📚 Common Mistakes in Cambridge Primary Mathematics Workbook 4, 2nd Edition | Cambridge Primary Mathematics Workbook 4 第二版常见错误总结
The Cambridge Primary Mathematics Workbook 4 (2nd Edition) helps learners consolidate key skills such as place value, four operations, fractions, measurement and data handling. However, certain errors crop up repeatedly, often due to misconceptions or careless mistakes. This article highlights those common pitfalls and provides clear corrections to help students improve.
Cambridge Primary Mathematics Workbook 4（第二版）帮助学生巩固位值、四则运算、分数、测量和数据处理等核心技能。但某些错误反复出现，往往源于误解或粗心。本文汇总这些常见陷阱并提供清晰的纠正，帮助学生提高学习效果。
1. Place Value and Partitioning Errors | 位值与拆分常见错误
When partitioning a number like 706, many pupils incorrectly write 70 + 6 instead of 700 + 6, forgetting that the 7 is in the hundreds place and must be written as 700.
拆分数字706时，许多学生错误地写成70 + 6，而正确的写法是700 + 6，他们忘记了7在百位，必须写成700。
Another common mistake is handling zeros in numbers such as 3 084. Some break it as 300 + 80 + 4, missing the thousands digit entirely and writing 3 000 as 300.
另一个常见错误是处理像3 084这样含有零的数字。有人会拆分成300 + 80 + 4，完全忽略了千位的数字，把3 000写成了300。
Always say the number aloud: ‘three thousand and eighty-four’ and then check each column: thousands, hundreds, tens, ones. This simple check prevents missing placeholders.
一定要大声读出数字：“三千零八十四”，然后核对数位：千位、百位、十位、个位。这个简单的检查可以防止漏掉占位符。
| Incorrect | Correct |
|---|---|
| 706 = 70 + 6 | 706 = 700 + 6 |
| 3 084 = 300 + 80 + 4 | 3 084 = 3 000 + 80 + 4 |
2. Addition with Regrouping (Carrying) Mistakes | 进位加法错误
When adding 278 + 156, some pupils forget to add the carried ten to the tens column. They may write 278 + 156 = 324 instead of 434, because they add 8 + 6 = 14, write 4 and carry 1, but then they do 7 + 5 = 12 and forget the extra 1, leaving 12 without change.
计算278 + 156时，有些学生会忘记把进位的十加到十位上。他们可能写出278 + 156 = 324，而不是434。因为他们算了个位8 + 6 = 14，写4进1，但接着算十位7 + 5 = 12时忘了加进位的1。
Another typical error is carrying into the wrong place value column. For example, after the ones column, the carried 1 is accidentally added to the hundreds instead of the tens.
另一个典型错误是把进位加到了错误的数位上。比如个位算完后，进位的1错误地加到了百位，而不是十位。
To avoid these errors, always use a clear vertical layout with labelled columns (H T O) and mark the carry-over digit in its own small box above the next column.
避免这些错误的方法是始终使用清晰的竖式，标注数位（百位 H、十位 T、个位 O），并将进位的数字标记在下一列上方的小方框里。
278 + 156 = 434
3. Subtraction with Borrowing (Regrouping) Errors | 借位减法错误
In a problem like 524 – 267, a frequent mistake is to subtract the smaller digit from the larger digit in each column without borrowing. This gives 524 – 267 = 363 (doing 7 – 4 = 3, 6 – 2 = 4, 5 – 2 = 3), which is completely wrong.
在计算524 – 267时，一个常见错误是在不借位的情况下，从每列中较大的数减去较小的数。这样会得出524 – 267 = 363（做7 – 4 = 3，6 – 2 = 4，5 – 2 = 3），这是完全错误的。
The correct method means borrowing: since 4 is less than 7, we borrow 1 ten from the 2 tens, making the 4 into 14. 14 – 7 = 7. The tens then become 1 ten – 6, which again requires borrowing from the hundreds. The final answer is 257.
正确的方法需要借位：因为4小于7，我们从十位的2个十里借1个十，把4变成14。14 – 7 = 7。然后十位剩下1个十 – 6个十不够，需要再从百位借。最终答案是257。
Even when children understand borrowing, they often forget to reduce the digit they borrowed from. So after borrowing from the tens, they still treat it as 2 tens instead of 1.
即使学生理解了借位，也常常忘记把被借位的数字减1。从十位借了1个十之后，他们还把它当作2个十，而不是1个十。
| Common wrong answer | Correct answer |
|---|---|
| 524 – 267 = 363 | 524 – 267 = 257 |
4. Multiplication Tables and Patterns Confusion | 乘法口诀与模式混淆
Pupils often mix up similar-sounding facts, such as 6 × 8 = 48 and 7 × 9 = 63. A slip of memory can turn 6 × 8 into 56 or 7 × 9 into 64.
学生经常混淆发音相似的口诀，比如6 × 8 = 48 和 7 × 9 = 63。记忆一疏忽，就会把6 × 8算成56，或把7 × 9算成64。
When applying multiplication to larger numbers, a common mistake is mishandling zeros. For example, they might think 4 × 30 = 12 because they recall 4 × 3 = 12, but forget to multiply the result by 10.
将乘法应用于更大的数时，常见的错误是处理不好零。比如，他们可能认为4 × 30 = 12，因为他们记得4 × 3 = 12，但忘了把结果再乘以10。
Another pattern error occurs in finding factors: when asked for all factor pairs of 24, a pupil might miss 3 × 8 because they think only 4 × 6 and 2 × 12. They need to check systematically.
另一个模式错误发生在找因数时：要求找出24的所有因数对，学生可能会漏掉3 × 8，因为他们只想到4 × 6和2 × 12。需要系统地检查一遍。
Remind learners to use known facts as building blocks: if 6 × 7 = 42, then 60 × 7 = 420 and 600 × 7 = 4 200.
提醒学生利用已知口诀作为台阶：如果6 × 7 = 42，那么60 × 7 = 420，600 × 7 = 4 200。
5. Division and Dealing with Remainders | 除法与处理余数
In dividing 45 by 6, many children correctly state 7 remainder 3, but they sometimes write the remainder larger than the divisor. For example, 38 ÷ 5 = 7 r 3 is correct, but they may write 6 r 8, where 8 is greater than 5.
在45除以6的计算中，很多孩子能正确地答出7余3，但他们有时会写出比除数还大的余数。比如38 ÷ 5 = 7 余 3是正确的，但他们可能写成6 余 8，这里的8比除数5大。
This means the division process was incomplete: they should have made the quotient larger until the remainder is less than the divisor.
这意味着除法过程没有完成：应该让商更大一些，直到余数小于除数。
Another slip is omitting the remainder altogether or writing it as a decimal without understanding. They might write 45 ÷ 6 = 7.5, which is correct, but then try 38 ÷ 5 and write 7.5 as well, without checking that 7.5 × 5 = 37.5, not 38.
另一个失误是完全忘记写余数，或者不加理解地写成小数。他们可能写45 ÷ 6 = 7.5，这是对的，但接着遇到38 ÷ 5也写7.5，却没有检查7.5 × 5 = 37.5而不是38。
Encourage the check: divisor × quotient + remainder = dividend. So 5 × 7 + 3 = 38.
鼓励做检验：除数 × 商 + 余数 = 被除数。所以5 × 7 + 3 = 38。
6. Fractions of Shapes and Sets of Objects | 图形与集合的分数问题
When asked to colour ⅓ of a flag divided into 3 equal stripes, some learners colour one stripe correctly, but if the next question shows a shape with 4 parts, they might think ⅓ simply means ‘colour one piece’ and use it for the shape with 4 parts, ignoring the denominator.
要求给被分成3等份条纹的旗帜涂上⅓的颜色，有些学生正确涂了1份。但如果下一题是一个被分成4份的形状，他们可能误以为⅓就是“涂1份”，于是也用在4份的形状上，忽略了分母。
For finding fractions of amounts, like ⅗ of 20, the correct method is to divide by the denominator (20 ÷ 5 = 4) and then multiply by the numerator (4 × 3 = 12). A common error is stopping after the division and giving 4 as the answer.
对于求一个数量的几分之几，比如20的⅗，正确方法是除以分母（20 ÷ 5 = 4），再乘以分子（4 × 3 = 12）。常见的错误是做完除法就停了，给出答案4。
Comparing unit fractions also confuses many: ¼ is actually bigger than ⅛, but children may think ⅛ is larger because 8 is larger than 4. Always use a diagram or think about parts of the same whole.
比较单位分数也会让很多人混淆：¼实际上比⅛大，但孩子们可能认为⅛更大，因为8大于4。一定要借助图形，或想象同一个整体被分成的份数。
⅗ of 20 = (20 ÷ 5) × 3 = 4 × 3 = 12
7. Measurement Conversions (cm to m, g to kg) | 测量单位转换（厘米与米，克与千克）
Converting length often causes errors: 150 cm = 1.5 m is correct, but some pupils write 15 m or 0.15 m because they are unsure about moving the decimal point two places to the left.
长度转换经常出错：150 厘米 = 1.5 米是正确的，但有些学生写成15米或0.15米，因为他们不确定如何将小数点向左移动两位。
For mass, 2 kg 350 g should be expressed as 2 350 g. A slip is writing 2 035 g, because they add 2 000 + 350 incorrectly in their head.
对于质量，2 千克 350 克应写成 2 350 克。一个失误是写成2 035克，因为他们心算2 000 + 350出了错。
When converting grams to kilograms, remember that 1 000 g = 1 kg, so 2 300 g = 2.3 kg. Some learners write 23 kg, multiplying by 10 instead of dividing by 1 000.
将克转换为千克时，记住1 000 克 = 1 千克，所以2 300 克 = 2.3 千克。有些学习者却写成23 千克，乘了10而不是除以1 000。
Always refer to the key facts and use a place value grid if needed.
务必查阅基本换算关系，必要时使用位值网格。
1 m = 100 cm, 1 kg = 1 000 g
8. Time Interval Problems | 时间间隔问题
Finding the duration from 9:45 a.m. to 10:30 a.m. is tricky. A wrong approach is to subtract 45 from 30, getting -15 minutes, and then guess. The right way is to think in steps: from 9:45 to 10:00 is 15 minutes, and 10:00 to 10:30 is 30 minutes, totalling 45 minutes.
计算上午9:45到10:30的时间间隔不容易。错误的方法是用30减45，得到-15分钟，然后猜测。正确的方法是分步思考：从9:45到10:00是15分钟，10:00到10:30是30分钟，总共45分钟。
Another frequent mistake is when crossing the hour or dealing with 12-hour clock times. For example, from 11:50 a.m. to 12:10 p.m., some children think the interval is 20 minutes because 50 to 10 looks like a 20-minute jump, but it is actually 20 minutes (10 minutes to noon, then 10 minutes after). But if they misjudge 12:10 as a.m. or p.m., they may add 12 hours.
另一个常见错误发生在跨越整点或涉及12小时制时。例如从上午11:50到下午12:10，有些孩子认为间隔是20分钟，看上去50到10差了20格，实际上确实是20分钟（到中午还有10分钟，再加10分钟）。但如果上午/下午弄错，他们可能会加上12小时。
It helps to draw a number line for time and label a.m. and p.m. clearly when reading clock faces.
在读取钟面时，画一条时间数轴并清楚标出上午和下午会很有帮助。
9. Perimeter of Rectangles and Squares | 长方形与正方形的周长
A rectangle with length 8 cm and width 3 cm has a perimeter of 2 × (8 + 3) = 22 cm. Many children simply add 8 + 3 = 11 cm and stop, forgetting that there are two lengths and two widths.
一个长8厘米、宽3厘米的长方形，周长是2 × (8 + 3) = 22 厘米。许多孩子只做了8 + 3 = 11厘米就停了，忘记了有两条长和两条宽。
Confusing perimeter with area is another classic error. They might use the formula for area, length × width, and write 24 cm as the perimeter when they should use the perimeter formula.
将周长与面积混淆是另一个经典错误。他们可能用了面积公式长×宽，写出24厘米当作周长，而应该用周长公式。
For a square of side 5 cm, they
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