📚 Cambridge Primary Maths Learner's Book 4 Key Topics | 剑桥小学数学学习者用书4核心主题
Cambridge Primary Mathematics Learner's Book 4, second edition, builds on the foundation laid in earlier stages. Learners consolidate whole-number operations, explore fractions and decimals, and begin to work with measurement, geometry and data. This article summarises the key knowledge and skills needed for success in this stage, following the CIE Cambridge Primary Maths framework.
剑桥小学数学学习者用书第4册（第二版）在前几个阶段的基础上进一步发展。学习者巩固整数的运算，探索分数和小数，并开始学习测量、几何和数据。本文总结了本阶段取得成功所需的关键知识和技能，并遵循 CIE 剑桥小学数学课程框架。
1. Place Value and Number Sense | 位值与数感
In Book 4, learners extend their understanding of place value to five-digit numbers. They read, write, order and compare numbers up to 10 000, using digit cards, place-value charts and number lines.
在第4册中，学习者将位值理解扩展到五位数。他们使用数字卡片、位值表和数轴来读、写、排序和比较最大到 10 000 的数。
The key columns are ten-thousands, thousands, hundreds, tens and ones. For example, in 7 352, the digit 7 has a value of 7 000, the digit 3 has a value of 300, the digit 5 has a value of 50, and the digit 2 has a value of 2.
关键的位值列是万位、千位、百位、十位和个位。例如，在 7 352 中，数字 7 的值是 7 000，数字 3 的值是 300，数字 5 的值是 50，数字 2 的值是 2。
- Partitioning: 4 806 = 4 000 + 800 + 6
- Comparing: 9 321 > 8 999 because 9 thousands > 8 thousands
Learners also round numbers to the nearest ten, hundred and thousand, which supports estimation and mental calculation.
学习者还将数字四舍五入到最接近的十、百和千，这有助于估算和心算。
2. Addition and Subtraction Strategies | 加法与减法策略
At this stage, learners add and subtract numbers up to four digits using column methods. They also develop mental strategies such as counting on, counting back, rounding and adjusting.
在本阶段，学习者使用竖式方法对最大四位数的数字进行加减运算。他们还发展了心算策略，例如继续数、倒着数、取整和调整。
For example, to calculate 3 456 + 1 278, learners align digits by place value and carry when a column total exceeds 9. To subtract 2 045 - 768, they use regrouping from the thousands and hundreds columns.
例如，计算 3 456 + 1 278 时，学习者按位值对齐数字，并在某一列总和超过 9 时进位。计算 2 045 - 768 时，他们需要从千位和百位借位。
A key mental strategy is compensation: 298 + 47 can be worked out as 300 + 47 - 2 = 345.
一个关键的心算策略是补偿法：298 + 47 可以计算为 300 + 47 - 2 = 345。
Learners also solve one-step and two-step word problems involving addition and subtraction, choosing the correct operation and checking answers by using inverse operations.
学习者还解决涉及加法和减法的一步和两步文字题，选择正确的运算并通过逆运算检查答案。
3. Multiplication and Division Facts | 乘法与除法事实
nd use known facts to derive new ones, such as 6 × 7 = 42, so 60 × 7 = 420 and 42 ÷ 6 = 7.
第4册巩固了 12 × 12 以内的乘法表和相关的除法事实。学习者练习快速回忆，并利用已知事实推导新事实，例如 6 × 7 = 42，所以 60 × 7 = 420，42 ÷ 6 = 7。
ormal short multiplication. For example, 23 × 4 is split as 20 × 4 + 3 × 4 = 80 + 12 = 92.
他们使用网格法和正式短乘法将两位数或三位数乘以一位数。例如，23 × 4 分解为 20 × 4 + 3 × 4 = 80 + 12 = 92。
s in real contexts, such as 25 ÷ 4 = 6 remainder 1, meaning 6 full groups and 1 left over.
除法作为平均分和分组来教授，包括有余数和没有余数的情况。学习者理解余数在实际情境中的含义，例如 25 ÷ 4 = 6 余 1，表示 6 个整组，剩下 1。
4. Fractions and Mixed Numbers | 分数与带分数
Learners build on their knowledge of unit and non-unit fractions. They recognise equivalent fractions, compare and order fractions with the same denominator, and begin to add and subtract fractions with the same denominator.
学习者在单位分数和非单位分数知识的基础上继续学习。他们识别等值分数，比较和排序同分母分数，并开始对同分母分数进行加减运算。
e shown using fraction walls and number lines. For example, 1/2 = 2/4 = 4/8 and 3/4 = 6/8.
等值分数通过分数墙和数轴展示。例如，1/2 = 2/4 = 4/8，3/4 = 6/8。
w the rule of keeping the denominator the same: 2/5 + 1/5 = 3/5 and 7/8 - 3/8 = 4/8 = 1/2.
加减运算遵循分母不变的规则：2/5 + 1/5 = 3/5，7/8 - 3/8 = 4/8 = 1/2。
s. Learners convert between improper fractions and mixed numbers, for example 5/2 = 2 1/2.
通过整体和部分的图片引入带分数，如 1 1/2 和 2 3/4。学习者在假分数和带分数之间进行转换，例如 5/2 = 2 1/2。
5. Decimals: Tenths and Hundredths | 小数：十分位和百分位
Decimals are introduced as another way of writing fractions with denominators 10 and 100. Learners connect tenths and hundredths to place value and to money and measurement contexts.
小数作为分母为 10 和 100 的分数的另一种写法引入。学习者将十分位和百分位与位值以及货币和测量情境联系起来。
For example, 0.3 means 3/10, and 0.25 means 25/100. On a place-value chart, the columns to the right of the decimal point are tenths and hundredths.
例如，0.3 表示 3/10，0.25 表示 25/100。在位值表中，小数点右边的列是十分位和百分位。
Learners compare decimals by looking at the tenths first, then the hundredths. They order decimals such as 0.6, 0.45 and 0.7 on a number line.
学习者先看十分位再看百分位来比较小数。他们在数轴上对 0.6、0.45 和 0.7 等小数进行排序。
nd subtraction of decimals up to two decimal places are practised in the context of money: £2.35 + £1.20 = £3.55 and £5.00 - £2.75 = £2.25.
在货币情境中练习最多两位小数的加法和减法：£2.35 + £1.20 = £3.55，£5.00 - £2.75 = £2.25。
0.25 = 25/100 = 1/4
6. Measurement: Length, Mass and Capacity | 测量：长度、质量与容量
Learners measure and convert between common units. For length, they use millimetres (mm), centimetres (cm), metres (m) and kilometres (km). For mass, they use grams (g) and kilograms (kg). For capacity, they use millilitres (ml) and litres (l).
学习者测量并换算常用单位。长度使用毫米（mm）、厘米（cm）、米（m）和千米（km）；质量使用克（g）和千克（kg）；容量使用毫升（ml）和升（l）。
ons include 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1 000 m, 1 kg = 1 000 g and 1 l = 1 000 ml.
关键换算包括 1 cm = 10 mm、1 m = 100 cm、1 km = 1 000 m、1 kg = 1 000 g 和 1 l = 1 000 ml。
Learners read scales on rulers, weighing scales and measuring jugs, including scales with intervals of 2, 5, 10, 20 and 100. They solve problems involving lengths, masses and capacities in real contexts.
学习者读取直尺、体重秤和量杯上的刻度，包括间隔为 2、5、10、20 和 100 的刻度。他们解决涉及长度、质量和容量的实际情境问题。
xample a rectangle with length 6 cm and width 4 cm has a perimeter of 2 × (6 + 4) = 20 cm.
简单图形的周长被引入。学习者将所有边长相加，例如长 6 cm、宽 4 cm 的长方形周长为 2 × (6 + 4) = 20 cm。
7. Time and Calendar | 时间与日历
This section focuses on reading analogue and digital clocks to the nearest minute. Learners convert between 12-hour and 24-hour time and calculate time intervals.
本节重点是读取模拟钟表和数字钟表，精确到分钟。学习者进行 12 小时制和 24 小时制之间的转换，并计算时间间隔。
For example, a film starts at 14:30 and ends at 16:10. The duration is 1 hour 40 minutes. Learners also solve problems involving days, weeks, months and years, including leap years.
例如，一部电影在 14:30 开始，16:10 结束，时长为 1 小时 40 分钟。学习者还解决涉及日、周、月、年的问题，包括闰年。
day = 24 hours, 1 week = 7 days, and 1 year = 12 months or 365 days (366 in a leap year).
关键事实包括：1 分钟 = 60 秒，1 小时 = 60 分钟，1 天 = 24 小时，1 周 = 7 天，1 年 = 12 个月或 365 天（闰年为 366 天）。
Using a calendar, learners find dates, count the number of days between two dates, and understand the order of months.
学习者使用日历查找日期，计算两个日期之间的天数，并理解月份的顺序。
8. Geometry: 2D and 3D Shapes | 几何：平面与立体图形
Learners identify, describe and classify 2D shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons. They use properties such as number of sides, number of vertices and whether sides are equal or parallel.
学习者识别、描述和分类平面图形，包括三角形、四边形、五边形、六边形和八边形。他们使用边数、顶点数以及边是否相等或平行等性质。
Triangles are classified as equilateral, isosceles or scalene based on side lengths, and as right-angled, acute-angled or obtuse-angled based on angles.
三角形根据边长分为等边三角形、等腰三角形和不等边三角形；根据角度分为直角三角形、锐角三角形和钝角三角形。
For 3D shapes, learners recognise cubes, cuboids, spheres, cylinders, cones, pyramids and prisms. They count faces, edges and vertices. For example, a cube has 6 faces, 12 edges and 8 vertices.
对于立体图形，学习者识别立方体、长方体、球体、圆柱体、圆锥体、棱锥体和棱柱体。他们数面、棱和顶点。例如，一个立方体有 6 个面、12 条棱和 8 个顶点。
Symmetry is also explored. Learners identify lines of symmetry in 2D shapes and complete symmetric patterns.
还探讨了对称性。学习者识别平面图形中的对称轴，并补全对称图案。
9. Data Handling and Graphs | 数据处理与图表
Learners collect, organise and represent data using pictograms, bar charts and tally charts. They interpret information from these representations and answer questions about the data.
学习者使用象形图、条形图和计数表收集、整理和表示数据。他们解读这些表示中的信息并回答有关数据的问题。
In a pictogram, each symbol may represent one unit or several units. Learners use a key to understand the scale, for example one circle represents 2 children.
在象形图中，每个符号可能代表一个单位或多个单位。学习者使用图例来理解比例，例如一个圆圈代表 2 个儿童。
Bar charts have labelled axes and bars of equal width. Learners read values from the vertical axis and compare the heights of bars. They also identify the mode as the most frequent value.
条形图有标记的坐标轴和等宽的条。学习者从纵轴读取数值并比较条形的高度。他们还识别众数为出现频率最高的值。
Simple two-way tables and Carroll diagrams are introduced to sort objects by two criteria, such as shape and colour.
引入简单的双向表和卡罗尔图，根据两个标准（如形状和颜色）对物体进行分类。
10. Problem Solving and Reasoning | 问题解决与推理
Throughout Book 4, learners apply their mathematical knowledge to solve routine and non-routine problems. They use strategies such as drawing diagrams, looking for patterns, working backwards and making a list.
在第4册中，学习者始终应用数学知识解决常规和非常规问题。他们使用画图、寻找规律、倒推和列表等策略。
For example, a problem may ask: 'Tom has twice as many marbles as Ali. Together they have 36 marbles. How many does each have?' Learners can use a bar model to see that Ali has 12 and Tom has 24.
例如，一道题可能会问：“汤姆的弹珠是阿里的两倍。他们一共有 36 颗弹珠。每人有多少颗？”学习者可以使用条形模型看出阿里有 12 颗，汤姆有 24 颗。
Reasoning tasks require learners to explain their thinking, justify whether a statement is always, sometimes or never true, and check answers using estimation or inverse operations.
推理任务要求学习者解释自己的思路，判断一个陈述是总是、有时还是从不为真，并使用估算或逆运算检查答案。
Developing these habits early helps learners build the confidence needed for more advanced primary mathematics and beyond.
尽早培养这些习惯有助于学习者建立信心，为更高级的小学数学及以后的学习做好准备。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图