Math Practice Animations: Common Mistakes for Levels G-3-5 | 数学练习动画：G-3-5易错点总结

📚 Math Practice Animations: Common Mistakes for Levels G-3-5 | 数学练习动画：G-3-5易错点总结

Interactive animated exercises reveal that many students repeatedly stumble over the same fundamental concepts at levels G-3-5. This article collects those high‑frequency errors, explains why they happen, and suggests how to overcome them.

互动动画练习显示，许多学生在G-3-5阶段反复在相同的基础概念上犯错。本文汇总这些高频错误，解释其成因，并提出如何避免它们。

1. Place Value and Regrouping Errors | 位值与进位错误

Learners often ignore zero as a placeholder, so a number like 2,058 is written as 258, completely changing its value.

学习者常常忽略零的占位作用，所以像2,058这样的数字被写成258，完全改变了数值。

When regrouping in addition, tens and hundreds are frequently mixed up; for example, 346 + 287 may be calculated as 523 instead of 633 because the carried hundred is placed in the tens column.

在加法进位时，十位和百位经常被混淆；例如346+287可能被算成523而非633，因为进位的百位数被放在了十位栏里。

Misunderstanding that the digit 5 in 5,432 represents 5 thousands, not 5, is another common place‑value slip.

误解5,432中的数字5表示5个千而不是5，也是常见的位值失误。

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2. Addition and Subtraction with Carrying/Borrowing | 带进位/借位的加减法

When subtracting across zeros, students frequently forget to adjust the borrowed digit, so 800 − 346 becomes 554 instead of 454.

跨零借位减法时，学生经常忘记调整被借的数字，因此800−346得出554而非454。

In multi‑digit addition, failing to carry the correct amount leads to errors like 758 + 469 = 1,117 rather than 1,227, because the tens‑column sum was not fully carried to the hundreds.

在多位数加法中，未能正确进位会导致如758+469=1,117而非1,227的错误，因为十位和未完全进到百位。

Adding numbers in the wrong order when using column method–writing 32 + 149 as 32 + 149 with columns misaligned–also produces incorrect results.

使用竖式时按错误顺序加数——把32+149写成列未对齐——也会产生不正确的结果。

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3. Multiplication Facts Misconceptions | 乘法口诀常见误解

Rote memorisation sometimes results in swapped products, such as insisting that 7 × 8 = 54 instead of 56.

机械记忆有时会产生乘积互换，比如坚称7×8=54而不是56。

When multiplying by multiples of 10, many children forget to annex the zero, treating 40 × 5 as 20 instead of 200.

当乘以10的倍数时，很多孩子忘记添加零，把40×5当成20而不是200。

Another typical error is partitioning incorrectly: 13 × 12 is thought to be (10 × 10) + (3 × 2) = 106, omitting the cross terms (10 × 2 + 3 × 10).

另一个典型错误是错误拆分：13×12被想成(10×10)+(3×2)=106，遗漏了交叉项(10×2+3×10)。

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4. Division and Handling Remainders | 除法与余数处理

Students often state a remainder without understanding its meaning; for example, 20 ÷ 6 = 3 r 2 is seen as a final answer even when the context requires a fraction or a decimal.

学生经常只说出余数而不理解其含义；比如20÷6=3余2被视为最终答案，即使上下文需要分数或小数。

Forgetting to place a zero in the quotient when a digit is smaller than the divisor is a classic mistake, such as calculating 3,618 ÷ 6 and writing 63 instead of 603.

当某一位数字小于除数时忘记在商中写零是一个典型错误，比如计算3,618÷6写成63而非603。

Confusing the divisor and dividend order in word problems, e.g., solving ‘How many 4s in 28?’ as 4 ÷ 28 instead of 28 ÷ 4, leads to an answer smaller than 1.

在应用题中混淆除数和被除数的顺序，例如把“28里面有多少个4”解为4÷28而不是28÷4，导致答案小于1。

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5. Fraction Equivalence and Ordering | 分数等价与排序

A deep‑rooted misconception is that a larger denominator means a larger fraction, so ¼ is judged greater than ⅓.

一个根深蒂固的误解是分母越大分数越大，因此¼被认为比⅓大。

When finding equivalent fractions, many add the same number to numerator and denominator, e.g., ⅖ → (2+3)/(5+3) = ⅝, which is not equivalent.

在找等值分数时，很多人将分子分母同加一个数，如⅖→(2+3)/(5+3)=⅝，这不相等。

Comparing ⅔ and ⅗ by cross‑multiplication is often done incorrectly: comparing 2 × 5 and 3 × 3, but then stating 10 > 9 so ⅔ < ⅗, reversing the inequality.

用交叉相乘比较⅔和⅗时经常做错：比较2×5和3×3，然后说10>9所以⅔<⅗，不等号方向反了。

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6. Decimal Misconceptions | 小数常见错误

Saying ‘zero point twenty‑five’ for 0.25 disrupts place‑value understanding; the correct reading ‘zero point two five’ reinforces that 0.25 is 2 tenths + 5 hundredths.

把0.25读作“零点二十五”会破坏位值理解；正确的读法“零点二五”强化了0.25是2个十分之一加5个百分之一。

Many learners think 0.7 is smaller than 0.24 because 7 < 24, not recognizing that 0.7 = 0.70 > 0.24.

许多学习者认为0.7小于0.24，因为7<24，却没有认识到0.7=0.70>0.24。

In addition of decimals, misaligned decimal points are commonplace: 4.5 + 2.38 written as 4.5 + 2.38 with the 8 under the 5, yielding 6.88 instead of 6.88? Actually 4.5 + 2.38 correctly aligned gives 6.88, but if misaligned as 4.5 + 23.8 they get 28.3, for example.

在小数加法中，小数点未对齐很常见：4.5+2.38如果把2.38误写成23.8对齐就会得到28.3，而正确的是6.88。

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7. Time Calculations | 时间计算

Children often treat time as base‑10, so 1 h 55 min + 2 h 45 min becomes 3 h 100 min instead of converting 100 min to 1 h 40 min, giving 4 h 40 min.

儿童常把时间当作十进制，因此1小时55分+2小时45分得出3小时100分，而不是将100分转换成1小时40分，得到4小时40分。

When crossing the hour mark, miscalculating minutes is frequent; for instance, the interval from 11:50 to 12:10 is thought to be 60 minutes rather than 20 minutes.

跨整点时，分钟计算常常出错；例如，从11:50到12:10的时间间隔被想成60分钟，而实际是20分钟。

Reading an analogue clock incorrectly, such as calling 2:50 as ‘ten to three’ but writing the digital time as 2:10, mixes up the hour hand position.

错误读取模拟时钟，比如把2:50叫作“差十分三点”却把数字时间写成2:10，混淆了时针位置。

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8. Measurement Conversions | 测量单位转换

Confusing grams and kilograms leads to statements like ‘a bag of flour weighs 1.5 g’ instead of 1.5 kg, and similar errors happen with millilitres and litres.

混淆克与千克导致类似“一袋面粉重1.5克”的说法而不是1.5公斤，毫升与升也出现类似错误。

When converting length, students frequently misplace the decimal: 150 cm is changed to 1.5 m correctly, but then 1.2 km might be written as 120 m instead of 1,200 m.

在转换长度时，学生经常点错小数点：150厘米正确转换为1.5米，但接下来1.2公里可能被写成120米而不是1,200米。

Perimeter and area units are often mixed up, with answers like ‘the perimeter is 24 cm²’ or ‘the area is 36 cm’.

周长和面积单位经常混淆，出现“周长是24平方厘米”或“面积是36厘米”的答案。

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9. Geometry: Angle Identification and Properties | 几何：角度识别与性质

Acute and obtuse angles are mislabelled because students rely on how ‘sharp’ or ‘wide’ the angle looks rather than comparing with 90°; a 110° angle may be called acute.

锐角和钝角被标错，因为学生依靠角度看起来多“尖”或多“宽”来判断，而不是与90°比较；110°角可能被称作锐角。

Using a protractor incorrectly–reading the inner scale when the arm aligns with the outer scale–gives a 50° angle as 130°.

错误使用量角器——当边与外圈刻度对齐时却读了内圈刻度——会把50°角读成130°。

Many pupils think a square is not a rectangle because they believe rectangles must be ‘longer’ one way, misunderstanding the subset relationship.

许多学生认为正方形不是长方形，因为他们觉得长方形必须一边更长，误解了子集关系。

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10. Data Handling and Graphs | 数据处理与图表

Reading scales on graphs where each unit represents 2, 5, or 10 often leads to raw counts being taken as final values; a bar rising to 4 units on a scale of 5 per unit is misread as 4, not 20.

在读图时，若每格代表2、5或10，常常把原始格数当作数值；在每格5单位的刻度上，柱高4格被误读为4而不是20。

When calculating the mean, forgetting to divide by the correct number of items–using the count of different values instead of total items–is common.

计算平均数时，忘记除以正确的项目数——用不同值的个数代替总数——很常见。

Interpretation of mode, median, and range is often swapped; for instance, listing the range as ‘the number that appears most’ instead of the difference between highest and lowest.

众数、中位数和极差的解读经常被互换；比如把极差说成“出现最多的数”，而不是最大值与最小值的差。

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11. Word Problem Pitfalls | 应用题陷阱

Rushing to choose an operation without understanding the context causes many errors; a problem about sharing 24 sweets among friends may be answered with 24 × 5 instead of 24 ÷ 5.

还没理解题意就匆忙选择运算导致许多错误；把24颗糖平均分给朋友的问题可能用24×5而不是24÷5来回答。

Ignoring key words like ‘altogether’, ‘difference’, or ‘each’ often results in addition when subtraction is needed or vice versa.

忽略“一共”、“差”、“每个”等关键词，经常导致需要减法时用了加法，反之亦然。

Multi‑step problems are simplified prematurely; a question asking cost of 3 pencils and 2 pens is tackled by adding the single prices only once.

多步问题被过早简化；问3支铅笔加2支钢笔的价格，学生只把单价加一次。

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Published by TutorHao | Mathematics Revision Series | aleveler.com

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