Common Mistakes in Cambridge Primary Mathematics Workbook 3, 2nd Edition | 剑桥小学数学练习册3（第二版）易错点总结

📚 Common Mistakes in Cambridge Primary Mathematics Workbook 3, 2nd Edition | 剑桥小学数学练习册3（第二版）易错点总结

Cambridge Primary Mathematics Workbook 3 (2nd Edition) is designed for learners aged 7–8, covering key concepts such as place value up to 1000, addition and subtraction with regrouping, multiplication tables for 3, 4 and 8, basic fractions, measurement, time, geometry and data handling. Many students encounter similar stumbling blocks when working through the exercises. This article summarises the most common mistakes and provides clear explanations to help learners avoid them.

《剑桥小学数学练习册3》（第二版）面向7至8岁的学生，涵盖了1000以内的位值、进位加法和退位减法、3、4和8的乘法表、基础分数、测量、时间、几何以及数据处理等核心知识。许多学生在完成练习时都会遇到相似的障碍。本文汇总了最常见的易错点，并给出清晰的解释，帮助学习者规避这些错误。

1. Place Value and Number Representation | 位值与数字表示

When writing three-digit numbers that contain a zero, pupils often omit the zero or place it in the wrong column. For instance, 806 may be written as 86 because the zero in the tens column is left out.

在书写包含零的三位数时，学生经常漏掉零或将其放错数位。例如，806可能被写成86，因为十位上的零被遗漏了。

Some learners reverse the order of digits when the number is spoken, such as writing ‘five hundred and thirteen’ as 531 instead of 513.

有些学习者在听写数字时会颠倒数位顺序，比如将“五百一十三”写成531而非513。

In comparing numbers up to 1000, a common error is to look only at the first digit, assuming 67 is larger than 102 because 6 > 1.

在比较1000以内的数时，常见的错误是只看第一个数字，误以为67大于102，因为6 > 1。

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2. Addition with Carrying | 进位加法

When adding two-digit numbers that require regrouping, learners often forget to add the carried ‘1’ to the tens column. For example, in 27 + 38, they may calculate 7 + 8 = 15, write 5, and then add 2 + 3 to get 5, writing the answer as 55 instead of 65.

在进行需要进位的两位数加法时，学生常常忘记将进位的“1”加到十位上。例如，在计算27 + 38时，他们可能算出7 + 8 = 15，写下5，然后计算2 + 3得5，得出答案55而非65。

Another mistake is carrying a digit but placing it in the wrong column, which happens especially when adding three-digit numbers.

另一个错误是进位了但将进位数字放错了数位，这在三位数加法中尤其常见。

Using a clear layout and a small ‘1’ above the next column reminds the student to include the carry.

使用清晰的书写格式，在下一列上方标出小小的“1”，可以提醒学生把进位算进去。

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3. Subtraction with Borrowing | 退位减法

The most frequent error in subtraction is failing to reduce the digit in the borrowing column after taking a ten. For 52 − 27, a pupil may say ‘2 − 7 cannot do, so borrow 1 from 5’, make it 12 − 7 = 5, but then forget to change the 5 to 4, so they subtract 2 from 5 and get 3, writing 35.

减法中最常见的错误是退位后忘记将被借位的那一列数字减少。例如52 − 27，学生可能会说“2 − 7不够，从5借1”，变成12 − 7 = 5，但随后忘记把5变成4，于是用5减2得3，写下35。

When borrowing across a zero, e.g. in 300 − 126, many children become confused because they need to borrow from the hundreds place and adjust the tens place. They might write 300 as 2 hundreds, 9 tens and 10 ones incorrectly.

当需要跨零借位时，例如300 − 126，很多孩子会感到混乱，因为他们需要从百位借位并调整十位。他们可能会错误地将300写成2个百、9个十和10个一。

To avoid this, encourage using decomposition step by step: 300 = 200 + 90 + 10, then subtract.

为避免此类错误，可鼓励逐步分解：300 = 200 + 90 + 10，再逐位相减。

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4. Multiplication Facts for 3, 4 and 8 | 3、4和8的乘法口诀

Many learners mix up multiplication facts, especially between the 3, 4 and 8 times tables. A typical slip is giving 4 × 8 = 36 or 3 × 8 = 28.

许多学习者会混淆乘法口诀，特别是在3、4和8的乘法表之间。常见的错误如4 × 8 = 36，或3 × 8 = 28。

Another issue is that pupils may know the recitation of tables but cannot apply them to missing-number problems like ___ × 8 = 48.

另一个问题是学生可能能够背诵口诀表，但无法将其应用于如 ___ × 8 = 48 这样的填空问题。

Drill and regular practice with related division facts are essential to build fluency. Displaying a multiplication grid helps them spot patterns.

通过反复练习和相关的除法事实进行巩固，对于建立流利度至关重要。展示乘法方格表有助于他们发现规律。

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5. Division and the Idea of Remainders | 除法与余数的概念

When dividing, some students think that any number that does not divide equally is ‘impossible’, rather than accepting a remainder. For instance, when asked 25 ÷ 4, they might answer ‘6 remainder 1’ but then write the answer as simply 6.

在进行除法运算时，一些学生认为不能整除的数“无法除”，而不是接受有余数。例如，当被问到25 ÷ 4时，他们可能回答“6余1”，但随后只写下6作为答案。

They also frequently misinterpret the remainder in context. In a problem like ‘28 children need to sit in groups of 6; how many groups are formed?’, the answer is 4 groups with 4 children left over, but a child might say 5 groups because they round up.

他们还经常误解余数在实际问题中的意义。在如“28个孩子需要每6人一组，能分成多少组？”的问题中，答案是4组，余下4个孩子，但孩子可能会说5组，因为他们向上取整了。

Using physical objects or drawing diagrams helps clarify why the remainder is part of the answer and what it represents.

使用实物或画图有助于阐明为什么余数是答案的一部分以及它代表什么。

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6. Understanding and Comparing Fractions | 分数的理解与比较

A very common misconception is that 1/5 is larger than 1/3 because 5 > 3. Learners fail to realise that the larger the denominator, the smaller each equal part becomes.

一个非常普遍的误解是认为1/5大于1/3，因为5 > 3。学习者没有意识到分母越大，每一等分就越小。

Another error is when identifying fractions of shapes that are not split into equal parts; a child might say a shape is 1/4 red even though the red part is clearly larger than the others.

另一个错误是在识别图形分数时，如果图形没有被均分，孩子可能会说一个图形有1/4是红色，即使红色部分明显比其他部分大。

When shading a fraction of a set of objects, they may shade the wrong number of objects because they confuse the numerator and denominator. They might shade 3 out of 4 objects when asked to show 1/4.

在给一组物体涂色表示分数时，他们可能涂错数量，因为混淆了分子和分母。当要求表示1/4时，他们可能涂了4个物体中的3个。

To counter these misconceptions, always use fraction strips and practical sharing activities with clear equal partitioning.

为纠正这些误解，应始终使用分数条和实际分享活动，并进行清晰的等分划分。

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7. Measurement Units and Conversions | 测量单位与换算

Pupils often struggle with converting between centimetres and metres, mistakenly thinking 1 m = 10 cm. Although they eventually memorise 1 m = 100 cm, they may then overgeneralise and think 1 km = 100 m.

学生经常在厘米和米的换算中犯错，误认为1米=10厘米。尽管他们最终记住1米=100厘米，但随后可能过度推广，认为1千米=100米。

Similarly, with mass, confusing grams and kilograms is common: they may state that 1 kg = 100 g, or estimate the mass of an apple as 2 kg instead of 200 g.

同样，在质量方面，混淆克和千克也很常见：他们可能说1千克=100克，或者估计一个苹果的质量为2千克而非200克。

When measuring length with a ruler, a typical mistake is not starting at the zero mark, so the reading is incorrect. The end of the object should line up with the zero line, not the edge of the ruler.

在用尺子测量长度时，典型的错误是未从零刻度开始测量，导致读数不正确。物体的一端应当对齐零刻度线，而非尺子的边缘。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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