📚 Year 7 CCEA Mathematics: Core Knowledge Checklist | Year 7 CCEA 数学：核心知识点梳理
Welcome to your essential guide for Year 7 CCEA Mathematics. This article pulls together the must-know topics you'll cover, from number and algebra to geometry and statistics. Whether you are revising for a test or building a solid foundation, these concise explanations will help you master each concept step by step.
欢迎来到 Year 7 CCEA 数学的核心知识梳理。本文汇集了你将接触的所有必学主题，从数字、代数到几何和统计。无论你是在为测试复习，还是想打好扎实基础，这些简洁的解释将帮助你一步步掌握每个概念。
1. Number and Place Value | 数字与位值
Understand the place value of digits in whole numbers up to millions. For example, in 3 482 571, the digit '4' represents four hundred thousand (400 000). You should be able to read, write, order and compare large numbers confidently.
理解整数中每一位数字的位值，最大到百万位。例如，在 3 482 571 中，数字“4”表示四十万（400 000）。你应该能够自信地读、写、排序和比较大数。
Rounding numbers is a key skill. To round to the nearest 10, 100 or 1000, look at the digit to the right: if it is 5 or more, round up; if it is less than 5, round down. For instance, 3 482 571 rounded to the nearest thousand is 3 483 000.
四舍五入是一项关键技能。舍入到最近的十、百或千时，看右边的一位数字：如果是 5 或以上，就向上进一；如果小于 5，就舍去。例如，3 482 571 四舍五入到最近的千位是 3 483 000。
You will also work with negative numbers on a number line and explore the concept of integers. Recognising the value of digits after the decimal point begins here too.
你还将利用数轴处理负数，并探索整数的概念。在这个阶段同样会开始认识小数点后数字的位值。
2. Decimals and Fractions | 小数与分数
ample 1/2 = 0.5, 1/4 = 0.25 and 3/10 = 0.3. Place value columns for decimals extend to tenths, hundredths and thousandths.
小数和分数都是表示整体部分的两种不同方式。在 Year 7 你需要掌握简单分数与小数之间的转换，例如 1/2 = 0.5, 1/4 = 0.25 和 3/10 = 0.3。小数的位值列延伸到十分位、百分位和千分位。
ng or dividing the numerator and denominator by the same number. For instance, 2/5 = 4/10 = 0.4.
对齐小数点后，比较和排序小数就变得很简单。对于分数，你可以通过分子和分母同乘或同除以同一个数找到等值形式。例如，2/5 = 4/10 = 0.4。
Adding and subtracting decimals follow the same rules as whole numbers, but you must keep the decimal points aligned. When adding fractions with the same denominator, simply add the numerators. With different denominators, first find a common denominator.
小数的加减法遵循整数相同的规则，但你必须对齐小数点。当同分母分数相加时，只需将分子相加。当分母不同时，首先要找到公分母。
3. Negative Numbers | 负数
Negative numbers appear to the left of zero on a number line. In Year 7 you learn to order, add and subtract positive and negative integers. Think of temperature climbing and falling: –5°C is colder than –2°C, and 3°C is warmer than both.
负数位于数轴上零的左侧。在 Year 7 你要学会正负整数的排序、加法和减法。想象温度上升和下降：–5°C 比 –2°C 更冷，而 3°C 比两者都暖和。
racting negative numbers: subtracting a negative is the same as adding a positive, e.g., 4 – (–3) = 4 + 3 = 7. Adding a negative moves left on the number line, e.g., 2 + (–5) = –3.
负数加减法的两条关键规则：减去一个负数等同于加上一个正数，例如 4 – (–3) = 4 + 3 = 7。加上一个负数在数轴上向左移动，例如 2 + (–5) = –3。
You will also explore real‑life contexts such as bank balances and elevations above and below sea level, helping to make negative numbers more concrete.
你还将探讨现实生活场景，如银行余额和海平面以上的海拔，有助于让负数概念变得更加具体。
4. Factors, Multiples and Primes | 因数、倍数与质数
A factor is a whole number that divides exactly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12. Multiples are the times‑table results: the multiples of 7 are 7, 14, 21, 28, …
因数是一个能整除另一个数的整数。例如，12 的因数有 1, 2, 3, 4, 6 和 12。倍数就是乘法表中的结果：7 的倍数有 7, 14, 21, 28……
arn to identify prime numbers up to 100 and use a factor tree to write a number as a product of prime factors, e.g., 12 = 2 × 2 × 3 = 2² × 3.
质数恰好有两个不同的因数：1 和它本身。2, 3, 5, 7, 11 和 13 是最小的几个质数。注意 1 不是质数。你将学会识别 100 以内的质数，并利用因数树将一个数写成质因数乘积的形式，例如 12 = 2 × 2 × 3 = 2² × 3。
Highest common factor (HCF) and lowest common multiple (LCM) are used to simplify fractions and solve problems. For 12 and 18, the HCF is 6 and the LCM is 36.
最大公因数 (HCF) 和最小公倍数 (LCM) 用于约分和解决问题。对于 12 和 18，HCF 是 6，LCM 是 36。
5. Order of Operations (BIDMAS) | 运算顺序 (BIDMAS)
BIDMAS tells you the correct order to carry out calculations: Brackets first, then Indices (powers), Division and Multiplication (left to right), Addition and Subtraction (left to right). This avoids confusion when an expression contains several operations.
BIDMAS 告诉你正确的运算顺序：先算括号，其次是指数（幂），然后乘除（从左到右），最后加减（从左到右）。当式子包含多种运算时，这能避免混乱。
14. The mnemonic can also be remembered as BODMAS or PEMDAS, but the rules are identical.
一个典型例子：3 + 4 × 2 = 3 + 8 = 11，而不是 7 × 2 = 14。有括号时：(3 + 4) × 2 = 7 × 2 = 14。这个记忆口诀也可以叫 BODMAS 或 PEMDAS，但规则完全相同。
Practice with more complex expressions like 10 – tep by step: brackets first (3+1=4), then index 2²=4, then 4×4=16, then 16÷4=4, finally 10–4=6.
通过更复杂的表达式进行练习，比如 10 – 2² × (3 + 1) ÷ 4。一步步计算：先算括号 (3+1=4)，然后指数 2²=4，接着 4×4=16，然后 16÷4=4，最后 10–4=6。
6. Introduction to Algebra | 代数入门
ers to represent unknown numbers. In Year 7 you learn to write simple expressions, such as '3 more than n' is written as n + 3, and '5 times y' s 5y. You will combine like terms: 2a + 3a = 5a, but 2a + 3b cannot be simplified further.
代数用字母表示未知数。Year 7 你需要学会写出简单的表达式，比如“比 n 多 3”写成 n + 3，“y 的 5 倍”写成 5y。你将会合并同类项：2a + 3a = 5a，但 2a + 3b 不能再化简。
3a + 2b = 3×4 + 2×2 = 12 + 4 = 16. You also explore simple sequences, describing the term‑to‑term rule and finding the next terms.
代入是指把字母替换成数字。如果 a = 4, b = 2，那么 3a + 2b = 3×4 + 2×2 = 12 + 4 = 16。你还会探索简单的数列，描述项与项之间的规则并找出接下来的项。
l also meet function machines that show inputs and outputs, linking to algebraic thinking.
解简单方程意味着求出未知数的值。对于 x + 5 = 12，两边减去 5 得 x = 7。你还会接触到函数机器，展示输入和输出，这与代数思维密切相关。
7. Angles and Shapes | 角与图形
Angles are measured in degrees (°). The main types you must recognise are acute (0° – 90°), right angle (90°), obtuse (90° – 180°) and reflex (180° – 360°). A straight line is exactly 180° and a full turn is 360°.
角度以度 (°) 为单位。你必须识别的主要类型有锐角 (0° – 90°)、直角 (90°)、钝角 (90° – 180°) 和优角 (180° – 360°)。一条直线正好是 180°，一整圈是 360°。
On a straight line, angles add up to 180°. Around a point, they sum to 360°. Vertically opposite angles are equal when two lines intersect. These facts allow you to calculate missing angles without measuring.
在直线上，角度之和为 180°。环绕一点的角度之和为 360°。两条直线相交时，对顶角相等。这些事实让你无需测量就能计算缺失的角度。
You will also name and classify 2D shapes (triangles, quadrilaterals, pentagons, hexagons) and 3D shapes (cubes, cuboids, prisms, pyramids, spheres). Properties include number of sides, faces, edges and vertices.
你还会命名和分类二维图形（三角形、四边形、五边形、六边形）和三维图形（立方体、长方体、棱柱、棱锥、球体）。属性包括边、面、棱和顶点的数量。
8. Perimeter, Area and Volume | 周长、面积与体积
ngths of all four sides, or using 2 × (length + width). Remember to include units (cm, m).
周长是围绕二维图形外部的距离。对于矩形，可以把四条边的长度相加，或者用 2 × (长 + 宽) 计算。记住要带单位（cm, m）。
Area measures the surface inside a shape. A rectangle' . Area of a triangle is half the base times the perpendicular height. Formulas are written as:
面积测量的是形状内部的表面。矩形的面积计算为长 × 宽。三角形的面积是底乘垂直高的一半。公式写为：
Area of rectangle = l × w Area of triangle = ½ × b × h
ic units such as cm³ and m³, and learn to count cubes to find the volume of simple solids.
体积是三维物体占据的空间。对于长方体，体积 = 长 × 宽 × 高。你将练习使用立方厘米 (cm³) 和立方米 (m³) 等单位，并学习通过数小方块来求简单立体的体积。
9. Coordinates and Transformations | 坐标与变换
Coordinates are written as (x, y) and plotted on a four‑quadrant grid. The x‑coordinate tells you how far to move horizontally from the origin; the y‑coordinate tells you the vertical movement. You will be able to read and plot points in all four quadrants.
坐标写作 (x, y) 的形式，并绘制在四象限网格上。x 坐标告诉你从原点水平移动多远；y 坐标告诉你垂直移动的距离。你将能够读取并绘制四个象限中的点。
Translation moves a shape without turning or flipping. Each point moves the same distance in the same direction. Reflection produces a mirror image across a given line such as the x‑axis, y‑axis or a vertical/horizontal line. Rotation turns a shape around a centre point by a given angle (often 90°, 180° or 270°).
平移是在不转动或翻转的情况下移动图形。每个点都沿相同方向移动相同的距离。反射是跨给定直线（如 x 轴、y 轴或一条垂直/水平线）产生镜像。旋转是绕一个中心点将图形转动一定角度（通常是 90°、180° 或 270°）。
When describing a transformation, you must state the type and give full details: for translation give the vector; for reflection give the mirror line; for rotation give the centre, angle and direction (clockwise/anticlockwise).
描述变换时，必须说明类型并给出完整细节：平移要给出位移向量；反射要给出镜像线；旋转要给出中心、角度和方向（顺时针/逆时针）。
10. Handling Data and Statistics | 数据处理与统计
Statistics involves collecting, organising and interpreting data. You will design tally charts and frequency tables to record information. Data can be displayed using bar charts, pictograms and simple pie charts. Each type of display helps to spot patterns quickly.
统计涉及收集、整理和解读数据。你将设计计数符号和频数表来记录信息。数据可以用条形图、象形图和简单的饼图展示。每种展示方式都有助于快速发现规律。
Three averages are introduced: the mean (sum of values divided by the number of values), the median (the middle value when ordered) and the mode (the most frequent value). You also calculate the range, which is the difference between the largest and smallest values.
引入了三种平均数：平均数（总和除以数值个数）、中位数（按序排列后的中间值）和众数（出现最频繁的值）。你还要计算极差，即最大值与最小值之差。
For example, data set: 3, 7, 7, 2, 5. Mean = (3+7+7+2+5) ÷ 5 = 4.8. Ordered: 2, 3, 5, 7, 7 ⇒ median = 5, mode = 7. Range = 7 – 2 = 5. Probability experiments also begin here, using words like 'likely', 'unlikely', 'certain' and numerical probabilities from 0 to 1.
例如，数据集：3, 7, 7, 2, 5。平均数 = (3+7+7+2+5) ÷ 5 = 4.8。排序后：2, 3, 5, 7, 7 ⇒ 中位数 = 5，众数 = 7。极差 = 7 – 2 = 5。概率实验也将在这里开始，使用“可能”、“不可能”、“一定”等词汇，以及从 0 到 1 的数字概率。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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