📚 Cambridge Primary Mathematics Learner’s Book 3, 2nd Edition Key Concepts | 剑桥小学数学第三册（第二版）核心知识点精讲
Cambridge Primary Mathematics Learner’s Book 3 (2nd Edition) builds on early number sense and introduces learners to numbers up to 1000, more formal methods for addition and subtraction, multiplication and division facts, fractions, measurement, geometry, and simple data handling. This article breaks down the key topics chapter by chapter, pairing each explanation in English and Chinese to support both classroom learning and revision. The content is aligned with the Cambridge Primary curriculum framework and is suitable for learners aged 7–9.
《剑桥小学数学第三册》（第二版）在早期数感的基础上，引导学生认识 1000 以内的数字，学习正式的加减法计算、乘除法口诀与运算、分数、测量、几何以及简单的数据处理。本文按章节梳理核心知识点，给出中英文对照的讲解，便于课堂学习与课后复习。内容紧扣剑桥小学课程框架，适合 7 至 9 岁学生使用。
1. Numbers to 1000 | 数字到 1000
Learners extend their knowledge of place value to three-digit numbers. They read, write, and represent numbers up to 1000 using base-ten blocks, place value charts, and number lines. Understanding that the digit in the hundreds place tells how many groups of one hundred, the tens digit tells groups of ten, and the ones digit tells the remaining ones is crucial.
学生将位值知识扩展到三位数。他们使用十进制积木、位值表和数轴来读、写和表示 1000 以内的数字。理解百位上的数字表示几个一百，十位表示几个十，个位表示几个一，这一点至关重要。
Comparing and ordering numbers is practised by looking first at the hundreds digit, then the tens, then the ones. Learners also round two- and three-digit numbers to the nearest ten or hundred. Estimating a number’s position on an empty number line helps develop a strong mental image of magnitude.
比较和排序数字时，先看百位，再看十位，最后看个位。学生还会把两位数和三位数四舍五入到最接近的十位或百位。在空白数轴上估算数字的位置，有助于形成对数字大小的清晰心像。
2. Addition and Subtraction | 加法与减法
Learners consolidate mental strategies for adding and subtracting two-digit numbers, such as bridging through ten and partitioning. They then progress to written methods for three-digit numbers, including column addition and subtraction without and with regrouping. The concept of compensation is also introduced: for example, adding 100 and then subtracting 1 when adding 99.
学生巩固两位数加法和减法的口算策略，如跨十法和拆分法。接着，他们学习三位数的笔算方法，包括不带进（退）位和带进（退）位的竖式加法和减法。同时还引入补偿策略，例如，加 99 时可以先加 100 再减 1。
Problem-solving tasks involve missing number sentences, estimating answers before calculating, and using the inverse relationship between addition and subtraction to check results. Word problems present real-life contexts such as buying items or measuring distances.
解决问题型的任务包括填写缺失数字的算式、计算前先估算答案，以及利用加法和减法的逆运算关系进行验算。应用题则呈现购物或测量距离等真实情境。
3. Multiplication Facts and Strategies | 乘法口诀与策略
The 2, 3, 4, 5, and 10 times tables are firmly established, and the 6, 7, 8, and 9 times tables are introduced. Learners use arrays, repeated addition, and skip counting to build understanding. They also explore the commutative property: 3 × 4 is the same as 4 × 3.
2、3、4、5 和 10 的乘法口诀已牢固掌握，在此基础上引入 6、7、8 和 9 的乘法口诀。学生通过阵列、重复加法和跳数来理解乘法。他们还会探究乘法交换律：3 × 4 等于 4 × 3。
Multiplying by 1 and 0 is discussed, establishing that any number multiplied by 1 stays the same, and any number multiplied by 0 gives 0. Doubling and halving are linked to multiplying by 2 and finding half of a number. Learners begin to solve simple multiplication word problems and complete missing factor sentences like ___ × 5 = 45.
还探讨了乘以 1 和 0 的规则：任何数乘以 1 结果不变，任何数乘以 0 都得 0。加倍和减半则分别与乘以 2 和求一个数的一半联系起来。学生开始解决简单的乘法应用题，并填写像 ___ × 5 = 45 这样缺失因子的算式。
4. Division Facts and Strategies | 除法口诀与策略
Division is introduced as sharing equally and as grouping (how many groups can be made). Learners use concrete objects, drawings, and arrays to visualise division. The link between multiplication and division is emphasised: if 6 × 4 = 24, then 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
除法被引入为等分（平均分配）和分组（能分成多少组）。学生使用具体物、图画和阵列来直观理解除法。乘法与除法之间的联系被重点强调：如果 6 × 4 = 24，那么 24 ÷ 4 = 6，24 ÷ 6 = 4。
Division facts for tables up to 10 × 10 are practised, and learners recognise remainders in simple real-world contexts, for example, 14 ÷ 3 leaves 2 remainder. They solve problems such as sharing 20 sweets among 4 children, or finding how many piles of 5 can be made from 35 books.
练习 10×10 以内的除法口诀，学生在简单的实际情境中认识余数，例如 14 ÷ 3 商 4 余 2。他们解决诸如把 20 颗糖分给 4 个小朋友，或从 35 本书中能分成多少堆每堆 5 本等问题。
5. Fractions | 分数
Learners recognise unit and non-unit fractions of shapes and numbers. They identify ½, ⅓, ¼, ⅕, ⅙, ⅛, and ⅒ of a whole, and shade parts of shapes to represent these fractions. Greater emphasis is placed on understanding that the denominator tells how many equal parts the whole is divided into, and the numerator tells how many of those parts are taken.
学生认识形状和数字的单位分数和非单位分数。他们能够辨认同一个整体中的 ½、⅓、¼、⅕、⅙、⅛ 和 ⅒，并给形状涂色以表示这些分数。重点在于理解分母表示整体被分成几等份，分子表示取几份。
Finding fractions of amounts, such as ¼ of 20, is done using division: divide by the denominator, then multiply by the numerator. Equivalent fractions are introduced with simple visual examples, showing that ½ = 2/4 = 3/6. Learners compare fractions with the same denominator.
求一个数量的几分之几，例如 20 的 ¼，可以使用除法：先除以分母，再乘以分子。通过简单的可视化例子引入等值分数，表明 ½ = 2/4 = 3/6。学生会比较同分母分数的大小。
6. Measurement: Length, Mass, and Capacity | 测量：长度、质量和容量
Learners measure, compare, add, and subtract lengths in metres (m), centimetres (cm), and begin to use millimetres (mm). They choose appropriate tools such as rulers, metre sticks, and tape measures. Conversion between units is practised: 1 m = 100 cm, 1 cm = 10 mm.
学生测量、比较、加法和减法较长度，单位使用米（m）、厘米（cm），并开始使用毫米（mm）。他们选择合适的工具，如直尺、米尺和卷尺。练习单位换算：1 米 = 100 厘米，1 厘米 = 10 毫米。
Mass is measured in kilograms (kg) and grams (g), with learners reading scales where each division represents 1 kg, 100 g, or 50 g. Capacity is investigated using litres (L) and millilitres (mL), with typical containers explored. Word problems integrate all three measures, building estimation and practical skills.
质量以千克（kg）和克（g）为单位测量，学生识读每格代表 1 kg、100 g 或 50 g 的秤。容量则使用升（L）和毫升（mL）进行探究，并使用常见的容器。应用题综合这三种测量，培养估算和实际操作能力。
7. Time | 时间
Reading and writing time to the nearest 5 minutes on analogue and digital clocks is a key skill. Learners practise saying times using ‘past’ and ‘to’ (e.g., twenty past nine, ten to four). They convert between analogue and digital formats, and understand a.m. and p.m. notations.
能够读写在指针式和数字式时钟上精确到 5 分钟的时间是一项关键技能。学生练习使用“过”和“差”来表达时间（如九点二十，差十分四点）。他们能在两种时钟格式之间转换，并理解上午（a.m.）和下午（p.m.）标记。
Calculating time intervals in hours and minutes is introduced, for instance, working out how long a television programme lasts from its start to end time. Learners also use calendars to find the number of days in months and solve simple problems involving dates.
引入了以小时和分钟为单位计算时间间隔，例如，计算一档电视节目从开始到结束持续多长时间。学生还使用日历来查看各个月份的天数，并解决简单的日期问题。
8. Geometry: 2D and 3D Shapes | 几何：平面图形与立体图形
Learners classify 2D shapes by the number of sides and vertices. They handle shapes such as triangles, quadrilaterals (square, rectangle, rhombus, parallelogram, trapezium), pentagons, hexagons, and octagons. The term ‘polygon’ is introduced for closed flat shapes with straight sides.
学生根据边和顶点的数量对平面图形进行分类。他们操作诸如三角形、四边形（正方形、长方形、菱形、平行四边形、梯形）、五边形、六边形和八边形等图形。引入了“多边形”一词，指由直线边构成的封闭平面图形。
3D shapes are described by faces, edges, and vertices (corners). Common shapes include cubes, cuboids, spheres, cylinders, cones, and pyramids. Learners identify 2D faces of 3D shapes and recognise shapes in the environment. Symmetry is explored by finding lines of symmetry on 2D shapes through folding and drawing.
立体图形通过面、棱和顶点来描述。常见立体图形包括立方体、长方体、球体、圆柱体、圆锥体和棱锥体。学生识别立体图形上的平面，并辨认环境中的形状。通过折叠和描画找出平面图形上的对称轴，探究对称性。
9. Angles and Turns | 角与转向
Angles are introduced as a measure of turn. Learners identify right angles as quarter turns (90°) and recognise them in squares, rectangles, and the corners of everyday objects. They compare angles relative to a right angle, using terms ‘greater than a right angle’ and ‘less than a right angle’.
角度被引入为转向的度量。学生将直角识别为四分之一转（90°），并能在正方形、长方形和日常物品的角上认出直角。他们使用“大于直角”和“小于直角”来比较各个角。
Turns are described in terms of quarter, half, three-quarter and full turns, both clockwise and anticlockwise. Learners follow and give instructions involving turns, linking to the points of a compass (N, E, S, W) and describing directions such as “turn east” or “face north-west”.
转向用四分之一转、半转、四分之三转和整转来描述，包括顺时针和逆时针方向。学生遵循并给出包含转向的指令，联系罗盘方位（北、东、南、西），并描述诸如“转向东”或“面向西北”等方向。
10. Data Handling | 数据处理
Learners collect, organise, and represent data using pictograms, bar charts, and Carroll diagrams. In a pictogram, each symbol represents one or more items; learners interpret and construct pictograms where one picture equals, say, 2 units. Bar charts are drawn with equal-width bars and a labelled scale.
学生收集、整理并使用象形图、条形图和卡罗尔图来呈现数据。在象形图中，每个符号代表一个或多个项目；学生解读并绘制象形图，其中一个图形可以表示例如 2 个单位。绘制条形图时要求条形等宽，并标有刻度。
Carroll diagrams sort objects by two criteria (e.g., has fur / does not have fur, and lives on land / lives in water). Venn diagrams sort items into overlapping sets based on shared attributes. Learners answer and ask questions about data, such as “How many more … than …?” and “What is the most common …?”
卡罗尔图按两种标准对物体进行分类（如有皮毛/无皮毛，陆生/水生）。维恩图则根据共有的属性将物体分入重叠的集合中。学生针对数据回答并提出问题，比如“……比……多多少？”和“最常见的……是什么？”。
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