📚 Year 8 WJEC Maths: Core Knowledge Overview | Year 8 WJEC 数学：核心知识点梳理
Year 8 mathematics under the WJEC curriculum builds on the foundations laid in Year 7, deepening students’ understanding of number, algebra, geometry, and statistics. This stage introduces more abstract reasoning, multi‑step problem solving, and the ability to communicate mathematical thinking clearly. A firm grasp of these core topics is essential for success in Key Stage 3 and future GCSE studies. In this article we highlight the key knowledge areas, presented in clear, paired English and Chinese paragraphs to support bilingual learners.
WJEC 课程的 Year 8 数学在 Year 7 基础上进一步深化数、代数、几何与统计的理解。该阶段开始引入更抽象的推理、多步骤问题解决以及清晰表达数学思维的能力。牢固掌握这些核心主题对 KS3 和未来 GCSE 学习至关重要。本文梳理了关键知识领域，以英中配对段落呈现，方便双语学习者使用。
1. Place Value and Rounding | 位值与四舍五入
Students must be confident reading, writing, ordering, and comparing numbers up to 10 million, and decimals to three decimal places. Rounding to the nearest 10, 100, 1000, or to a given number of decimal places or significant figures is a core skill, often used in estimation and checking answers.
学生必须能熟练读写、排序和比较大至一千万的整数以及三位小数。将数字四舍五入到最近的 10、100、1000，或指定的小数位数、有效数字，是一项核心技能，常用于估算和检验答案。
For example, 3 847 295 rounded to the nearest million is 4 000 000, and 0.0468 rounded to two significant figures is 0.047.
例如，3 847 295 四舍五入到最近的百万是 4 000 000，0.0468 保留两位有效数字为 0.047。
2. Negative Numbers in Context | 负数的实际应用
Pupils extend their understanding of negative numbers by performing all four operations, including calculations like –5 + (–3) = –8 and 6 – (–2) = 8. They also apply negative numbers to real‑life contexts such as temperature changes, bank balances, and elevation above/below sea level.
学生通过四则运算扩展负数的理解，包括如 –5 + (–3) = –8 和 6 – (–2) = 8 的计算。他们还将负数应用于实际情境，如温度变化、银行余额和海拔高度。
Multiplying and dividing follow the rule: when signs are the same, the result is positive; when signs differ, the result is negative. For instance, (–4) × 6 = –24, and (–12) ÷ (–3) = 4.
乘除法则：同号得正，异号得负。例如 (–4) × 6 = –24，而 (–12) ÷ (–3) = 4。
3. Fractions, Decimals, and Percentages (FDP) | 分数、小数与百分数的互化
Year 8 students must fluently convert between fractions, decimals, and percentages, both with and without a calculator. Common equivalences such as ½ = 0.5 = 50%, ⅓ ≈ 0.333 = 33.3%, and ⅕ = 0.2 = 20% should be memorised.
Year 8 学生必须能够灵活进行分数、小数和百分数的互化，包括使用和不使用计算器。应熟记常见等价关系，如 ½ = 0.5 = 50%，⅓ ≈ 0.333 = 33.3%，⅕ = 0.2 = 20%。
Ordering a mixed list of fractions, decimals, and percentages requires converting to a common format. They also calculate a percentage of a quantity, e.g. 15% of £240 = £36, and express one quantity as a percentage of another.
对混合的分数、小数和百分数列表排序需要转换为统一格式。他们还计算一个数的百分比，如 240 英镑的 15% 为 36 英镑，并会将一个量表达为另一个量的百分比。
4. Ratio and Proportion | 比与比例
Ratio notation is used to compare parts of a whole, such as mixing paint in the ratio 3 : 2. Students simplify ratios, divide a quantity into a given ratio, and solve problems involving unequal sharing. Direct proportion is explored through recipes, scale factors, and real‑life scenarios.
比用于比较整体中的各部分，例如按 3 : 2 混合颜料。学生会化简比、按给定比分配数量，并解决涉及不平均分配的问题。通过食谱、比例因子和现实情境探索正比例关系。
If a recipe for 4 people needs 300 g of flour, then for 6 people, using the multiplier 6/4 = 1.5, the flour required is 300 × 1.5 = 450 g. The unitary method (finding the amount for 1 unit first) is also essential.
若 4 人份食谱需 300 克面粉，则 6 人份使用倍数 6/4 = 1.5，所需面粉为 300 × 1.5 = 450 克。单位法（先求单一数量）也很重要。
5. Algebraic Expressions and Simplification | 代数表达式与化简
Pupils learn to form expressions from worded descriptions, for example ‘n more than 7’ becomes n + 7. They simplify by collecting like terms: 3a + 2b – a + 5b = 2a + 7b. The distributive law is used to expand brackets: 4(x + 3) = 4x + 12, and later to factorise expressions such as 6y – 9 = 3(2y – 3).
学生学会从文字描述建立表达式，如“比 7 多 n”变为 n + 7。他们通过合并同类项化简：3a + 2b – a + 5b = 2a + 7b。运用分配律展开括号：4(x + 3) = 4x + 12，之后也会因式分解如 6y – 9 = 3(2y – 3)。
Substitution of positive and negative integers into formulas is practised regularly, for instance evaluating 3p – 2q when p = –1 and q = 4 gives 3(–1) – 2(4) = –3 – 8 = –11.
经常练习将正负整数代入公式，例如当 p = –1 和 q = 4 时，求 3p – 2q 的值：3(–1) – 2(4) = –3 – 8 = –11。
6. Solving Linear Equations | 解一元一次方程
One‑step and two‑step equations are solved using inverse operations, maintaining balance. For example, 2x + 5 = 17 leads to 2x = 12, then x = 6. Students also solve equations with variables on both sides, such as 5y – 3 = 2y + 9, giving 3y = 12, y = 4.
通过逆运算求解一步和两步方程，并保持等号平衡。例如 2x + 5 = 17 得到 2x = 12，然后 x = 6。学生也解带有两边未知数的方程，如 5y – 3 = 2y + 9，得出 3y = 12，y = 4。
Verification by substituting the solution back into the original equation is a crucial habit. Word problems that require setting up an equation from a context, e.g. ‘I think of a number, double it and subtract 7 to get 15’, are common.
将解代回原方程验证是关键习惯。根据情境建立方程的文字题很常见，如“我想一个数，将它加倍再减去 7 得到 15”。
7. Sequences and the nth Term | 数列与第 n 项
Students recognise linear (arithmetic) sequences and find the term‑to‑term rule. They generate terms of a sequence given the nth term formula, e.g. the nth term 3n + 1 produces the sequence 4, 7, 10, 13, … . They also work backwards to derive the nth term from a given linear sequence: for 5, 9, 13, 17, … the difference is 4, so the nth term is 4n + 1.
学生识别线性（等差）数列并找出逐项规律。他们根据第 n 项公式生成数列各项，如第 n 项为 3n + 1 产生数列 4, 7, 10, 13, …。他们也会逆向从已知线性数列推导第 n 项：对于 5, 9, 13, 17, … 公差为 4，所以第 n 项为 4n + 1。
Patterns presented in diagrams or matches are linked to sequences, leading to simple generalisations. Distinguishing between arithmetic and non‑linear (e.g. square or cube) sequences is also practised.
以图表或火柴棍呈现的模式与数列相联系，从而得出简单的通项。区分等差序列与非线性序列（如平方或立方序列）也在练习之列。
8. Angles and Properties of Shapes | 角度与图形性质
In geometry, Year 8 students apply angle facts: angles at a point sum to 360°, on a straight line sum to 180°, vertically opposite angles are equal, and angles in a triangle sum to 180°. They use these to find missing angles without a protractor.
在几何中，Year 8 学生应用角度知识：一点处角度和为 360°，直线上的和为 180°，对顶角相等，三角形内角和为 180°。他们运用这些知识不用量角器求出未知角。
Properties of quadrilaterals are explored: for example, in a parallelogram opposite angles are equal and consecutive angles sum to 180°. Angles in parallel lines (alternate, corresponding, and co‑interior) are introduced and used to solve multi‑step problems.
探索四边形性质：例如平行四边形对角相等，邻角互补。引入平行线上的角（内错角、同位角、同旁内角）并用于解决多步骤问题。
9. Perimeter, Area, and Volume | 周长、面积与体积
Pupils calculate the perimeter of rectilinear shapes and the circumference of a circle using C = πd or C = 2πr. Area formulas for rectangles, triangles, parallelograms, and trapeziums are applied. For a triangle, A = ½ × base × height; for a trapezium, A = ½(a + b)h.
学生计算直线图形的周长和圆的周长，使用 C = πd 或 C = 2πr。运用矩形、三角形、平行四边形和梯形的面积公式。对于三角形，A = ½ × 底 × 高；对于梯形，A = ½(a + b)h。
Volume of cubes and cuboids is found using V = l × w × h, and they convert between units, e.g. 1 m³ = 1 000 000 cm³. Surface area of 3D shapes is introduced by counting faces and calculating net areas.
用 V = 长 × 宽 × 高 计算立方体和长方体的体积，并在单位间转换，如 1 立方米 = 1 000 000 立方厘米。通过计算各个面的面积引入三维图形的表面积。
10. Coordinates and Transformations | 坐标与变换
Work in all four quadrants is consolidated. Students plot points, find midpoints, and apply transformations: reflection (using mirror lines such as x = 3 or y = –1), translation (described by a column vector, e.g. (3, –2) ), and rotation (about a point, by 90°, 180°, 270°).
巩固在全四象限的工作。学生绘制点、求中点，并应用变换：反射（使用如 x = 3 或 y = –1 的对称线）、平移（用列向量描述，如 (3, –2) ）和旋转（绕一点旋转 90°、180°、270°）。
Scale factor enlargements are introduced, starting from a centre of enlargement. A shape enlarged by a scale factor of 2 about a point will have side lengths doubled, and the area multiplies by the square of the scale factor.
从放大中心出发，引入比例因子放大。一个图形绕某点以比例因子 2 放大，则边长加倍，面积乘以比例因子的平方。
11. Statistics and Data Representation | 统计与数据表示
Students construct and interpret pie charts, using the fact that the total angle is 360°. To represent 30 out of 120 people, the sector angle = (30/120) × 360° = 90°. Bar charts, dual bar charts, and line graphs are used for comparisons and trends.
学生利用总角度为 360° 来绘制和解释饼图。要表示 120 人中的 30 人，扇区角度 = (30/120) × 360° = 90°。使用条形图、双条形图和折线图进行比较和趋势分析。
Averages are extended to include the mode, median, mean, and range. Mean is calculated as sum of values ÷ number of values. The median is the middle value when ordered; if there are two middle values, it is their mean. Outliers are discussed.
平均数扩展到包括众数、中位数、均值和极差。均值 = 总和 ÷ 数据个数。中位数是有序数据中的中间值；若有两个中间值则取它们的均值。讨论异常值。
12. Probability Basics | 概率基础
The probability scale runs from 0 (impossible) to 1 (certain). Probabilities can be written as fractions, decimals, or percentages. For a fair six‑sided dice, P(3) = 1/6. The sum of probabilities of all mutually exclusive outcomes is 1.
概率标度从 0（不可能）到 1（确定）。概率可写成分数、小数或百分数。对于一个公平的六面骰子，P(3) = 1/6。所有互斥结果的概率之和为 1。
Venn diagrams and sample space diagrams help enumerate outcomes for two events, such as tossing a coin and rolling a dice. Students learn that P(not A) = 1 – P(A), and find expected frequencies: if P(rain) = 0.3, in 200 days we expect 0.3 × 200 = 60 rainy days.
维恩图和样本空间图帮助列举两个事件的结果，如抛硬币和掷骰子。学生学习 P(非A) = 1 – P(A)，并求期望频数：若 P(雨) = 0.3，则在 200 天中期望有 0.3 × 200 = 60 天下雨。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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