📚 Year 7 WJEC Maths: Vocabulary & Terminology Quick-Memory Guide | Year 7 WJEC 数学：词汇术语速记指南
Mastering Year 7 maths is as much about language as it is about numbers. When you understand the key terms, questions become clearer, and you can explain your reasoning confidently. This guide covers the essential vocabulary from the WJEC Year 7 curriculum, presented side‑by‑side in English and Chinese. Use it to build a solid foundation for every topic, from number operations to geometry and data handling.
掌握 Year 7 数学，语言和数字同等重要。当你理解了关键术语，题目就会变得更清晰，你也能够自信地解释自己的推理过程。本指南涵盖了 WJEC Year 7 课程中的核心词汇，以中英对照的方式呈现。用它来为每一个专题打下坚实的基础——从数字运算到几何与数据处理。
1. Place Value and Integers | 位值与整数
Place value tells us the value of a digit based on its position in a number. In the number 3,724, the digit '3' is in the thousands place, so it represents 3,000. Understanding place value is essential for ordering, comparing and rounding whole numbers.
位值（place value）指的是一个数字在数中所处位置代表的值。在 3,724 中，数字 '3' 在千位，因此表示 3,000。理解位值对于排序、比较和取整整数至关重要。
Integers are whole numbers that can be positive, negative or zero. On a number line, negative integers lie to the left of zero, and positive integers lie to the right. The greater the integer, the further right it appears.
整数（integer）是可以为正、负或零的整数。在数轴上，负整数位于零的左侧，正整数位于右侧。整数越大，它在数轴上越靠右。
- Digit – a single symbol used to make numerals (0, 1, 2, …, 9). / 数字 – 用于构成数值的单个符号 (0 到 9)。
- Greater than (>) – shows that one number is larger than another. / 大于 (>) – 表示一个数比另一个数大。
- Less than (<) – shows that one number is smaller than another. / 小于 (<) – 表示一个数比另一个数小。
- Round – to approximate a number to a given place value. / 四舍五入 – 将一个数近似到指定位值。
- Number line – a straight line with numbers placed at equal intervals. / 数轴 – 一条直线，上面等间隔地标有数字。
2. Addition, Subtraction, Multiplication and Division | 加、减、乘、除
The four basic operations are addition, subtraction, multiplication and division. Recognising their related vocabulary helps you choose the right method for a word problem. For example, 'sum' means the result of addition, while 'product' means the result of multiplication.
四种基本运算是加、减、乘、除。识别与它们相关的词汇有助于你在文字题中选择正确的方法。例如，'sum' 指加法结果，而 'product' 指乘法结果。
Inverse operations are opposite actions that undo each other. Addition and subtraction are inverse operations; multiplication and division are inverse operations. This relationship is vital for checking answers and solving equations.
逆运算（inverse operations）是相互抵消的相反操作。加法和减法互为逆运算；乘法和除法互为逆运算。这种关系对于检查答案和解方程至关重要。
- Sum – the result of adding two or more numbers. / 和 – 两个或多个数相加的结果。
- Difference – the result of subtracting one number from another. / 差 – 一个数减去另一个数的结果。
- Product – the result of multiplying. / 积 – 相乘的结果。
- Quotient – the result of dividing. / 商 – 相除的结果。
- Remainder – the amount left over when a number cannot be divided exactly. / 余数 – 当一个数不能被整除时剩下的部分。
- Inverse operation – the operation that reverses the effect of another. / 逆运算 – 能抵消另一运算效果的运算。
3. Factors, Multiples and Primes | 因数、倍数与质数
A factor is a whole number that divides exactly into another number, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is the product of a number and any integer; the multiples of 3 include 3, 6, 9, 12, …
因数（factor）是能整除另一个数的整数，没有余数。例如，12 的因数有 1, 2, 3, 4, 6 和 12。倍数（multiple）是一个数与任意整数的乘积；3 的倍数包括 3, 6, 9, 12 等等。
Prime numbers are integers greater than 1 that have exactly two factors: 1 and the number itself. 2, 3, 5, 7, 11 are the first five primes. Composite numbers have more than two factors. 1 is neither prime nor composite.
质数（prime number）是大于 1 且只有两个因数（1 和它本身）的整数。前五个质数是 2, 3, 5, 7, 11。合数（composite number）有超过两个因数。1 既不是质数也不是合数。
- Factor pair – two numbers that multiply together to make a given number. / 因数对 – 相乘得到给定数的两个数。
- Common factor – a factor that is shared by two or more numbers. / 公因数 – 两个或多个数共有的因数。
- Highest common factor (HCF) – the largest factor common to two or more numbers. / 最大公因数 (HCF) – 两个或多个数共有的最大因数。
- Lowest common multiple (LCM) – the smallest multiple that is common to two or more numbers. / 最小公倍数 (LCM) – 两个或多个数共有的最小倍数。
- Prime factor – a factor that is also a prime number. / 质因数 – 同时也是质数的因数。
4. Fractions | 分数
A fraction represents a part of a whole or a part of a set. It is written with a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many parts you have.
分数（fraction）表示整体或集合的一部分。它用分子（numerator，上部数字）和分母（denominator，下部数字）来书写。分母表示整体被分成了多少等份；分子表示你取了多少份。
Equivalent fractions have the same value, even though they use different numbers. You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same non‑zero number.
等值分数（equivalent fractions）尽管使用了不同的数字，但值相同。你可以通过将分子与分母同时乘以或除以同一个非零数，来找到等值分数。
- Unit fraction – a fraction where the numerator is 1. / 单位分数 – 分子为 1 的分数。
- Improper fraction – a fraction where the numerator is greater than or equal to the denominator. / 假分数 – 分子大于或等于分母的分数。
- Mixed number – a whole number combined with a proper fraction, e.g. 2 ½. / 带分数 – 整数与真分数结合，例如 2 ½。
- Simplify (reduce) – to write a fraction in its lowest terms by cancelling common factors. / 化简 (约分) – 通过约去公因数，将分数写成最简形式。
- Common denominator – a shared multiple of the denominators of two or more fractions. / 公分母 – 两个或多个分数的分母共有的倍数。
5. Decimals and Percentages | 小数与百分数
A decimal is another way of writing a fraction whose denominator is a power of ten. The decimal point separates the whole number part from the fractional part. For example, 0.75 means 75 hundredths, which is the same as ¾.
小数（decimal）是以 10 的幂为分母的分数的另一种写法。小数点将整数部分与小数部分分开。例如，0.75 表示 75 个百分之一，等于 ¾。
Percent means 'out of 100'. Percentages can be converted to decimals by dividing by 100, and to fractions by writing the percentage over 100 and simplifying. A solid grasp of these conversions is key for solving real‑world problems like discounts and interest.
百分数（percent）表示“每一百份中的多少份”。百分数可以通过除以 100 转换为小数，通过写成分母为 100 的分数再化简转换为分数。扎实掌握这些转换是解决折扣、利息等实际问题的关键。
- Tenth – one part out of ten equal parts (0.1). / 十分之一 – 十等份中的一份 (0.1)。
- Hundredth – one part out of one hundred equal parts (0.01). / 百分之一 – 一百等份中的一份 (0.01)。
- Recurring decimal – a decimal that repeats a pattern of digits forever. / 循环小数 – 小数中有一段数字无限重复。
- Percentage increase / decrease – the amount a value goes up or down, expressed as a percent. / 百分比增加 / 减少 – 数值上升或下降的量，以百分数表示。
- Finding a percentage of an amount – multiplying the amount by the percent written as a decimal. / 求一个数的百分之几 – 将该数乘以写成小数的百分数。
6. Ratio and Proportion | 比与比例
Ratio compares the sizes of two or more quantities. It can be written in the form a : b or as a fraction. For example, if a fruit bowl has 3 apples and 2 bananas, the ratio of apples to bananas is 3 : 2. Ratios can be simplified just like fractions by dividing each part by a common factor.
比（ratio）比较两个或多个数量的大小。它可以写成 a : b 的形式，也可以写成分数。例如，如果果盘里有 3 个苹果和 2 根香蕉，苹果与香蕉的比就是 3 : 2。比和分数一样，可以通过将每部分除以公因数来化简。
Proportion describes a part in relation to the whole. Direct proportion means that as one quantity increases, the other increases at the same rate. Using the same fruit bowl, the proportion of apples to the total fruit is 3 out of 5, or 3/5.
比例（proportion）描述部分与整体的关系。正比例（direct proportion）意味着当一个量增加时，另一个量也以相同速率增加。以同一个果盘为例，苹果占总水果的比例是 3 比 5，即 3/5。
- Part‑to‑part ratio – compares separate parts of a group. / 部分对部分的比 – 比较一组中的不同部分。
- Part‑to‑whole ratio – compares one part to the total group. / 部分对整体的比 – 比较部分与整体。
- Equivalent ratios – ratios that have the same value, like 1:2 and 3:6. / 等值比 – 值相等的比，如 1:2 与 3:6。
- Unitary method – finding the value of one unit first, then scaling up or down. / 归一法 – 先找出一个单位的值，再进行缩放。
- Splitting in a given ratio – sharing an amount by adding the parts and finding what each part is worth. / 按给定比分配 – 通过将比的各项相加并计算每份价值来分配数量。
7. Algebraic Expressions | 代数表达式
Algebra uses letters (variables) to stand for unknown numbers. An expression is a collection of symbols representing numbers and operations, such as 3a + 2b – 5. It does not have an equals sign. Learning to read and write expressions is the first step toward solving equations.
代数（algebra）用字母（变量）来代表未知数。表达式（expression）是一组表示数字和运算的符号，例如 3a + 2b – 5。它没有等号。学会读、写表达式是解方程的第一步。
Terms are the parts of an expression separated by + or – signs. Like terms have exactly the same variable part; they can be collected together to simplify the expression. For instance, 4x and 2x are like terms, while 4x and 3y are unlike terms.
项（term）是表达式中被 + 或 – 号分隔的部分。同类项（like terms）含有完全相同的变量部分；它们可以合并以简化表达式。例如，4x 和 2x 是同类项，而 4x 和 3y 不是同类项。
- Variable – a symbol, usually a letter, that represents an unknown number. / 变量 – 一个符号，通常是字母，表示未知数。
- Coefficient – the number multiplying a variable, e.g. in 5y, 5 is the coefficient. / 系数 – 乘以变量的数字，例如在 5y 中，5 是系数。
- Constant – a term with a fixed value, e.g. 7 in 2x + 7. / 常数 – 有固定值的项，例如 2x + 7 中的 7。
- Substitution – replacing a variable with a given number. / 代入 – 用给定的数字替换变量。
- Simplify – to collect like terms and make an expression shorter. / 化简 – 合并同类项，使表达式更短。
8. Equations and Formulae | 方程与公式
). Solving an equation means finding the value of the variable that makes the statement true. A formula is a special type of equation that shows the relationship between different quantities.
方程（equation）用等号 (=) 表示两个表达式相等。解方程（solving an equation）就是找到使等式成立的变量的值。公式（formula）是一种特殊的方程，展示不同量之间的关系。
The balance method is a key technique: whatever you do to one side of the equation, you must do to the other to keep it balanced. This principle builds on inverse operations learned earlier.
天平法（balance method）是一个关键技巧：你对等式的一边做了什么，就必须对另一边做同样的操作，以保持平衡。这一原理建立在前面学过的逆运算基础之上。
- Equation – a mathematical statement with an equals sign. / 方程 – 带有等号的数学陈述。
- Solve – to work out the value of the unknown. / 求解 – 算出未知数的值。
- Unknown – the variable whose value you need to find. / 未知数 – 你需要找出其值的变量。
- Balance method – keeping both sides of an equation equal while solving. / 天平法 – 在求解过程中保持等式两边相等的方法。
- Checking by substitution – putting your answer back into the original equation to verify. / 代入检验 – 将答案代回原方程以验证。
9. Angles and Lines | 角与线
Angles are measured in degrees (°). A full turn is 360°, a straight line is 180°, and a right angle is exactly 90°. Acute angles are less than 90°, obtuse angles are between 90° and 180°, and reflex angles are greater than 180° but less than 360°.
角度以度（°）为单位测量。一整圈是 360°，一条直线是 180°，直角恰好是 90°。锐角小于 90°，钝角在 90° 到 180° 之间，优角（反射角）大于 180° 但小于 360°。
When lines intersect, special angle relationships appear. Vertically opposite angles are equal. Angles on a straight line sum to 180°, and angles around a point sum to 360°. These facts are used to find missing angles without a protractor.
当直线相交时，会出现特殊的角关系。对顶角（vertically opposite angles）相等。直线上的角之和为 180°，一点周围的角度之和为 360°。这些事实用于在没有量角器的情况下求未知角度。
- Acute angle – between 0° and 90°. / 锐角 – 0° 到 90° 之间。
- Right angle – exactly 90°. / 直角 – 恰好 90°。
- Obtuse angle – between 90° and 180°. / 钝角 – 90° 到 180° 之间。
- Reflex angle – between 180° and 360°. / 优角 – 180° 到 360° 之间。
- Adjacent angles – share a common side and vertex. / 邻角 – 共享一条公共边和顶点。
- Complementary angles – two angles that add up to 90°. / 余角 – 两个角和为 90°。
- Supplementary angles – two angles that add up to 180°. / 补角 – 两个角和为 180°。
10. 2D Shapes and Symmetry | 二维图形与对称
A polygon is a closed 2D shape made up of straight sides. Triangles are polygons with three sides; quadrilaterals have four. Knowing the properties of these shapes—such as the number of equal sides and parallel lines—helps you classify them correctly.
多边形（polygon）是由直线边组成的封闭二维图形。三角形是有三条边的多边形；四边形有四条边。了解这些形状的性质——比如相等边的数量和是否平行——有助于正确分类。
Symmetry describes how a shape can be reflected or rotated and still look the same. A line of symmetry divides a shape into two identical mirror‑image halves. Rotational symmetry tells you how many times a shape fits onto itself in a full turn.
对称（symmetry）描述一个形状经反射或旋转后仍看起来相同的性质。对称轴（line of symmetry）将形状分为两个完全相同的镜像部分。旋转对称（rotational symmetry）表示一个形状在一整圈旋转中能与自身重合多少次。
- Isosceles triangle – two equal sides and two equal angles. / 等腰三角形 – 两条等边，两个等角。
- Equilateral triangle – three equal sides and three 60° angles. / 等边三角形 – 三条等边，三个 60° 角。
- Parallelogram – quadrilateral with two pairs of parallel sides. / 平行四边形 – 有两组对边平行的四边形。
- Rhombus – parallelogram with four equal sides. / 菱形 – 四条边相等的平行四边形。
- Trapezium – quadrilateral with at least one pair of parallel sides. / 梯形 – 至少有一组对边平行的四边形。
- Line of symmetry – a line that splits a shape into two mirror‑image halves. / 对称轴 – 将形状分成两个镜像部分的一条线。
- Order of rotational symmetry – the number of times a shape maps onto itself in a full turn. / 旋转对称阶数 – 形状在一整圈旋转中与自身重合的次数。
11. Perimeter, Area and Volume | 周长、面积与体积
(length + width). Area measures the amount of space inside a 2D shape and is recorded in square units, such as cm² or m².
周长（perimeter）是围绕二维图形外缘的距离。把所有边的长度加起来就能求得。对于矩形，周长 = 2 × (长 + 宽)。面积（area）衡量二维图形内部的空间大小，以平方单位记录，如 cm² 或 m²。
cuboid, volume = length × width × height. Remember that 1 cm³ is the same as 1 millilitre—a useful conversion in practical problems.
体积（volume）是三维立体所占空间的大小，以立方单位测量，如 cm³。对于长方体（cuboid），体积 = 长 × 宽 × 高。记住 1 cm³ 等于 1 毫升——这在解决实际问题时是一个有用的换算。
- Perimeter – the total length around a shape. / 周长 – 形状周围的总长度。
- Area – the measure of surface covered, e.g. area of rectangle = length × width. / 面积 – 所覆盖表面的度量，例如矩形面积 = 长 × 宽。
- Square unit – a unit of area, such as cm², m². / 平方单位 – 面积的单位，如 cm², m²。
- Volume – the space occupied by a 3D shape, in cubic units. / 体积 – 三维形状所占的空间，以立方单位表示。
- Cuboid – a 3D shape with six rectangular faces. / 长方体 – 有六个矩形面的三维形状。
- Compound shape – a shape made up of two or more simpler shapes. / 组合图形 – 由两个或更多简单图形组成的形状。
12. Statistics and Averages | 统计与平均数
Statistics involves collecting, presenting and interpreting data. The mean is the average found by adding all values and dividing by how many there are. The mode is the value that appears most often, the median is the middle value when data is ordered, and the range is the difference between the largest and smallest values.
统计（statistics）涉及收集、展示和解读数据。平均数（mean）是将所有值相加再除以个数得到的平均值。众数（mode）是出现最频繁的值，中位数（median）是数据排序后中间的值，极差（range）是最大值与最小值之差。
Data can be presented in bar charts, pictograms and line graphs. A tally chart uses groups of five (|||| with a diagonal for the fifth) to count frequencies quickly. Reading and interpreting these diagrams is an essential skill for Year 7.
数据可以用条形图、象形图和折线图来展示。计数表（tally chart）使用五个一组（四个竖线加一个斜线表示第五个）来快速计算频数。阅读和解读这些图表是 Year 7 的基本技能。
- Mean – sum of values ÷ number of values. / 平均数 (均值) – 所有值之和 ÷ 值的个数。
- Mode – the most frequent value. / 众数 – 出现频率最高的值。
- Median – the middle value when data is ordered. / 中位数 – 数据排序后位于中间的值。
- Range – largest value minus smallest value. / 极差 – 最大值减去最小值。
- Frequency – how many times something occurs. / 频数 – 某事物出现的次数。
- Tally – a quick way of counting, usually in groups of five. / 计数符号 – 一种快速计数的方法，通常五个一组。
- Bar chart – uses bars of equal width to show frequencies. / 条形图 – 用等宽的长条表示频数。
- Pictogram – uses pictures to represent data. / 象形图 – 用图片表示数据。
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