenging topics, pause and try examples yourself. Note down any new methods in your revision notebook. 在遇到挑战性主题时观看简短的教学视频，暂停并自己尝试例题。把新方法记在复习笔记本上。
Use spreadsheet software to practise making tables and simple charts, reinforcing data handling skills. 使用电子表格软件练习制作表格和简单图表，巩固数据处理技能。
Set a timer for online practice: 20 minutes of focused digital work followed by a 5‑minute screen break protects your eyes. 在线练习时设定计时器：20分钟专注数字化学习，然后休息5分钟保护视力。
12. Staying Motivated and Balanced | 保持动力与平衡
Set small, achievable goals for each week — like ‘complete three geometry past paper questions without hints’. Tick them off on a progress chart. 每周设定小而可实现的目标——如“不看提示完成三道几何真题”。在进度表上打勾完成。
Mix study with physical activity. A brisk walk or a short exercise session between revision blocks improves concentration and mood. 学习与身体活动相结合。在复习间隙快步走或做短暂运动能提升专注力和情绪。
Explain a new concept to a family member or even a toy — teaching is one of the best ways to check your own understanding. 向家人或者甚至一个玩具解释新概念——教别人是检验自己理解的最好方法之一。
Remember that a restful holiday includes time to recharge. Balance revision with sleep, healthy meals and hobbies. A refreshed brain learns faster. 记住一个放松的假期需要充电时间。复习与睡眠、健康饮食和爱好相平衡。焕然一新的大脑学得更快。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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