📚 Year 7 Cambridge Mathematics Complete Syllabus Breakdown | Year 7 剑桥数学课程大纲全面解析
Year 7 Cambridge Mathematics, corresponding to Stage 7 of the Cambridge Lower Secondary curriculum, builds a strong foundation in number, algebra, geometry, measurement, and data handling. This guide breaks down every major topic, highlighting the key skills and concepts students must master. It serves as a clear roadmap for learners, parents, and tutors aiming to navigate the first year of secondary-level mathematics with confidence.
Year 7 剑桥数学对应剑桥初中课程第七阶段，为数、代数、几何、测量和数据处理打下坚实基础。本解析将逐一梳理每个主要课题，突出学生必须掌握的关键技能与概念，为学习者、家长和辅导老师提供一份清晰的路线图，以自信地驾驭中学第一年的数学学习。
1. Number and Place Value | 数字与位值
Students extend their understanding of whole numbers up to millions and beyond, learning to read, write, order, and compare large numbers. They explore place value in depth, recognising that the value of a digit depends on its position.
学生将整数的理解扩展到百万及以上，学会读、写、排序和比较较大的数。他们深入学习位值，认识到一个数字的值取决于它所在的位置。
Negative numbers are introduced through real-life contexts such as temperature and debt. Learners order positive and negative integers on a number line and begin to add and subtract with negative values.
通过温度和负债等实际情境引入负数。学生在数轴上对正整数和负整数进行排序，并开始进行负数的加减运算。
Multiplying and dividing by 10, 100, and 1000 is consolidated, with emphasis on moving digits left or right and using zero as a placeholder. Square and cube numbers are identified, and learners find square roots and cube roots of simple perfect squares and cubes.
巩固乘除以 10、100 和 1000 的运算，重点放在数字向左或向右移动以及零占位上。识别平方数和立方数，并求出简单完全平方数和立方数的平方根与立方根。
2. Fractions, Decimals, and Percentages | 分数、小数与百分比
Learners work with equivalent fractions, simplifying and comparing fractions with different denominators. They convert between improper fractions and mixed numbers and express one quantity as a fraction of another.
学生学习等值分数，化简并比较分母不同的分数。他们要在假分数和带分数之间进行转换，并将一个量表示为另一个量的分数。
Decimal place value is extended to thousandths, and students round decimals to a given number of decimal places. They perform addition, subtraction, multiplication, and division with decimals, including in money and measurement contexts.
小数位值扩展到千分位，学生将小数舍入到指定位数。他们在货币和测量等情境中进行小数的加减乘除运算。
Percentages are understood as ‘parts per hundred’, and students convert between fractions, decimals, and percentages. They calculate percentages of quantities and apply percentage increases and decreases in simple real-life problems.
理解百分比是”每一百份中的若干份”，学生在分数、小数和百分比之间进行转换。他们计算一个数量的百分比，并在简单的生活问题中应用百分比的增减。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/5 | 0.6 | 60% |
3. Operations and Calculation Strategies | 运算与计算策略
Year 7 students refine written and mental methods for all four operations, including long multiplication and short division. They are encouraged to choose the most efficient strategy, whether mental, written, or using a calculator.
七年级学生要完善四则运算的笔算和心算方法，包括长乘法和短除法。鼓励他们选择最高效的策略，无论是心算、笔算还是使用计算器。
Order of operations (BODMAS/BIDMAS) is introduced formally. Students evaluate expressions involving brackets, indices, division, multiplication, addition, and subtraction, and they learn to insert brackets to change the outcome.
正式引入运算顺序（括号、指数、乘除、加减）。学生计算含有括号、指数、乘除和加减的表达式，并学习插入括号来改变运算结果。
Estimating and checking answers by rounding is a key skill. Students learn to use inverse operations to verify results and develop number sense through mental arithmetic challenges.
通过近似估算和检验答案是关键技能。学生学会用逆运算来验证结果，并通过心算挑战培养数感。
4. Ratio and Proportion | 比与比例
Ratio is introduced as a way to compare two or more quantities. Students simplify ratios, write them in their simplest form, and divide a quantity into a given ratio.
比作为比较两个或多个数量的方式引入。学生化简比，写出最简形式的比，并将一个量按给定比例分配。
They distinguish between ratio and proportion, solving simple proportion problems such as scaling recipes or maps. Direct proportion is explored through tables and the concept of a constant multiplier.
他们区分比和比例，解决简单的比例问题，例如按比例调整食谱或理解地图。通过表格和常数乘数的概念探究正比例。
5. Algebraic Expressions and Equations | 代数表达式与方程
Pupils use letters to represent unknown numbers or variables. They form simple algebraic expressions, such as 2n + 3, and substitute positive and negative integer values into expressions and formulae.
学生使用字母表示未知数或变量。他们构建简单的代数表达式，如 2n + 3，并将正整数和负整数值代入表达式和公式。
Collecting like terms is practised, e.g. simplifying 3a + 2b – a + 4b to 2a + 6b. The distinction between a term, an expression, an equation, and a formula is made clear.
练习合并同类项，例如将 3a + 2b – a + 4b 化简为 2a + 6b。明确项、表达式、方程和公式的区别。
Solving linear equations in one unknown begins, using inverse operations. Students solve equations like 2x + 5 = 13 and learn to check their solution by substitution.
开始解一元一次方程，使用逆运算。学生求解诸如 2x + 5 = 13 的方程，并学会通过代入来检验解。
6. Sequences, Functions, and Graphs | 数列、函数与图像
Students generate terms of linear sequences from a given rule, often expressed in words or as an algebraic nth term. They find missing terms and describe the term-to-term rule.
学生根据给定规则生成线性数列的项，规则通常用文字或第 n 项代数式表达。他们找出缺失项并描述逐项变化规律。
Using coordinates in all four quadrants is consolidated. Learners plot points, read coordinates from graphs, and begin to plot simple linear functions such as y = 2x + 1, producing straight-line graphs.
巩固在全部四个象限中使用坐标。学习者描点、读取图像坐标，并开始绘制如 y = 2x + 1 这样的简单线性函数，得到直线图像。
Input-output function machines are used to introduce the idea of a function, linking to algebraic expressions and sequences.
使用输入输出功能机引入函数概念，连接代数表达式和数列。
7. Geometry: Angles and Shapes | 几何：角度与图形
Learners measure and draw angles accurately with a protractor. They classify angles as acute, right, obtuse, straight, and reflex, and use angle notation such as ∠ABC.
学习者使用量角器精确测量和绘制角度。他们将角分类为锐角、直角、钝角、平角和优角，并使用如 ∠ABC 的角度符号。
Angle facts on a straight line (sum 180°), around a point (360°), and vertically opposite angles are explored. Students calculate missing angles using these properties, often without diagrams drawn to scale.
探究直线上的角（和为 180°）、点周角（360°）以及对顶角的性质。学生利用这些性质计算缺失的角度，通常在不按比例的图里完成。
Properties of triangles (equilateral, isosceles, scalene, right-angled) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite) are investigated. Learners identify lines of symmetry and rotational symmetry in 2D shapes.
研究三角形（等边、等腰、不等边、直角）和四边形（正方形、长方形、平行四边形、菱形、梯形、筝形）的性质。学习者识别二维图形的对称轴和旋转对称。
8. Perimeter, Area, and Volume | 周长、面积与体积
Students calculate the perimeter of regular and irregular polygons, including composite shapes made from rectangles. They use and convert between metric units of length (mm, cm, m, km).
学生计算规则与不规则多边形的周长，包括由矩形组合而成的复合图形。他们使用并互相转换公制长度单位（毫米、厘米、米、千米）。
Area formulas for rectangles and right-angled triangles are derived and applied. Learners find the area of shapes by counting squares and by using the formula: area = length × width for rectangles, and ½ × base × height for triangles.
推导并应用矩形和直角三角形的面积公式。学习者通过数方格和使用公式（矩形面积 = 长 × 宽，三角形面积 = ½ × 底 × 高）来求图形面积。
Volume of cubes and cuboids is introduced, linking to the concept of layers. Students use the formula volume = length × width × height and solve problems involving stacking and packing.
引入立方体和长方体的体积，与层数概念相联系。学生使用体积 = 长 × 宽 × 高的公式，并解决涉及堆叠和装箱的问题。
9. Transformations and Symmetry | 变换与对称
Reflection, translation, and rotation are introduced as transformations of 2D shapes. Students reflect shapes over mirror lines, including horizontal, vertical, and diagonal lines.
引入反射（对称）、平移和旋转作为二维图形的变换。学生在镜像线上反射图形，包括水平、垂直和对角线。
Translations are described using column vectors (left/right and up/down). Rotations are performed around a centre by a given angle, focusing on quarter and half turns.
使用列向量（左/右和上/下）描述平移。围绕中心按给定角度进行旋转，重点在四分之一转和半转。
Symmetry is deepened: students locate mirror lines and determine the order of rotational symmetry. Tessellations and patterns help visualise how shapes fit together without gaps.
深化对称性：学生定位镜像线并确定旋转对称的阶数。镶嵌和图案有助于可视化形状如何无间隙地拼合在一起。
10. Data Handling and Statistics | 数据处理与统计
Learners collect, organise, and represent data using frequency tables, bar charts, pictograms, and line graphs. They interpret data from dual bar charts and pie charts, relating sectors to proportions.
学习者使用频数表、条形图、象形图和折线图收集、整理和呈现数据。他们解释双条形图和饼图的数据，将扇形与比例联系起来。
Averages and range are covered: mode, median, and mean are calculated for small data sets. Students find the range as a measure of spread and choose the most appropriate average to describe a data set.
涵盖平均数和极差：计算小数据集的众数、中位数和平均数。学生求出极差作为衡量离散程度的量，并选择最合适的平均数来描述数据集。
Statistical investigations are encouraged: posing a question, collecting data, and drawing conclusions. The difference between discrete and continuous data is discussed.
鼓励统计调查：提出问题、收集数据并得出结论。讨论离散数据与连续数据的区别。
11. Probability | 概率
Probability is introduced on a scale from 0 (impossible) to 1 (certain). Students use words such as impossible, unlikely, even chance, likely, and certain to describe likelihood, and place events on the probability scale.
概率按 0（不可能）至 1（必然）的尺度引入。学生使用不可能、不太可能、等可能、很可能、必然等词语描述可能性，并将事件放在概率尺度上。
They calculate theoretical probability as number of favourable outcomes divided by total number of outcomes, for simple scenarios like rolling a fair dice or spinning a spinner.
他们计算理论概率，即有利结果数除以总结果数，用于如掷公平骰子或旋转转盘等简单场景。
Simple experiments are carried out, comparing experimental probability with theoretical probability. Students learn that probability does not predict short-term outcomes reliably.
进行简单实验，比较实验概率和理论概率。学生认识到概率无法可靠预测短期结果。
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