Cambridge Primary Mathematics Workbook 1: A Complete Guide to Stage 1 Maths — 剑桥小学数学练习册1完全指南

📚 Cambridge Primary Mathematics Workbook 1: A Complete Guide to Stage 1 Maths | 剑桥小学数学练习册1完全指南：第一学段数学核心内容

剑桥小学数学（Cambridge Primary Mathematics）是剑桥大学国际考评部（Cambridge Assessment International Education）为全球5至11岁儿童设计的数学课程，覆盖第一学段到第六学段（Stage 1 至 Stage 6）。练习册1（Workbook 1）是整套系列的第一本，专为第一学段（Stage 1，约5至6岁，相当于英国小学一年级）的学生编写，与剑桥小学学生用书（Learner’s Book 1）配套使用。本书由 Cherri Moseley 和 Janet Rees 编写，第二版在内容和活动设计上更加注重动手操作、游戏化学习和数学思维的启蒙。

Cambridge Primary Mathematics is the mathematics curriculum designed by Cambridge Assessment International Education for children aged 5 to 11 around the world, covering Stage 1 to Stage 6. Workbook 1 is the first book in the whole series, written for Stage 1 learners (around 5 to 6 years old, equivalent to Year 1 in the UK). It is used together with Cambridge Primary Mathematics Learner’s Book 1. Written by Cherri Moseley and Janet Rees, the second edition places even more emphasis on hands-on activities, game-based learning and the early development of mathematical thinking.

这篇指南将逐单元梳理练习册1的核心内容，包括数数、加减法、图形、位置与运动、度量、数据处理和问题解决，并为家长提供在家辅导的具体方法。无论你的孩子正在使用这套教材，还是你想了解国际小学数学课程的框架，这篇文章都能帮你建立清晰的全局认识。

This guide walks through the core content of Workbook 1 unit by unit, including counting, addition and subtraction, shapes, position and movement, measures, handling data and problem solving, and gives parents practical ideas for supporting learning at home. Whether your child is using this textbook series or you simply want to understand the framework of an international primary mathematics curriculum, this article will give you a clear picture of the whole landscape.

1. How Workbook 1 Is Organised: Units, Progression and Working Style | 练习册1的编排：单元结构、进阶逻辑与学习方式

练习册1按照剑桥小学数学课程大纲（Cambridge Primary Mathematics Curriculum Framework）组织内容，覆盖第一学段的全部核心知识点。全书分为若干单元，每个单元围绕一个主题展开，例如”数到10″”数到20″”10以内的加减法””图形””位置与运动””度量””时间””数据处理”等。每个单元内的小节由浅入深，从最简单的认数开始，逐步过渡到计算、应用和推理。

Workbook 1 is organised according to the Cambridge Primary Mathematics Curriculum Framework and covers all the core learning objectives of Stage 1. The book is divided into units, each built around one theme such as Numbers to 10, Numbers to 20, Addition and Subtraction within 10, Shapes, Position and Movement, Measures, Time and Handling Data. Within each unit, sections progress from the simplest number recognition to calculation, application and reasoning.

这套教材强调”做中学”（learning by doing）。练习册中的活动大量使用实物操作（如数小棒、串珠子）、涂色、连线、画图、贴纸和游戏，而不是枯燥的机械计算。每道练习都配有清晰的图示，即使识字不多的孩子也能根据图形理解题目要求。这种设计符合5至6岁儿童的认知特点：具体形象思维占主导，抽象的数字符号必须建立在丰富的实物经验之上。

This series emphasises learning by doing. The activities in the workbook make extensive use of concrete manipulation (such as counting sticks and threading beads), colouring, matching, drawing, stickers and games, rather than dull mechanical calculation. Every exercise has clear pictures, so even children who cannot read well can understand what is being asked. This design matches the cognitive characteristics of 5 to 6 year olds: concrete and pictorial thinking dominates, and abstract number symbols must be built on rich hands-on experience.

单元主题	核心知识点	Unit theme	Core skills
数到10	数数、写数、比较多少	Numbers to 10	Counting, writing, comparing
数到20	十几的数、接着数、数轴	Numbers to 20	Teen numbers, counting on, number track
加减法	10以内加减、数字组合	Addition and subtraction	Within 10, number bonds
图形	平面与立体图形、模式	Shapes	2D and 3D shapes, patterns
位置与运动	左右、上下、旋转	Position and movement	Left and right, turns
度量	长度、质量、容量、时间	Measures	Length, mass, capacity, time
数据处理	分类、统计表、象形图	Handling data	Sorting, tally, pictograms

2. Numbers to 10: Counting, Writing and Comparing as the Foundation of Number Sense | 数到10：数数、写数与比较，数感的基石

第一学段的数学学习从”数到10″开始。这一单元的目标是让孩子能够：熟练地从0数到10，并能倒数；用手指、实物或图片一一对应地数出物体的数量；正确认读和书写数字0至9以及数字10；理解”多几个””少几个””一样多”的概念；掌握”比10多1″和”比10少1″（one more and one less）。这些技能看似简单，却是整个小学数学的地基：如果孩子不能把”5″这个符号和五根手指、五个圆点对应起来，后续所有的计算都会变成无意义的符号操练。

Mathematics learning in Stage 1 begins with Numbers to 10. The goals of this unit are for children to: count from 0 to 10 fluently and count backwards; count objects one by one using fingers, real objects or pictures; read and write the numerals 0 to 9 and the number 10 correctly; understand the ideas of more, fewer and the same; and master one more and one less. These skills look simple, but they are the foundation of all primary mathematics. If a child cannot connect the symbol 5 with five fingers or five dots, all later calculation becomes meaningless symbol manipulation.

练习册中常见的活动包括：给一排小动物涂上正确的颜色来表示数量；把数字和对应的圆点数量连线；在十格阵（ten-frame）里画圆点，直观感受5加几等于10；比较两组物体的多少，并在多的一组旁边画勾。家长在家可以用一副扑克牌或一把小石子做同样的事情：随手摆出4个和7个，问孩子哪边多、多几个。每天五分钟的口头数数（上楼梯数台阶、摆餐具数碗筷）就能显著提升孩子的数感。

Typical activities in the workbook include: colouring the correct number of animals to show a quantity; matching numerals to the correct number of dots; drawing dots in a ten-frame to see how many more are needed to make 10; and comparing two groups of objects, ticking the group with more. At home, parents can do the same with a pack of cards or a handful of pebbles: lay out 4 and 7 objects and ask which side has more and how many more. Just five minutes of oral counting every day (counting stairs, counting bowls and chopsticks at the table) significantly strengthens number sense.

这一单元还引入”零”的概念。0表示”一个也没有”，它既是一个数字，也表示”空”。孩子需要理解：当一个物体都没有的时候，我们用0来表示。练习册会用空篮子、空鱼缸这样的图来帮助孩子建立0的直观印象。理解0是理解位值（place value）和后续十位、个位概念的起点。

This unit also introduces zero. Zero means nothing is there; it is both a numeral and a symbol for empty. Children need to understand that when there are no objects, we write 0. The workbook uses pictures of empty baskets and empty fish tanks to build this intuition. Understanding zero is the starting point for place value and, later, the tens and ones concepts.

3. Numbers to 20: Teen Numbers, Counting On and the Number Track | 数到20：十几的数、接着数与数轴

掌握0到10之后，孩子进入”数到20″的单元。这一单元的难点在于”十几”的数（11至19）：这些数字的名称和书写并不规则（例如11不是”十和一”的直译），孩子需要通过数数实践来熟悉它们的顺序和大小。练习册会用”10个一组再加零头”的方式展示十几的数，例如10个圆点加3个圆点就是13，帮助孩子理解十几 = 10 + 几的结构。

After mastering 0 to 10, children move to the Numbers to 20 unit. The tricky part here is the teen numbers (11 to 19): their names and spellings are irregular (11 is not literally ten-one), so children need counting practice to become familiar with their order and size. The workbook shows teen numbers as one group of ten plus some extra ones, for example ten dots plus three dots is 13, helping children understand that a teen number means 10 plus some more.

“接着数”（counting on）是这一单元引入的重要策略：从任意一个数开始继续数下去。例如，数出8个积木后再放3个，孩子不需要重新从1开始数，而是从8接着数：9、10、11。这是从”数数”过渡到”加法”的关键一步。练习册会用数轴（number track 或 number line）让孩子看到数字的先后顺序，并用箭头表示”向前走”和”向后走”，为加减法的图像化打下基础。

Counting on is a key strategy introduced in this unit: starting from any number and continuing to count. For example, after counting 8 blocks and adding 3 more, the child does not need to start again from 1; they count on from 8: 9, 10, 11. This is the crucial step from counting to addition. The workbook uses number tracks and number lines to show the order of numbers, with arrows for moving forwards and backwards, laying the pictorial foundation for addition and subtraction.

到这一单元结束时，孩子应该能够：从任意数数到20并倒数；正确书写11至20；比较20以内的两个数的大小；说出任何一个20以内数的”前一个”和”后一个”。家长可以在外出散步时和孩子玩”接着数”游戏：你说”从12开始数5个”，孩子数13、14、15、16、17。这类口头游戏不需要任何材料，随时可以进行。

By the end of this unit, children should be able to: count from any number up to 20 and backwards; write 11 to 20 correctly; compare the size of two numbers within 20; and say the number before and the number after any number within 20. Parents can play a counting-on game on a walk: you say start from 12 and count 5 numbers, and the child counts 13, 14, 15, 16, 17. These oral games need no materials and can be played anywhere.

4. Addition Within 10: Number Bonds and the Part-Whole Model | 10以内加法：数字组合与整体-部分模型

加法是运算能力的第一步。在第一学段，孩子只需要掌握10以内的加法，但重点是理解加法的意义，而不只是背答案。加法的两种常见情境是”合并”（把两组东西合在一起）和”增加”（在一组东西上再添几个）。练习册会反复用实物图呈现这两种情境，让孩子先说故事（例如”树上有3只鸟，又飞来了2只，现在一共有5只”），再写算式3 + 2 = 5。

Addition is the first step in calculation. In Stage 1, children only need addition within 10, but the focus is on understanding what addition means, not just memorising answers. The two common situations for addition are combining (putting two groups together) and increasing (adding more to a group). The workbook repeatedly uses pictures of real objects for both situations, asking children first to tell a story (for example, there are 3 birds in the tree, 2 more fly in, now there are 5) and then to write the equation 3 + 2 = 5.

“数字组合”（number bonds）是这一单元的核心工具：一个数可以拆成两个（或更多）部分的和。例如，10可以拆成1和9、2和8、3和7、4和6、5和5。熟练记住10以内的数字组合，是将来学习进位加法和退位减法的前提。练习册用”整体-部分”图（part-whole diagram）：一个大圆圈代表整体，两个小圆圈代表部分，让孩子在空白处填数。这种模型把加减法统一起来：知道两个部分可以求整体（加法），知道整体和一个部分可以求另一个部分（减法）。

Number bonds are the core tool of this unit: a number can be split into the sum of two (or more) parts. For example, 10 can be split into 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5. Fluency with number bonds within 10 is the prerequisite for later carrying addition and borrowing subtraction. The workbook uses part-whole diagrams: one large circle for the whole and two small circles for the parts, with blanks for children to fill in. This model unifies addition and subtraction: knowing the parts lets you find the whole (addition); knowing the whole and one part lets you find the other part (subtraction).

整体	部分1 + 部分2	Whole	Part 1 + Part 2
6	1 + 5, 2 + 4, 3 + 3	6	1 + 5, 2 + 4, 3 + 3
8	1 + 7, 2 + 6, 3 + 5, 4 + 4	8	1 + 7, 2 + 6, 3 + 5, 4 + 4
10	1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5	10	1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5

练习册还会通过”调换顺序结果不变”（加法的交换律）来减少记忆负担：3 + 4 和 4 + 3 的结果一样，所以记住一个就算记住两个。家长在家玩”凑十”游戏非常有效：轮流掷骰子，掷出几就在十格阵上补几，看谁能最快凑满10。这种游戏化练习能让数字组合的掌握变得自然而牢固。

The workbook also uses the commutative property (swapping the order does not change the answer) to reduce memory load: 3 + 4 and 4 + 3 give the same result, so learning one covers both. A make-ten game at home works brilliantly: take turns rolling a dice, then fill the ten-frame with the rolled number and see who can complete 10 fastest. Game-based practice makes number bonds stick naturally and firmly.

5. Subtraction Within 10: Taking Away, Finding the Difference and Fact Families | 10以内减法：拿走、求差与算式家族

减法与加法同样重要，而且它们是一对”好朋友”。第一学段的孩子需要掌握两种减法情境：一是”拿走”（take away），例如盘子里有7块饼干，吃掉3块，还剩几块；二是”求差”（finding the difference），例如小明有7张贴纸，小红有4张，小明比小红多几张。练习册分别用”划掉”（cross out）和”一一对应连线”两种图示来呈现这两种情境，帮助孩子理解减法的两种含义。

Subtraction is just as important as addition, and the two are best friends. Stage 1 children need two subtraction situations: taking away (there are 7 biscuits on the plate, 3 are eaten, how many are left?) and finding the difference (Xiaoming has 7 stickers and Xiaohong has 4; how many more does Xiaoming have?). The workbook uses crossing out for the first situation and one-to-one matching lines for the second, helping children understand the two meanings of subtraction.

“算式家族”（fact families）是连接加减法的桥梁：三个相关的数可以组成四个算式。以2、5、7为例：2 + 5 = 7，5 + 2 = 7，7 – 2 = 5，7 – 5 = 2。孩子只要理解整体-部分模型，就能从一个加法事实推出另外三个。练习册会用三角形排列三个数（两个小角是部分，顶角是整体），让孩子把四个算式都写出来。这种训练能极大提升计算流畅度，也为将来的心算打基础。

Fact families are the bridge connecting addition and subtraction: three related numbers make four equations. Take 2, 5 and 7: 2 + 5 = 7, 5 + 2 = 7, 7 – 2 = 5 and 7 – 5 = 2. Once a child understands the part-whole model, they can derive the other three facts from a single addition. The workbook arranges the three numbers in a triangle (the two corners are the parts, the top is the whole) and asks children to write all four equations. This training greatly improves calculation fluency and lays the foundation for mental arithmetic.

这一单元结束时，孩子应该能熟练口算10以内的加减法，并会用”画图”或”数手指”来检查自己的答案。需要提醒的是，第一学段不要求速度竞赛，理解优先：宁可让孩子慢慢画图算对，也不要急于背诵结果而忽略了加减法的意义。

By the end of this unit, children should be able to calculate addition and subtraction within 10 fluently and check their answers by drawing or using fingers. One reminder: Stage 1 does not require speed contests. Understanding comes first. It is better for a child to draw carefully and get the right answer than to memorise results quickly while missing the meaning of addition and subtraction.

6. 2D and 3D Shapes: Naming, Sorting and Describing Properties | 二维与三维图形：命名、分类与描述特征

几何学习从认识图形开始。练习册1要求孩子认识并命名常见的平面图形：圆形（circle）、三角形（triangle）、正方形（square）、长方形（rectangle），以及常见的立体图形：正方体（cube）、长方体（cuboid）、球（sphere）、圆柱（cylinder）和圆锥（cone）。孩子不需要背诵术语定义，而是通过观察、触摸、滚动和堆叠来积累经验：球能滚动，圆柱也能滚动但只能沿一个方向；正方体的六个面都一样大，长方体则不一定。

Geometry begins with recognising shapes. Workbook 1 asks children to recognise and name common 2D shapes (circle, triangle, square, rectangle) and common 3D shapes (cube, cuboid, sphere, cylinder and cone). Children do not need to recite definitions; instead they build experience by looking, touching, rolling and stacking: a sphere rolls, a cylinder also rolls but only one way; all six faces of a cube are the same size, while a cuboid’s faces may differ.

描述图形特征是本单元的语言训练重点。对平面图形，孩子要学会说”有几条边””有几个角”：三角形有3条边3个角，正方形和长方形都有4条边4个角。对立体图形，孩子要接触”面”（face）的概念：正方体和长方体都有6个面，圆柱有2个圆形底面加1个曲面。练习册的典型活动包括：按形状给图形分类，找出”不属于同一类”的图形，以及用图形拼出图案（pattern）。

Describing properties is the language focus of this unit. For 2D shapes, children learn to say how many sides and corners: a triangle has 3 sides and 3 corners; a square and a rectangle both have 4 sides and 4 corners. For 3D shapes, children meet the idea of faces: a cube and a cuboid both have 6 faces; a cylinder has 2 circular faces plus 1 curved surface. Typical workbook activities include sorting shapes into groups, finding the odd one out, and making patterns with shapes.

“模式”（pattern）是早期代数思维的萌芽。练习册让孩子观察并延续重复模式，例如红-蓝-红-蓝，或者圆形-三角形-圆形-三角形，并自己创造新的模式。识别和延续模式能训练孩子的预测能力和规律意识，这是将来学习数列、乘法口诀和函数概念的隐性准备。家长可以和孩子一起用乐高积木或贴纸摆出 ABAB 模式，再挑战 ABCABC 模式。

Patterns are the seed of early algebraic thinking. The workbook asks children to observe and continue repeating patterns such as red-blue-red-blue or circle-triangle-circle-triangle, and to invent their own. Recognising and continuing patterns trains prediction and an awareness of regularity, which is the hidden preparation for number sequences, times tables and functions later on. Parents can build ABAB patterns with building bricks or stickers, then challenge the child with ABCABC patterns.

7. Position and Movement: Left and Right, Above and Below, and Turns | 位置与运动：左右、上下与旋转方向

位置与运动单元培养孩子的空间意识。孩子需要掌握描述位置的词汇：上面（above）、下面（below）、前面（in front of）、后面（behind）、左边（left）、右边（right）、里面（inside）、外面（outside）。练习册用”小动物在哪里”这样的场景图，让孩子根据描述指出物体位置，或者自己用语言描述图中物体的位置。

The Position and Movement unit develops spatial awareness. Children need vocabulary for describing position: above, below, in front of, behind, left, right, inside and outside. The workbook uses scenes such as where is the little animal, asking children to point at an object from a description or to describe the position of objects in the picture themselves.

这一单元还引入”旋转”（turns）的初步概念：四分之一转（quarter turn）、半转（half turn）、整转（full turn）以及顺时针（clockwise）和逆时针（anticlockwise）。孩子通过实际转动身体或玩具车来体验这些概念。例如，面朝教室门站着，向右做四分之一转，会面朝窗户。这种身体参与的学习方式（kinesthetic learning）对空间感的发展非常有效。

This unit also introduces the early idea of turns: quarter turns, half turns, full turns, and clockwise and anticlockwise directions. Children experience these by physically turning their bodies or toy cars. For example, facing the classroom door, a quarter turn to the right means facing the window. This kind of kinesthetic learning is very effective for developing spatial sense.

家长在家可以玩”机器人指令”游戏：孩子当机器人，家长发指令，例如”向前走两步，向左转，再走一步”，看机器人能否走到目标位置；然后交换角色。这类游戏同时训练听力理解、方向词汇和动作协调，是练习册活动的自然延伸。

At home, parents can play the robot game: the child is the robot, the parent gives commands such as take two steps forward, turn left, then one more step, and see whether the robot reaches the target; then swap roles. This game trains listening comprehension, direction vocabulary and motor coordination at the same time, and is a natural extension of the workbook activities.

8. Measures: Length, Mass, Capacity and Time | 度量：长度、质量、容量与时间

度量单元让孩子用比较的眼光看世界。在长度（length）方面，第一学段不要求使用尺子，而是先学会比较：比长、比短、比高、比矮。孩子用”一个接一个”（直接比较）或”用回形针、积木作单位”（非标准单位测量）来比较物体长度。例如，一支铅笔的长度大约等于6个回形针，另一支大约等于4个回形针，所以第一支更长。

The Measures unit teaches children to look at the world through comparison. For length, Stage 1 does not require rulers. Children first learn to compare: longer and shorter, taller and shorter. They compare by placing objects side by side (direct comparison) or by measuring with non-standard units such as paper clips or blocks. For example, one pencil is about 6 paper clips long and another is about 4, so the first one is longer.

质量（mass）和容量（capacity）同样以比较为主：哪个更重（heavier）、哪个更轻（lighter）、哪个容器装得更多（holds more）。练习册用天平（balance scale）的图画来表示质量比较，用大小不同的杯子表示容量比较。孩子需要理解：大的容器不一定装得更多，还要看形状。这类经验为将来学习标准单位（克、千克、升、毫升）打下直观基础。

Mass and capacity are also mainly about comparison: which is heavier, which is lighter, which container holds more. The workbook uses pictures of balance scales for mass and different-sized cups for capacity. Children learn that a bigger container does not always hold more; shape matters too. These experiences build the intuitive foundation for standard units (grams, kilograms, litres, millilitres) later.

时间（time）是本单元的另一重点。孩子要学习：按顺序排列日常事件（起床、吃早饭、上学）；认识一周七天的名称和先后顺序；认识一年十二个月；学会看整点时钟（o’clock），例如7点整、12点整。练习册会用”一天的活动”图画排序、星期表盘和整点时钟图来训练这些技能。家长可以每天固定时间问孩子：”现在几点了？””今天星期几？”让时间概念融入日常生活。

Time is another focus of this unit. Children learn to: order daily events (wake up, eat breakfast, go to school); know the seven days of the week in order; know the twelve months of the year; and read clocks at the hour (o’clock), for example 7 o’clock and 12 o’clock. The workbook uses picture sequencing of a day, week wheels and hour clock faces for these skills. Parents can ask at fixed times every day: what time is it now? what day is it today? to weave time concepts into daily life.

9. Handling Data: Sorting Objects, Tally Marks and Pictograms | 数据处理：分类、统计表与象形图

数据处理单元让孩子第一次接触”用图表说话”。首先是分类（sorting）：按照一个特征把物体分组，例如按颜色、按形状、按大小。分类是逻辑思维的起点，练习册会让孩子把一堆混合的图形卡片分成几堆，并说明分类的标准。

The Handling Data unit gives children their first taste of letting charts speak. It starts with sorting: grouping objects by one attribute such as colour, shape or size. Sorting is the starting point of logical thinking. The workbook asks children to sort a mixed pile of shape cards into groups and to explain the sorting rule.

接着是统计表（tally chart）和象形图（pictogram）。象形图用”一个图形代表一个物体”的方式记录数据，例如用一只小猫的图案代表一只宠物，把全班同学的宠物统计画成象形图，一眼就能看出哪种宠物最多。孩子要学会从图中读取信息：哪种最多（most）、哪种最少（fewest）、两种相差多少，并用”一共”（altogether）把总数加起来。

Next come tally charts and pictograms. A pictogram uses one picture to stand for one object, for example one cat picture for one pet, turning a class survey of pets into a pictogram where you can see at a glance which pet is most popular. Children learn to read information from the chart: which is the most, which is the fewest, how many more one is than another, and to add up the total (altogether).

家长在家可以和孩子做一次”家庭调查”：统计家里每个人最喜欢的颜色或水果，用贴纸或画勾的方式记录在纸上，然后一起讨论结果。整个过程不超过十分钟，却完整覆盖了”收集数据、记录数据、解读数据”的数据处理全流程，是练习册活动的最佳生活化延伸。

At home, parents can run a family survey: record everyone’s favourite colour or fruit with stickers or ticks on paper, then discuss the results together. The whole activity takes less than ten minutes yet covers the full data cycle of collecting, recording and interpreting data, making it the best real-life extension of the workbook activities.

10. Problem Solving and Reasoning: Word Problems That Build Thinking | 问题解决与推理：培养思维能力的文字题

数学学习的最终目标不是会算，而是会用。练习册1在每个单元都安排了问题解决（problem solving）活动，通常以文字题或情境图的形式出现。孩子需要：读懂题目（或看懂图），选择正确的运算，写出算式，并检查答案是否合理。例如：”小猫有4条鱼，又钓到3条，现在一共有几条？”孩子要能识别这是”合并”情境，用加法解决。

The ultimate goal of mathematics is not to calculate but to use. Workbook 1 includes problem solving activities in every unit, usually as word problems or picture situations. Children need to: read the question (or understand the picture), choose the right operation, write the equation and check whether the answer makes sense. For example: a cat has 4 fish and catches 3 more; how many does it have now? The child must recognise the combining situation and use addition.

推理（reasoning）在低年级以”解释和验证”的形式出现。练习册会问：”你是怎么知道的？””还有别的办法吗？””这个答案对吗？”这些问题没有标准答案，却训练孩子用语言组织自己的思考过程。能够把思考过程说出来，是数学理解成熟的标志。这也是剑桥课程强调的”数学交流”（mathematical communication）能力的一部分。

Reasoning appears at this age in the form of explaining and checking. The workbook asks: how do you know? is there another way? is this answer right? These questions have no standard answers but train children to organise their thinking in words. Being able to explain one’s thinking is a sign of mature mathematical understanding, and it is part of the mathematical communication that the Cambridge curriculum emphasises.

家长在辅导文字题时，最有效的做法不是直接告诉答案，而是提问引导：”题目里告诉了我们什么？””要求我们求什么？””用什么方法可以解决？””我们怎么检查答案？”这四个问题对应着审题、目标、策略和检验四个步骤，是小学阶段所有应用题通用的解题框架。

When helping with word problems, the most effective approach is not to give the answer but to ask guiding questions: what does the question tell us? what are we asked to find? what method can we use? how do we check the answer? These four questions correspond to the four steps of reading the problem, setting the goal, choosing a strategy and checking, a framework that works for all word problems through primary school.

11. How Parents Can Help: Using Workbook 1 at Home Effectively | 家长辅导建议：在家高效使用练习册1

练习册1的设计本身就对家长友好：每页都有明确的指令、图示和示例，家长即使不懂英语也可以根据图画理解题目要求。建议每天安排15至20分钟的固定练习时间，分两次进行：先做一页新内容，再做一页复习。短时高频的效果远好于周末一次性长时间突击。

Workbook 1 is designed to be parent-friendly: every page has clear instructions, pictures and examples, so parents who do not read English can still understand the tasks from the pictures. We recommend a fixed practice time of 15 to 20 minutes each day, split into two parts: one page of new content first, then one page of revision. Short frequent sessions work far better than one long weekend session.

以下是几条经过验证的辅导原则：第一，错误是学习资源，不要急着纠正，先让孩子自己检查（”你觉得对吗？怎么验证？”）；第二，把抽象题目变成实物操作，孩子卡住时拿出积木、珠子或手指；第三，用提问代替讲解，让孩子自己说出思路；第四，及时肯定努力而非结果（”你试了两种方法，很棒！”）；第五，把数学带进生活，购物时数零钱、分水果时平均分、做饭时看时间。

Here are several proven principles for tutoring: first, mistakes are learning resources; do not rush to correct, let the child check first (do you think it is right? how can you verify?). Second, turn abstract questions into concrete operations: bring out blocks, beads or fingers when the child is stuck. Third, replace explaining with questioning so the child voices their own reasoning. Fourth, praise effort rather than results (you tried two methods, well done!). Fifth, bring maths into life: count change when shopping, share fruit fairly, read the clock when cooking.

最后，保持合理预期。第一学段的数学目标不是提前学完更高年级的内容，而是建立扎实的数感、空间感和学习自信。如果孩子对某个知识点需要反复练习，这是完全正常的，正如练习册的名字一样，它本来就是用来”练”的。每天进步一点点，一年后的积累会非常可观。

Finally, keep expectations realistic. The goal of Stage 1 mathematics is not to finish higher-grade content early but to build solid number sense, spatial sense and learning confidence. If a child needs to practise a concept many times, that is completely normal; after all, as the name of the book says, it is a workbook, made for practising. A little progress every day adds up to something impressive over a year.

Summary | 总结

剑桥小学数学练习册1覆盖了第一学段的全部核心内容：从数到10、数到20的数数技能，到10以内加减法和数字组合，再到图形、位置与运动、度量、数据处理和问题解决。整本书的设计遵循”具体经验、图形表征、符号抽象”的认知路径，让孩子在动手操作中建立真正的数学理解，而不是机械记忆。

Cambridge Primary Mathematics Workbook 1 covers all the core content of Stage 1: counting skills from numbers to 10 and to 20, addition and subtraction within 10 with number bonds, then shapes, position and movement, measures, handling data and problem solving. The whole book follows the cognitive path of concrete experience, pictorial representation and symbolic abstraction, building genuine mathematical understanding through hands-on activity rather than rote memorisation.

对于家长来说，这套教材最大的价值在于它提供了一条清晰、系统、可操作的数学启蒙路线图。配合每天15至20分钟的练习、生活中的数学对话和充满耐心的鼓励，孩子完全可以在第一学段结束时具备扎实的数感、流畅的10以内计算能力和初步的问题解决思维，为第二学段乃至整个小学阶段的数学学习打下坚实的基础。

For parents, the greatest value of this textbook series is that it provides a clear, systematic and practical roadmap for early mathematics. Combined with 15 to 20 minutes of daily practice, mathematical conversations in daily life and patient encouragement, children can finish Stage 1 with solid number sense, fluent calculation within 10 and early problem-solving thinking, laying a strong foundation for Stage 2 and the whole of primary mathematics.

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