📚 Cambridge Primary Mathematics Workbook 3 (2nd Edition) – Key Concepts Explained | 剑桥小学数学练习册3第二版知识点精讲
Cambridge Primary Mathematics Workbook 3 (2nd Edition) is designed to help learners in Year 3 consolidate fundamental mathematical skills. This article provides a clear, topic-by-topic review of the key concepts covered in the workbook, enabling students and parents to understand and master each area with confidence.
剑桥小学数学练习册3（第二版）旨在帮助三年级学生巩固基础数学技能。本文将按主题逐一复习练习册中的关键知识点，涵盖数字、运算、几何、测量、数据处理和问题解决，帮助学生和家长深入理解并熟练掌握每个领域。
1. Numbers to 1000 | 数字到1000
Reading and writing numbers up to 1000 is the starting point of Workbook 3. Learners should be able to say a number aloud, write it in numerals, and write it in words. For example, 467 is written in numerals as 467 and in words as 'four hundred and sixty-seven'.
阅读和书写1000以内的数字是练习册3的起点。学习者应能说出一个数字、用阿拉伯数字写出它，并用英文单词写出它。例如，467用阿拉伯数字写作 467，用英文单词写作 'four hundred and sixty-seven'（四百六十七）。
Counting on and back in steps of 1, 10 and 100 from any starting number builds number sense. From 380, counting back in tens gives 370, 360, 350, 340 ...; counting on in hundreds from 380 gives 480, 580, 680 ...; and counting back in ones from 380 gives 379, 378, 377 ...
从任意数开始按1、10、100的步长正数或倒数可以培养数感。从380开始每次减十：370, 360, 350, 340……；从380开始每次加百：480, 580, 680……；从380开始每次减一：379, 378, 377……
Comparing and ordering numbers uses the symbols > (greater than) and < (less than). The rule is simple: the number with more hundreds is are greater; if the hundreds are equal, compare the tens; if the tens are also equal, compare the ones. For example, 532 < 541 because the hundreds are the same and 3 tens is less than 4 tens.
数字比较和排序使用 >（大于）和 <（小于）符号。规则很简单：百位数字大的数更大；百位相同则比较十位；十位也相同再比较个位。比如 532 < 541，因为百位相同，而3个十小于4个十。
Placing the numbers on a number line makes the order visible: numbers further to the right are greater, numbers further to the left are smaller. Learners should also be able to name the number that is 1, 10 or 100 more or less than a given number without counting from the beginning.
把这些数字放在数轴上就能直观看到顺序：越靠右的数越大，越靠左的数越小。学习者还应能说出比给定数多1、多10、多100或少1、少10、少100的数，而不必从头数起。
467 = four hundred and sixty-seven ＝ 四百六十七 | 532 < 541
2. Place Value and Partitioning | 位值与数的分拆
Place value explains what each digit in a number is worth. In a three-digit number the digits stand for hundreds, tens and ones, written in columns labelled H, T and O. In 467, the digit 4 is worth 400, the digit 6 is worth 60, and the digit 7 is worth 7.
位值说明了一个数中每个数字代表多少。三位数中的数字分别代表百、十、个，写在标有 H、T、O 的数列中。在 467 中，数字4代表400，数字6代表60，数字7代表7。
Partitioning means splitting a number into its parts. 467 can be partitioned as 400 + 60 + 7, or in other ways such as 450 + 17, or 300 + 160 + 7. Flexible partitioning helps learners add and subtract mentally.
分拆就是把一个数拆成几个部分。467可以分拆为 400 + 60 + 7，也可以拆成 450 + 17，或 300 + 160 + 7。灵活的分拆有助于心算加减法。
| Number 数字 | Hundreds 百 | Tens 十 | Ones 个 | Partition 分拆 |
| 467 | 4 (400) | 6 (60) | 7 (7) | 400 + 60 + 7 |
| 530 | 5 (500) | 3 (30) | 0 (0) | 500 + 30 |
| 806 | 8 (800) | 0 (0) | 6 (6) | 800 + 6 |
Zero is an important placeholder: in 806 the 0 shows that there are no tens, and the number is read as 'eight hundred and six'.
零是重要的占位符：在 806 中，0 表示没有十，这个数读作 'eight hundred and six'（八百零六）。
3. Addition and Subtraction | 加法与减法
Workbook 3 develops both mental and written strategies. Useful mental strategies include number bonds to 10, 20 and 100, adding near multiples of ten (to add 19, add 20 and subtract 1), doubling and halving, and using known facts to derive new ones.
练习册3同时发展心算和笔算策略。实用的心算策略包括10、20、100的数的分解组合，加接近整十的数（加19可以先加20再减1），加倍与减半，以及用已知事实推导新事实。
For written work, learners use the column method. Numbers are lined up by place value, then added or subtracted column by column, starting from the ones. When a column makes 10 or more, ten ones are exchanged for one ten; when subtracting and the top digit is too small, one ten is exchanged for ten ones.
笔算使用竖式。数字按位值对齐，然后从个位开始逐列相加或相减。当某一列满十或超过十时，十个一换成十；减法中上面的数字不够减时，借十换十。
werful way to check answers. If 245 + 138 = 383, then 383 − 138 = 245 and 383 − 245 = 138.
加法和减法互为逆运算，这是检查答案的有力方法。如果 245 + 138 = 383，那么 383 − 138 = 245，383 − 245 = 138。
245 + 138 = 383 ⇔ 383 − 138 = 245
ing first (for example, 245 + 138 is about 200 + 100 = 300) helps check whether an answer is reasonable.
学习者还应识别应用题中的关键词：和、总共、一共、差、多多少、少多少、还剩多少。先估算（例如 245 + 138 大约是 200 + 100 = 300）有助于检验答案是否合理。
4. Multiplication and Division | 乘法与除法
ion facts. Learners should be able to answer 8 × 5 = 40 quickly and also state 40 ÷ 5 = 8.
三年级要求牢固掌握2、3、4、5、6、10的乘法口诀及相应的除法事实。学习者应能快速回答 8 × 5 = 40，也能说出 40 ÷ 5 = 8。
= 12 and 3 × 4 = 12. The array also shows that 3 × 4 = 4 × 3, an example of commutativity.
乘法首先理解为重复相加和阵列。三行每行四个圆片表示 4 + 4 + 4 = 12 和 3 × 4 = 12。阵列同时显示 3 × 4 = 4 × 3，这是交换律的例子。
of 3 makes 4 groups). Division may leave a remainder, for example 13 ÷ 4 = 3 remainder 1.
除法有两种含义：平均分（12颗糖分给3个小朋友，每人4颗）和按组包含（12颗糖每3颗一组，可以分4组）。除法可能有余数，例如 13 ÷ 4 = 3 余 1。
3 × 4 = 12 ⇔ 12 ÷ 4 = 3 ⇔ 12 ÷ 3 = 4
Multiplication facts also connect to doubling, halving, odd and even numbers, and multiples. Learners should be able to spot patterns such as every multiple of 5 ends in 0 or 5, and every multiple of 10 ends in 0.
乘法事实还与加倍、减半、奇偶数、倍数相关。学习者应能发现规律，例如5的倍数个位总是0或5，10的倍数个位总是0。
5. Fractions | 分数
In Workbook 3 fractions are introduced through shapes and quantities. Learners find halves, quarters, thirds, fifths and tenths of a whole, and write them in the form ½, ¼, ⅓, ⅕ and 1/10.
练习册3通过图形和数量引入分数。学习者找出整体的二分之一、四分之一、三分之一、五分之一和十分之一，并写成 ½、¼、⅓、⅕ 和 1/10 的形式。
The two parts of a fraction have names: the denominator (bottom number) says how many equal parts the whole is divided into, and the numerator (top number) says how many of those parts are taken.
分数的两个部分各有名称：分母（下面的数）表示整体被平均分成多少份，分子（上面的数）表示取了其中多少份。
= 9. ¼ of 20 = 20 ÷ 4 = 5. To find ¾ of 20, first find ¼ (5) then multiply by 3 to get 15.
求一个量的几分之几要用除法，有时还要用乘法。18的½ = 18 ÷ 2 = 9。20的¼ = 20 ÷ 4 = 5。求20的¾，先求¼（得5），再乘3得15。
½ of 18 = 9 ¼ of 20 = 5 ¾ of 20 = 15
ractions with the same denominator, such as 3/5 > 2/5, and use fraction walls or number lines to see that fractions are numbers in their own right.
等值分数也会涉及：½ = 2/4 = 5/10。学习者会比较分母相同的分数，例如 3/5 > 2/5，并借助分数墙或数轴理解分数本身也是数。
6. Measures: Length and Mass | 测量：长度与质量
Length is measured in millimetres (mm), centimetres (cm), metres (m) and kilometres (km). Learners choose a sensible unit: a pencil in cm, a room in m, a journey in km. Mass is measured in grams (g) and kilograms (kg), with a kilogram used for heavier objects such as a bag of flour.
长度用毫米（mm）、厘米（cm）、米（m）和千米（km）测量。学习者要选择合适的单位：铅笔用厘米，房间用米，路程用千米。质量用克（g）和千克（kg）测量，较重物体如一带面粉用千克。
Key conversions must be known by heart:
以下关键换算必须熟记：
- 1 cm = 10 mm | 1厘米 = 10毫米
- 1 m = 100 cm | 1米 = 100厘米
- 1 km = 1000 m | 1千米 = 1000米
- 1 kg = 1000 g | 1千克 = 1000克
Practical measuring skills matter as much as arithmetic. Learners read a ruler from zero, not from the edge, and read a scale on a balance or kitchen scale by counting the intervals between the marked numbers.
实际操作能力与运算同样重要。学习者要从刻度0开始读尺子，而不是从尺子边缘开始；读天平或厨房秤的刻度时，要数清标注数字之间的分格。
1 m = 100 cm = 1000 mm 1 kg = 1000 g
Comparing and ordering measures is a common question type: 1 m 20 cm is longer than 95 cm, and 2 kg is heavier than 1500 g. Converting both measurements to the same unit first avoids mistakes.
比较和排序是常见题型：1米20厘米比95厘米长，2千克比1500克重。先把两个量换算成同一单位再比较，可以避免错误。
7. Measures: Capacity and Time | 测量：容积与时间
. Learners read measuring jugs, estimate capacity (a teaspoon about 5 ml, a bucket about 10 l), and solve problems such as 'a bottle holds 500 ml; how much do 4 bottles hold?'
容积用毫升（ml）和升（l）测量，其中 1升 = 1000毫升。学习者要会读量杯、估算容积（一茶匙约5毫升，一桶约10升），并解决问题，例如"一瓶装500毫升，4瓶共装多少？"
Time work at this stage includes reading analogue and digital clocks to the nearest minute, using the vocabulary of o'clock, half past, quarter past and quarter to, and understanding a.m. and p.m.
本阶段的时间学习包括：读指针钟和数字钟（精确到分钟），使用整点、半点、过一刻、差一刻等说法，以及理解上午（a.m.）和下午（p.m.）。
The 24-hour clock is introduced through simple conversions: 3 p.m. is 15:00, 8:30 p.m. is 20:30. Learners also calculate durations, for example from 09:45 to 11:15 is 1 hour 30 minutes.
通过简单换算引入24小时制：下午3点是 15:00，晚上8点30分是 20:30。学习者还要计算时间间隔，例如从09:45到11:15是1小时30分钟。
1 hour = 60 minutes 1 minute = 60 seconds 1 l = 1000 ml
Calendar work covers days of the week, months of the year, and the number of days in each month, including the idea of a leap year having 366 days.
日历学习包括星期、月份、每个月的天数，以及闰年有366天的概念。
8. Money | 货币
cognise coins and notes, write amounts using the pound sign and decimal point (for example £3.45), and understand that £1 = 100 pence.
货币问题把运算与日常生活联系起来。学习者要认识硬币和纸币，用英镑符号和小数点写金额（例如 £3.45），并理解 1英镑 = 100便士。
Adding and subtracting money follows the same column rules as other numbers, keeping the decimal points lined up. Finding change is subtraction: paying £10 for an item costing £6.75 gives £3.25 change.
货币的加减法与其他数字的竖式规则相同，小数点要对齐。找零就是减法：用10英镑买6.75英镑的东西，找零3.25英镑。
£1 = 100p £10.00 − £6.75 = £3.25
Word problems often combine money with multiplication or division: 'Four pens cost £2.40. How much is one pen?' (division) or 'One notebook costs 85p. How much do 5 cost?' (multiplication). Estimating before calculating, such as rounding £2.40 to £2.50, helps check the answer is sensible.
应用题常把货币与乘除法结合："四支笔2.40英镑，每支多少？"（除法）或"一本笔记本85便士，五本多少？"（乘法）。计算前先估算，例如把2.40英镑看作2.50英镑，有助于判断答案是否合理。
9. Geometry: 2D and 3D Shapes | 几何：平面图形与立体图形
Learners describe 2D shapes by their number of sides and vertices (corners): a triangle has 3 sides, a quadrilateral 4, a pentagon 5, a hexagon 6 and an octagon 8. Circles have a curved edge and no vertices.
学习者通过边数和顶点数描述平面图形：三角形3条边，四边形4条，五边形5条，六边形6条，八边形8条。圆有曲线边，没有顶点。
3D shapes are described by faces, edges and vertices. A cube has 6 square faces, 12 edges and 8 vertices; a cuboid is like a stretched cube; a sphere has one curved surface and no edges; a cylinder has two circular faces and one curved surface; a cone has one circular face, one vertex and one curved surface.
立体图形通过面、棱和顶点描述。正方体有6个正方形面、12条棱、8个顶点；长方体像被拉长的正方体；球有一个曲面，没有棱；圆柱有两个圆面和一个曲面；圆锥有一个圆面、一个顶点和一个曲面。
| Shape 图形 | style="border:1px solid #ccc;
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