📚 Cambridge Primary Mathematics Workbook 1, 2nd Edition Knowledge Points Explained | 剑桥小学数学练习册第一册（第二版）知识点精讲
Cambridge Primary Mathematics Workbook 1 (2nd Edition) is designed for young learners beginning their formal mathematics journey. It covers foundational topics such as numbers to 10, addition and subtraction, shapes, measurement, time, and simple data handling. Each section uses clear illustrations and step-by-step activities to build confidence and fluency. This article breaks down all key knowledge points to support parents, teachers, and students using the workbook.
《剑桥小学数学练习册第一册（第二版）》专为刚刚步入正式数学学习的小学习者设计。它涵盖数字到10、加减法、图形、测量、时间和简单数据处理等基础主题。每个部分都运用清晰的插图和循序渐进的练习来建立信心与流利度。本文逐一精讲所有核心知识点，为使用该练习册的家长、教师和学生提供支持。
1. Numbers to 10 | 数字到10
Recognising and writing numbers from 0 to 10 is the very first step. Learners practise tracing the digits, saying the number names, and counting real objects such as cubes, counters, or fingers. The number zero is introduced as representing ‘none’.
认识并书写0到10的数字是第一步。学习者练习描摹数字、说出数字名称，并点数实物，如立方块、计数片或手指。数字0作为“没有”的代表被引入。
Each number has a matching quantity. For example, the digit 5 stands for a group of five items. Pictures of animals, dots, or classroom objects help children connect the numeral with a set. Matching activities and ‘circle the correct number’ exercises are used throughout the workbook.
每一个数字都有对应的数量。例如，数字5代表一组五个物品。动物、点或教室物品的图片帮助儿童将数字符号与集合联系起来。练习册中随处可见连线活动和“圈出正确数字”的练习。
Counting forwards from 1 to 10 and backwards from 10 to 1 is practised rhythmically. Missing number sequences, such as 3, 4, __, 6, encourage logical thinking. Children also learn to count objects arranged in a line, in a circle, or scattered.
有节奏地练习从1数到10的正向数数和从10数到1的倒向数数。缺失数字序列，如3、4、__、6，能激发逻辑思维。儿童还学习点数排成一排、围成一圈或散落摆放的物体。
2. Counting and Ordinal Numbers | 计数与序数
Beyond simple counting, children extend their skills to count up to 20, recognising the pattern of teen numbers. They learn that numbers after ten follow a ‘ten and some more’ structure, such as fourteen is 10 and 4.
除了简单计数，孩子们将技能扩展到点数至20，认知“十几”数字的规律。他们了解到十之后的数字遵循“十加几”的结构，例如十四就是10加4。
Ordinal numbers describe position or order: first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth. Typical questions may show a line of animals and ask, ‘Colour the third frog.’
序数词描述位置或顺序：第一、第二、第三、第四、第五、第六、第七、第八、第九、第十。典型的题目会画出一排动物，并要求“给第三只青蛙涂颜色。”
Using the words before, after, and between helps children describe relative positions. For instance, ‘Which number comes after 7?’ or ‘What is between 12 and 14?’ These activities reinforce sequencing and number sense.
使用前、后和之间等词语帮助儿童描述相对位置。例如，“7后面是哪个数字？”或“12和14之间是什么？”这些活动加强了顺序感和数感。
3. Comparing Numbers | 比较数字
Comparing quantities is done by matching objects one-to-one or by counting. Children use the phrases ‘more than’, ‘fewer than’, and ‘the same as’ to describe groups. They may circle the group that has more or draw lines to pair items.
通过一一对应或点数来比较数量。孩子们用“比……多”、“比……少”和“和……一样多”来描述集合。他们可能圈出数量更多的组，或者画线配对物品。
The concept of one more and one less is a key part of early addition and subtraction readiness. Learners find the number that is one more than a given number by counting on, and one less by counting back. This is often done using a number track.
多一个和少一个的概念是早期加减法准备的关键部分。学习者通过继续往后数找到一个数多一的数字，通过往前倒数找到少一的数字。这通常借助数字跑道来完成。
Although the inequality symbols (<, >) are not formally introduced in Workbook 1, the ideas of greater and smaller are firmly established. Children order sets of objects from least to greatest or greatest to least.
尽管不等号（<、>）在练习册第一册中没有正式引入，但更大和更小的概念已经牢固建立。孩子们将几组物体从最少到最多或从最多到最少进行排序。
4. Addition within 10 | 10以内的加法
Addition is introduced as putting two parts together to make a whole. The plus sign (+) and equals sign (=) are used in number sentences such as 3 + 2 = 5. Children relate these to stories and picture problems: ‘Three birds on a wire, two more join. How many altogether?’
加法被引入为将两部分放在一起组成整体。加号（+）和等号（=）用于像3 + 2 = 5这样的数字句子中。孩子们将这些与故事和图片问题联系起来：“电线上有三只鸟，又飞来了两只。一共有多少只？”
Number bonds to 10 are essential. Learners memorise pairs of numbers that add to 10, such as 4 + 6, 7 + 3, and 5 + 5. The workbook often uses part-whole diagrams and ten frames to visualise these facts.
10的组成至关重要。学习者记忆加起来等于10的数字对，例如4 + 6、7 + 3和5 + 5。练习册经常使用部分-整体图和十格框来直观显示这些事实。
| 0 + 10 = 10 | 1 + 9 = 10 |
| 2 + 8 = 10 | 3 + 7 = 10 |
| 4 + 6 = 10 | 5 + 5 = 10 |
Counting on is a strategy for finding totals. To add 6 and 3, start with 6 and say ‘7, 8, 9’. Using a number line or fingers supports this method. Practical addition with cubes or counters builds deep understanding.
接着数是一种求和的策略。要计算6加3，从6开始数“7、8、9”。使用数轴或手指可以辅助这个方法。用立方块或计数片的实物加法能建立深刻的理解。
5. Subtraction within 10 | 10以内的减法
Subtraction is understood as taking away or finding how many are left. The minus sign (−) is used. For example, 9 − 4 = 5 means starting with 9 and removing 4 to leave 5. Crossing out pictures is a common first step.
减法被理解为拿走或求出还剩多少。使用减号（−）。例如，9 − 4 = 5 表示从9开始，去掉4，剩下5。划掉图片是常见的第一步。
Subtraction is also linked to finding the difference between two quantities. Learners compare two sets and see how many more one has than the other. This is often illustrated with bar models or objects lined up side by side.
减法还与求两量之间的差有关。学习者比较两组物品，看一组比另一组多多少。这通常用条形模型或并排排列的物品来说明。
Counting back is a key strategy. For 7 − 2, put 7 in your head and count back two steps: 6, 5, so the answer is 5. Structured number tracks help children see the backward jumps clearly.
往回数是关键策略。对于7 − 2，脑中记住7，往回数两步：6、5，所以答案是5。结构化的数字跑道能帮助儿童清晰地看到向后的跳跃。
Children also learn that addition and subtraction are related. If 3 + 4 = 7, then 7 − 4 = 3 and 7 − 3 = 4. These ‘fact families’ reinforce understanding of how operations connect.
孩子们还了解到加法和减法是相关联的。如果3 + 4 = 7，那么7 − 4 = 3且7 − 3 = 4。这些“运算家族”加强了对运算之间联系的理解。
6. Shapes and Patterns | 图形与模式
Learners explore common 2D flat shapes: circle, triangle, square, and rectangle. They describe shapes by the number of straight sides and corners (vertices). A square has 4 sides all the same length; a rectangle also has 4 sides but with opposite sides equal.
学习者探索常见的二维平面图形：圆形、三角形、正方形和长方形。他们通过直边和角（顶点）的数量描述图形。正方形有4条长度相等的边；长方形也有4条边，但对边相等。
3D solid shapes include cube, cuboid, sphere, and cylinder. Children learn to identify and name these solids, and they handle real objects to feel the faces, edges, and vertices. A cube has 6 square faces all the same size.
三维立体图形包括立方体、长方体、球体和圆柱体。孩子们学习辨认并命名这些立体图形，并通过触摸实物来感受面、棱和顶点。一个立方体有6个大小相同的正方形面。
Repeating patterns are made by arranging shapes, colours, or objects in a sequence that repeats. Common patterns include AB, AAB, ABB, and ABC. Learners copy, extend, and create their own patterns, which develops early algebraic thinking.
重复模式是通过按重复序列排列形状、颜色或物体而形成的。常见模式包括AB、AAB、ABB和ABC。学习者复制、拓展并创造自己的模式，这能够发展早期的代数思维。
7. Length and Height | 长度与高度
Comparing lengths and heights builds measurement vocabulary. Children use words like longer, shorter, taller, and the same to describe objects. Direct comparison means placing objects side by side and aligning the ends to see which extends further.
比较长度和高度能够丰富测量词汇。孩子们使用更长、更短、更高和一样来描述物体。直接比较意味着将物体并排放置并对齐一端，看哪一个延伸得更远。
Non-standard units are introduced next. Learners measure the length of a pencil using cubes, paperclips, or hand spans. They count how many units long an item is and record the number. This lays the groundwork for understanding standard units later.
接下来引入非标准单位。学习者用立方块、回形针或手拃测量铅笔的长度。他们点数物品有几个单位长并记录数字。这为以后理解标准单位打下基础。
Ordering objects from shortest to tallest or longest to shortest is a common task. Children may cut out pictures and arrange them. Problem-solving questions ask, ‘Which is longer, the pencil or the crayon? How many cubes longer?’
将物体从最短到最高或从最长到最短排序是一项常见任务。孩子们可能剪下图片并进行排列。解决问题的提问会问：“铅笔和蜡笔哪个更长？长几个方块？”
8. Mass and Capacity | 质量与容量
Mass is the amount of matter in an object, often felt as weight. Young learners compare mass by hefting objects in their hands. They use a balance scale to see which side is heavier or lighter. The language ‘ heavier than’, ‘ lighter than’, and ‘ about the same’ is practised.
质量是物体所含物质的量，通常感觉为轻重。低龄学习者通过用手掂量来比较质量。他们使用天平来看哪一边更重或更轻。练习了“比……重”、“比……轻”和“差不多一样”这些说法。
Capacity refers to how much a container can hold. Children compare the capacity of two containers by pouring water or rice from one to the other. They describe one as holding more and the other as holding less.
容量指的是一个容器能装多少东西。孩子们通过将一个容器里的水或大米倒入另一个来比较容量。他们会描述其中一个能装更多，另一个能装更少。
Practical activities involve deciding which container is the best for a given amount, or estimating how many small cups of water will fill a larger jug. These explorations are entirely hands-on and form the basis of measuring with standard units later.
实践活动包括决定哪个容器最适合给定的量，或者估计多少小杯水能装满一个大壶。这些探索完全是动手操作，为以后用标准单位测量打下基础。
9. Time | 时间
Children begin to understand time by sequencing events. They use words like morning, afternoon, evening, before, after, next, and then. Pictures of daily routines, such as waking up, eating breakfast, and going to school, are put in order.
孩子们通过给事件排序开始理解时间。他们使用早晨、下午、晚上、之前、之后、接下来和然后这样的词语。日常作息的图片，如起床、吃早餐和上学，会被按顺序排列。
Reading the hour on an analogue clock is introduced. Learners recognise the hour hand (short hand) and the minute hand (long hand). When the minute hand points to 12, the time is o’clock. They read and write times like 3 o’clock and 7 o’clock.
引入了读模拟钟面上的整点。学习者认识时针（短针）和分针（长针）。当分针指向12时，时间就是几点整。他们读写像3点整和7点整这样的时间。
Days of the week are learned in order: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. Questions might ask, ‘What day comes after Wednesday?’ or ‘Tomorrow is Friday, what day is it today?’
星期几的顺序是：星期一、星期二、星期三、星期四、星期五、星期六、星期日。问题可能会问：“星期三之后是星期几？”或者“明天是星期五，今天是星期几？”
10. Handling Data | 数据处理
Handling data in Year 1 involves collecting and organising simple information. Children sort objects by one or two attributes, such as colour and shape. They can then count how many items are in each group.
一年级的数据处理涉及收集和整理简单信息。孩子们按照一或两个属性（如颜色和形状）给物体分类。然后他们能点数每个组有多少个物品。
Pictograms are introduced as a way to show data. Each picture in a pictogram represents one object or person. Learners interpret pictograms by answering questions like, ‘Which has the most?’ or ‘How many children like apples?’
象形图被引入作为展示数据的一种方式。象形图中的每个图画代表一个物体或人。学习者通过回答问题来解释象形图，例如：“哪一个最多？”或“多少个孩子喜欢苹果？”
Block graphs are another simple chart. One block is coloured for each item counted. Children can compare the heights of the columns to see which is greatest or least. They might also use tally marks as a way to record data before making a graph.
方块图是另一种简单的图表。每数一个物品就涂一个方块。孩子们可以通过比较柱子的高低来看哪个最多或最少。他们还可能在制作图表前，使用画记符号来记录数据。
Understanding these early data representations helps children answer questions, draw conclusions, and begin to talk about information mathematically. This sets the stage for more advanced statistics in later years.
理解这些早期的数据表示法能帮助儿童回答问题、得出结论并开始用数学语言谈论信息。这为高年级更高级的统计学学习做好了准备。
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