📚 Year 7 WJEC Mathematics: Essential Concepts Review | Year 7 WJEC 数学：核心知识点梳理
This article summarises the most important knowledge points you will meet in Year 7 WJEC Mathematics. From place value to averages, each section builds the foundation for success in Key Stage 3 and beyond. Read through the English and Chinese explanations side by side to strengthen both your mathematical understanding and your bilingual skills.
本文梳理了 Year 7 WJEC 数学课程中最核心的知识点。从位值到平均数，每一部分都为你在第三学段及更高年级的学习打下坚实基础。通过中英双语的对照讲解，你既能牢固掌握数学概念，也能提升双语能力。
1. Place Value and Number Systems | 位值与数系
In Year 7, you must feel confident reading, writing and ordering whole numbers up to at least 10 million. Each digit has a place value – for example, in 5 382 714, the digit 5 stands for five million, 3 stands for three hundred thousand, and so on. Understanding place value makes it easy to compare numbers or to multiply and divide by 10, 100 and 1000 mentally.
在 Year 7，你需要熟练读写并排序至少到千万的整数。每个数字都有位值——例如在 5 382 714 中，数字 5 代表五百万，3 代表三十万，以此类推。理解位值能帮助你轻松比较数字大小，以及心算乘除以 10、100 和 1000。
You also extend this idea to decimals. The first column after the decimal point is tenths (¹⁄₁₀), then hundredths (¹⁄₁₀₀), then thousandths (¹⁄₁₀₀₀). Place value grids can help you avoid common mistakes when lining up digits for addition or subtraction.
你还要把位值概念扩展到小数。小数点后第一位是十分位 (¹⁄₁₀)，接着是百分位 (¹⁄₁₀₀)，再是千分位 (¹⁄₁₀₀₀)。利用位值表可以帮助你在列竖式加减时对齐数位，避免常见错误。
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths |
| 3 | 4 | 5 | 2 | 6 | 9 | 0 | . | 7 | 4 |
2. Addition and Subtraction | 加法与减法
Building on primary skills, Year 7 pushes you to add and subtract large numbers, decimals and negative integers. Always align digits by place value, especially when working with decimals. For example, 12.6 + 3.84 should be set out like this:
在小学技能的基础上，Year 7 要求你能够对大数、小数和负数进行加减运算。务必按位值对齐数字，处理小数时尤其如此。例如，12.6 + 3.84 应这样列竖式：
12.60 + 3.84 = 16.44
Negative numbers often cause difficulty. Remember that adding a negative is the same as subtracting: 5 + (−3) = 5 − 3 = 2, and subtracting a negative is like adding: 5 − (−3) = 5 + 3 = 8. Use a number line to visualise these moves.
负数常常让人困惑。记住，加上一个负数等于减去其绝对值：5 + (−3) = 5 − 3 = 2；而减去一个负数等于加上其绝对值：5 − (−3) = 5 + 3 = 8。借助数轴可以直观地理解这些移动。
3. Multiplication and Division | 乘法与除法
In Year 7 you must be fluent with multiplication tables up to 12 × 12 and be able to use formal written methods (column multiplication and short/long division) for larger numbers. Multiplication by 10, 100, 1000 is also practised regularly – simply shift digits to the left, adding zeros as placeholders.
Year 7 要求你熟练掌握 12 × 12 以内的乘法表，并能用规范的竖式方法（列乘法竖式和短除法/长除法）进行大数计算。乘 10、100、1000 的练习也十分频繁——只需将数字向左移动，用零占位即可。
When multiplying decimals, ignore the decimal points at first, multiply as if they were whole numbers, then put the decimal point back so that the answer has the same number of decimal places as the factors combined. For division, you may meet remainders expressed as fractions or decimals.
进行小数乘法时，先忽略小数点，按整数相乘，然后根据两个因数的小数位数总和点回小数点。在除法中，你可能会遇到余数用分数或小数表示的情况。
1.2 × 0.3 → 12 × 3 = 36 → put decimal to give 0.36
4. Fractions, Decimals and Percentages | 分数、小数和百分比
You need to convert freely between fractions, decimals and percentages. For example, ½ = 0.5 = 50%. Equivalent fractions and simplifying are key: ³⁄₆ = ¹⁄₂. Add and subtract fractions by finding a common denominator, and multiply fractions by multiplying numerators and denominators. Divide a fraction by a whole number by multiplying the denominator.
你需要能够在分数、小数和百分比之间自由转换。例如，½ = 0.5 = 50%。等值分数与约分是关键：³⁄₆ = ¹⁄₂。进行分数加减时要先通分，找到公分母；分数相乘则分子乘分子、分母乘分母。分数除以整数可以通过乘以分母来实现。
Percentage means ‘out of 100’. To find a percentage of a quantity, you can find 1% first, then multiply. Common percentages like 10%, 25%, 50% and 75% should be known automatically. You also learn to increase or decrease a quantity by a given percentage, linking to real-life contexts such as discounts.
百分比的意思是“每百份中的几份”。求一个数的百分之几，可以先求 1% 再相乘。像 10%、25%、50% 和 75% 这样的常见百分比应当脱口而出。你还会学习按给定百分比增加或减少一个量，并与折扣等实际情境联系起来。
5. Introduction to Algebra | 代数入门
Algebra begins by using letters to stand for unknown numbers or variables. You will write simple expressions like 3a + 2 or 5 − 2b. Understand that 3a means 3 × a, and a² means a × a. Collecting like terms is a fundamental skill: 3y + 5y = 8y, but 3y + 5x cannot be simplified further.
代数从用字母表示未知数或变量开始。你会写出像 3a + 2 或 5 − 2b 这样的简单表达式。要明白 3a 表示 3 × a，a² 表示 a × a。合并同类项是一项基本技能：3y + 5y = 8y，但 3y + 5x 不能再化简。
Simple one-step and two-step equations are introduced. For example, to solve x + 4 = 10, subtract 4 from both sides to get x = 6. To solve 2x = 14, divide both sides by 2. Always keep the equation balanced by doing the same thing to both sides.
你会接触到简单的一步和两步方程。例如，解 x + 4 = 10，两边同时减去 4，得 x = 6。解 2x = 14，两边同时除以 2。务必通过等号两边做相同运算来保持方程平衡。
Sequences are another part of algebra in Year 7. You learn to spot term-to-term rules for linear sequences (e.g. add 3 each time) and to find the next terms or missing terms.
数列是 Year 7 代数的另一部分。你需要学会找出线性数列中的逐项规律（例如每次加 3），并根据规律找出后续项或缺失项。
6. Coordinates and Graphs | 坐标与图表
You work with coordinates in all four quadrants. The x-coordinate comes first, then the y: (x, y). Plots points on a Cartesian grid and learn that the origin is (0, 0). You will also interpret and draw simple line graphs and, when data is linear, recognise the relationship between two variables.
你将在四个象限中处理坐标。先写 x 坐标，再写 y 坐标：(x, y)。在方格纸上描点，并知道原点为 (0, 0)。你还会分析和绘制简单的折线图，当数据呈线性时，能识别两个变量之间的关系。
You may also convert between coordinates and real-life contexts, like reading a map or plotting a journey on a distance-time graph. Linking tables of values to graphs helps build the foundation for later work on straight lines.
你还可能将坐标应用到实际情境中，如阅读地图或在距离－时间图上绘制行程。将数值表与图形联系起来，能为以后学习直线图像打下基础。
7. Angles and Lines | 角与线
Year 7 revises angle vocabulary: acute, obtuse, reflex and right angles. You will use a protractor to measure angles to the nearest degree and draw angles accurately. Key facts include: angles on a straight line add up to 180°, angles around a point add up to 360°, and vertically opposite angles are equal.
Year 7 会复习角的基本术语：锐角、钝角、优角和直角。你需要用量角器测量角度，精确到度，并能准确地画出给定角度。关键事实包括：平角（直线上的角）之和为 180°，一点周围的角之和为 360°，对顶角相等。
Angles in a triangle always sum to 180°. You will also meet alternate angles and corresponding angles on parallel lines, using them to find missing angles without needing to measure every time.
三角形的内角和始终为 180°。你还会学习平行线中的内错角和同位角，并利用这些性质求未知角，而无需每次都测量。
a + b + c = 180° (triangle) a + b = 180° (straight line)
8. Perimeter and Area | 周长与面积
Perimeter is the distance around the outside of a shape; simply add the lengths of all sides. For a rectangle, perimeter = 2(l + w). Area measures the space inside a shape, in square units. For a rectangle or square, area = length × width. Remember to include the correct units (e.g. cm, cm²).
周长是图形外部边缘的总长度；只需把所有边长相加。对于矩形，周长 = 2 × (长 + 宽)。面积测量图形内部的空间大小，单位为平方单位。对于长方形或正方形，面积 = 长 × 宽。别忘了带上正确的单位（如 cm、cm²）。
You also learn to find the area of compound shapes (L-shapes or T-shapes) by splitting them into rectangles, working out each area separately, then adding. For triangles, the rule area = ½ × base × height is introduced.
你还会学习计算组合图形（如 L 形或 T 形）的面积，方法是将其分割成若干矩形，分别求得面积后再相加。对于三角形，你会学到面积 = ½ × 底 × 高。
9. Data Handling and Averages | 数据处理与平均数
Data is collected, organised and presented using frequency tables, bar charts, pictograms and line graphs. You should be able to read and interpret these charts, as well as construct them with appropriate scales and labels.
数据可以通过频数表、条形图、象形图和折线图进行收集、整理和展示。你需要能够阅读和解读这些图表，并选用合适的刻度和标签来亲手绘制。
The three measures of average are mode, median and mean. The mode is the most frequent value, the median is the middle value when ordered, and the mean is the sum of all values divided by the number of values. For small data sets, you will calculate the mean, median, mode and range (the difference between largest and smallest) and understand what each tells you about the data.
三种集中趋势量数是众数、中位数和平均数。众数是出现频率最高的值，中位数是按顺序排列后位于中间的值，平均数则是所有数值之和除以数值的个数。对于小规模数据集，你将计算平均数、中位数、众数和极差（最大值与最小值的差），并理解它们各自说明了数据的什么特征。
Mean = (sum of values) ÷ (number of values)
10. Problem Solving and Mathematical Reasoning | 问题解决与数学推理
Throughout Year 7, you are expected to apply your knowledge to solve word problems and puzzles. Read the question carefully, underline key information, and decide what operations are needed. Drawing a diagram or using a bar model often helps to visualise the problem.
贯穿整个 Year 7，你都需要运用所学知识解决文字题和谜题。仔细读题，圈画出关键信息，再判断该用哪种运算。画图或使用条形模型通常有助于将问题可视化。
Explain your reasoning clearly, using correct mathematical language. Answers should always be checked: does your final answer make sense in the context? Estimation and rounding are useful tools to see if a calculated answer is reasonable.
清晰地说出你的推理过程，并采用正确的数学语言。答案一定要检验：你的最终结果在题目情境下合理吗？估算和四舍五入是检验计算结果是否合理的好工具。
Finally, consistent practice with past paper questions and timed exercises will build the confidence needed to tackle WJEC assessments successfully.
最后，通过反复练习历年真题和限时训练，你就能建立起成功应对 WJEC 评估所需的信心。
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