📚 Cambridge Primary Mathematics Workbook 4 (2nd Edition) | 剑桥小学数学练习册4（第二版）
This revision guide covers the key content in Cambridge Primary Mathematics Workbook 4, 2nd Edition by Mary Wood and Emma Low. The workbook is designed for learners aged 8 to 10 and follows the Cambridge Primary Maths framework. Each section below summarises a major topic, highlights common misconceptions, and offers practical strategies for independent practice or guided revision.
本复习指南涵盖Mary Wood与Emma Low编写的《剑桥小学数学练习册4（第二版）》的核心内容。该练习册面向8至10岁学习者，遵循剑桥小学数学课程框架。以下各节总结主要主题，指出常见误区，并提供独立练习或指导复习的实用策略。
1. Place Value and Number Sense | 位值与数感
Learners extend their understanding of whole numbers up to 10 000, reading and writing four-digit numbers, and recognising the value of each digit. For example, in 3 742 the digit 3 represents 3 000, 7 represents 700, 4 represents 40 and 2 represents 2.
学习者将整数理解扩展到10 000，读写四位数，并识别每个数字的值。例如，在3 742中，数字3表示3 000，7表示700，4表示40，2表示2。
A common mistake is confusing the digit value with the digit itself, especially with zeros. In 2 087, the zero is a place holder, so the number is 2 000 + 80 + 7, not 2 000 + 800 + 7 or 2 000 + 87.
一个常见错误是将数字本身与其位值混淆，尤其是在有零的情况下。在2 087中，零是占位符，因此该数为2 000 + 80 + 7，而不是2 000 + 800 + 7或2 000 + 87。
Practice activities include ordering numbers, using number lines, and partitioning numbers in different ways. These skills are essential for later work in addition, subtraction, estimation and mental calculation.
练习活动包括排列数字、使用数轴以及以不同方式拆分数字。这些技能对以后的加法、减法、估算和心算至关重要。
2. Addition and Subtraction Strategies | 加法与减法策略
Workbook 4 reinforces column addition and subtraction with up to four digits, including regrouping. Learners are encouraged to choose between mental methods, number lines, and written column methods depending on the size of the numbers.
练习册4强化了最多四位数的竖式加法和减法，包括进位和借位。鼓励学习者根据数字大小选择心算、数轴或竖式书写方法。
When subtracting across zeros, such as 5 000 - 2 364, learners often make errors because they try to subtract in one step. A reliable method is to regroup step by step: 5 000 becomes 4 999 + 1, then subtract 2 364 from 4 999 and add 1, giving 2 636.
在跨零减法中，例如5 000 - 2 364，学习者常常因为试图一步完成而出错。一个可靠的方法是逐步重组：将5 000写成4 999 + 1，然后从4 999中减去2 364再加1，得到2 636。
Estimation is also practised: rounding to the nearest 10 or 100 before calculating helps learners check whether their answer is reasonable.
估算也需要练习：计算前先四舍五入到最接近的10或100，有助于学习者判断答案是否合理。
3. Multiplication and Division Facts | 乘法与除法事实
he workbook provides repeated practice through grids, puzzles, and missing-number problems.
到第四阶段结束时，学习者应能记住12 × 12以内的乘法事实以及相关的除法事实。练习册通过网格、谜题和缺失数字问题提供反复练习。
= 420. This links place value to multiplication and prepares learners for written methods.
关键策略包括利用已知事实推导新事实：如果6 × 7 = 42，那么60 × 7 = 420，6 × 70 = 420。这将位值与乘法联系起来，为书写方法做好准备。
Learners must interpret the remainder in context, such as 38 pupils being placed in groups of 5 leaves 3 pupils without a full group.
引入带余数的除法，例如38 ÷ 5 = 7余3。学习者必须根据情境解释余数，例如38名学生按5人分组，则余3人无法组成完整小组。
4. Fractions and Equivalence | 分数与等值
Workbook 4 develops understanding of unit and non-unit fractions, equivalent fractions, and fractions of quantities. Learners use fraction walls, bar models, and number lines to compare fractions such as ½, ¼, ¾, ⅓, and ⅔.
练习册4发展了对单位分数和非单位分数、等值分数以及数量的几分之几的理解。学习者使用分数墙、条形模型和数轴来比较½、¼、¾、⅓和⅔等分数。
dividing both numerator and denominator by the same number creates an equivalent fraction.
一个关键概念是同一个分数可以写成多种形式：½ = 2/4 = 3/6 = 4/8。将分子和分母同时乘以或除以同一个数可得到等值分数。
dividing by the denominator and multiplying by the numerator: 20 ÷ 4 = 5, then 5 × 3 = 15.
求一个数量的几分之几，例如20的¾，方法是先除以分母再乘以分子：20 ÷ 4 = 5，然后5 × 3 = 15。
5. Decimals and Money | 小数与货币
d measurement. They learn that 0.1 = 1/10 and 0.01 = 1/100, and that 0.5 is the same as ½.
学习者主要通过货币和测量接触十分位和百分位的小数记法。他们学习0.1 = 1/10，0.01 = 1/100，以及0.5等于½。
Money contexts such as £3.45 help learners understand place value in decimals: 3 pounds, 4 tenths of a pound (40p), and 5 hundredths of a pound (5p). Comparing amounts and giving change are common tasks.
英镑3.45等货币情境帮助学习者理解小数的位值：3英镑、4个十分之一英镑（40便士）和5个百分之一英镑（5便士）。比较金额和找零是常见任务。
A common error is writing 3.5 as 3.05 or thinking 3.9 is smaller than 3.10 because 9 is less than 10. Using a number line from 3.0 to 4.0 helps clarify the order.
常见错误是将3.5写成3.05，或者认为3.9小于3.10，因为9小于10。使用3.0到4.0的数轴有助于澄清顺序。
6. Measurement: Length, Mass and Capacity | 测量：长度、质量与容量
. Learners convert between units such as 1 km = 1 000 m, 1 m = 100 cm, and 1 kg = 1 000 g.
本节涵盖标准单位：毫米、厘米、米、千米、克、千克、毫升和升。学习者进行单位换算，例如1 km = 1 000 m，1 m = 100 cm，1 kg = 1 000 g。
Reading scales is a central skill. Learners must identify the value of each
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