Common Mistakes in Cambridge Primary Mathematics Learner’s Book 2, 2nd Edition | 剑桥小学数学教材第2册第二版易错点总结

📚 Common Mistakes in Cambridge Primary Mathematics Learner’s Book 2, 2nd Edition | 剑桥小学数学教材第2册第二版易错点总结

This article highlights the most common mistakes that learners make while studying Cambridge Primary Mathematics Learner’s Book 2, 2nd Edition. Understanding these pitfalls can help students build a stronger foundation in early mathematics, from place value and basic operations to measurement, shape, and simple fractions. Each section provides an explanation of the typical error, followed by tips on how to avoid it.

本文梳理了学生在学习《剑桥小学数学教材第2册·第二版》时最常犯的错误。了解这些易错点能帮助孩子在位值、基本运算、测量、图形和简单分数等方面打下更扎实的数学基础。每一部分都会先指出常见错误，再给出避免这些小陷阱的方法。

1. Place Value Confusion | 位值混淆

A very common mistake is writing ‘twenty-three’ as 203 instead of 23. Learners sometimes hear ‘twenty’ and ‘three’ and place the 3 after a zero, not understanding that the 2 in the tens place already represents twenty.

一个很常见的错误是把“二十三”写成 203 而不是 23。孩子们有时听到“二十”和“三”，就会把 3 写在一个 0 的后面，没有理解十位上的 2 已经表示 20，因此只需要在个位写 3。

Another frequent error occurs when reading numbers with a zero, such as 105. Many children say ‘one hundred and five’ correctly but write it as 1005. They incorrectly treat the zero as needing an extra place.

另一个常见易错点出现在读含有零的数字时，比如 105。很多孩子会正确地说出“一百零五”，但写下来却变成 1005，误以为零要单独占一个数位。

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2. Addition with Carrying | 进位加法

When adding two-digit numbers such as 27 + 56, children often add the tens first without carrying properly. A typical mistake is to write 7 + 6 = 13, put down 13 in the ones column, and then add the tens, getting 713 instead of 83.

计算两位数加法如 27 + 56 时，孩子们常先加十位却没有正确处理进位。典型的错误是：个位 7 + 6 = 13，就在个位列写下 13，然后再加上十位，结果得出 713，而不是正确的 83。

To avoid this, learners must be reminded to carry the extra ten to the tens column. Using concrete objects or place value cards can help visualise the regrouping.

为了避免这种错误，需要提醒孩子将多出来的 1 个十进位到十位列。使用实物教具或位值卡片可以帮助他们将“重组”的过程形象化。

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3. Subtraction with Borrowing | 借位减法

The most frequent subtraction mistake is subtracting the smaller digit from the larger one regardless of the order, for example in 43 – 27, a child might say ‘3 – 7 can’t do it, so do 7 – 3 = 4’ and then ‘4 – 2 = 2’, giving 24 instead of 16.

最常犯的减法错误是不顾顺序用大数减小数。比如 43 – 27，孩子可能会说“3 减 7 不够，那就用 7 减 3 等于 4”，然后“4 减 2 等于 2”，得出 24 而不是正确的 16。

Another error arises when borrowing across a zero, such as 102 – 45. Learners may borrow from the hundreds but forget to adjust the tens correctly, often leaving the answer as 157 instead of 57.

跨越 0 借位时也会出错，例如 102 – 45。学生可能会从百位借了 1，却忘记正确调整十位，经常得出 157 而非正确的 57。

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4. Understanding Multiplication as Repeated Addition | 理解乘法为重复加法

Many children can chant times tables but struggle to link 3 × 4 to 4 + 4 + 4. A common mistake is to write 3 × 4 = 7, confusing the multiplication symbol with addition.

很多孩子会背乘法表，却很难把 3 × 4 与 4 + 4 + 4 联系起来。一个常见错误是把 3 × 4 算成 7，将乘号与加号混淆。

When using arrays, a child might count the total of objects but miscount rows or columns, leading to an incorrect multiplication sentence, for example describing a 3 × 5 array as 4 × 5.

使用阵列图时，孩子可能会数出物体的总数，但数错行数或列数，导致写出错误的乘法算式，比如把一个 3 × 5 的阵列写成 4 × 5。

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5. Division as Equal Sharing | 除法作为公平分享

In simple division, children often forget that groups must be equal. They might share 10 counters among 2 people as 6 and 4, instead of 5 and 5. The concept of ‘equal groups’ needs to be constantly reinforced.

在简单的除法中，孩子们经常忘记每组必须相等。他们可能会把 10 个计数片分给 2 个人当成 6 和 4，而不是 5 和 5。“等量分组”的概念需要不断巩固。

A typical written mistake is writing 10 ÷ 2 = 8, because the child thinks of division as taking away the second number.

典型的书写错误是把 10 ÷ 2 写成等于 8，因为孩子把除法想成了减去第二个数。

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6. Fractions – Halves, Quarters and Thirds | 分数 – 二分之一、四分之一、三分之一

Learners often believe that ½ is a bigger number than ¼, but when asked to cut a cake into quarters, they may cut into two halves and then halve one half again, leaving pieces of unequal size. A common mistake is thinking that four quarters make less than a whole because each piece looks small.

孩子们通常知道 ½ 比 ¼ 大，但当要求把蛋糕切成四等份时，他们可能会先切成两半，然后把其中一半再对半切，导致四份大小不均。常见错误是认为四个 ¼ 合起来比一个整体少，因为每块看起来很小。

Confusion also arises with thirds. Many children try to fold a strip into 3 equal parts but create two folds, resulting in four sections, and then call each section a third.

三分之一的混淆也很常见。很多孩子试图把一条纸带折成三等份，却折了两下得到四段，然后说每一段是三分之一。

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7. Time – Reading Clocks | 时间 – 认读时钟

When reading analogue clocks, a classic mistake is to read the hour hand as pointing to a number without considering that it moves slowly towards the next hour. So for 2:50, the hour hand is almost at 3, and the child may read the time as 3:50.

在认读模拟钟面时，经典的错误是只看时针指向的数字，不考虑它正在缓慢走向下一个小时。所以在 2:50 时，时针已经接近 3，孩子可能会把时间读成 3:50。

Another error is confusing the minute hand with the hour hand when writing the time. A child might record 3:10 as 10:3, swapping the positions.

另一个易错点在书写时间时混淆了时针和分针。孩子可能会把 3:10 写成 10:3，交换了位置。

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8. Money – Counting Coins and Change | 钱币 – 数钱和找零

Children often add the value of coins by counting the number of coins, not their value. For example, one 50p coin and two 10p coins might be counted as 3 coins, so they say 3p instead of 70p.

孩子们加硬币时常数硬币的个数，而不是按面值相加。例如，一枚 50p 和两枚 10p 可能会被数成 3 枚硬币，所以说成 3p 而不是 70p。

When giving change, a common mistake is to subtract the price from the amount paid incorrectly due to the previous subtraction errors. A child might pay £1 for an item costing 65p and count change as 45p instead of 35p, forgetting to reach 100p.

找零时，由于前面的减法错误，儿童从支付金额中减去价格时也容易出错。一个孩子用 £1 买 65p 的物品，可能找回 45p 而不是 35p，忘记要凑到 100p。

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9. Measurement – Length, Mass and Capacity | 测量 – 长度、质量和容量

A typical error when measuring length is aligning the object from the end of the ruler instead of the zero mark. This leads to a measurement that is off by the small gap at the ruler’s edge.

测量长度时的典型错误是从直尺边缘开始量物体，而不是对齐 0 刻度线。这会因尺子边缘的空白造成测量偏差。

With mass, learners may think larger objects are always heavier, not appreciating that a small bag of rice can be heavier than a large bag of cotton wool. Misreading scales, especially when the needle is between lines, is also common.

在质量方面，孩子们常认为体积大的物体就更重，而不能理解一小袋大米可能比一大袋棉花重。读秤时，尤其当指针指在两格之间，读错也是很常见的。

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10. 2D and 3D Shapes Properties | 二维和三维图形性质

Confusing the number of sides with corners is a regular mistake. A child may say a pentagon has five corners but count six sides because they double-count a vertex. Recognising a square as a special rectangle also causes difficulty.

混淆边数与顶点数是反复出现的错误。孩子可能会说五边形有五个角，却在数边时多数，得到一个顶点数了两遍。认识到正方形是特殊的长方形也很难。

For 3D shapes, learners often call a cube a square and a sphere a circle. They struggle to identify faces on 3D shapes when shown a picture, for example thinking a cylinder has no flat faces.

说到三维图形时，孩子常把立方体叫作正方形，把球体叫作圆。看图片时，他们很难识别三维图形的面，比如误以为圆柱体没有平面。

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11. Data Handling – Pictograms | 数据处理 – 象形图

When representing data with pictograms where one symbol represents more than one item, children frequently forget the key and count symbols as single items. So a pictogram showing 4 smiley faces with each face = 2 children might be read as 4 children instead of 8.

用象形图表示数据，且一个符号代表多于一个单位时，孩子常常忘记图例，把每个符号当作一个来数。所以一幅图显示 4 个笑脸，每个笑脸代表 2 个孩子，可能会被读成 4 个孩子而不是 8 个孩子。

Another mistake is misaligning symbols in columns, making it hard to compare frequencies. They might think a taller column in a loose pictogram necessarily means more items, even if the symbols in the shorter column represent a larger quantity.

另一个错误是把符号排在柱子上时对不齐，导致难以比较频数。他们可能认为松散的象形图中较高的柱子就代表更多，即使较矮的柱子中的符号代表更大的数量。

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12. Patterns and Sequences | 规律与序列

Learners often recognise a repeating pattern but fail to extend it beyond the given set, especially when the pattern changes after a few terms. A child might continue A, B, B, A, B, B as A, B, B, A, B, B, A, B, B, but then get stuck when asked what the 20th term is, because they haven’t formalised the rule.

学生常常能辨认重复规律，却很难把它延伸到给定序列之外，尤其是规律在几项后发生变化。孩子可能会把 A, B, B, A, B, B 延续下去，但当问到第 20 项是什么时就卡住了，因为他们没有把规则形式化。

With number patterns, a common error is misapplying a pattern like ‘add 3, then subtract 1’. The child may keep adding 3 and forget to subtract, or apply the subtraction to the wrong term.

在数字规律中，常见的错误是用错如“加 3，再减 1”的模式。孩子可能一直加 3 而忘记减，或者把减法用错了项。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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