Cambridge Primary Mathematics Learner’s Book 2 (2nd Edition) Core Topics | 剑桥小学数学第二册（第二版）核心知识点精讲

📚 Cambridge Primary Mathematics Learner’s Book 2 (2nd Edition) Core Topics | 剑桥小学数学第二册（第二版）核心知识点精讲

Welcome to our comprehensive guide to the key concepts in Cambridge Primary Mathematics Learner’s Book 2, 2nd Edition. This resource supports young learners in building a strong foundation in numbers, operations, geometry, measurement, and data handling. Every topic is explained with clear examples in both English and Chinese, making it ideal for bilingual classrooms or home study.

欢迎阅读剑桥小学数学第二册（第二版）核心知识点精讲。本文通过中英文双语清晰讲解，帮助小学生建立数字、运算、几何、测量和数据处理方面的扎实基础。每个主题都配有详细的例子，非常适合双语课堂或家庭学习。

1. Numbers to 1000 | 数字到1000

In this unit, learners count, read, and write numbers up to 1000. They discover that three‑digit numbers are built from hundreds, tens, and ones. For example, 482 is read as ‘four hundred and eighty‑two’.

本单元学生学习数数、读数并写出1000以内的数字。他们发现三位数由百位、十位和个位组成。例如，482读作“四百八十二”。

We practise counting in steps of 1, 10, and 100. Counting by 100s gives 100, 200, 300, all the way to 1000. Counting by 10s from 235 gives 245, 255, 265, and so on.

我们练习以1、10和100为单位跳数。以100为单位数：100、200、300，直到1000。从235开始以10为单位跳数，得到245、255、265等。

Comparing numbers uses the symbols > (greater than), < (less than), and = (equal to). For instance, 756 > 675 because 7 hundreds is greater than 6 hundreds. 309 < 330 because the tens digit 0 is less than 3.

比较数字用大于号(>)、小于号(<)和等号(=)。例如，756 > 675，因为7个百比6个百大。而309 < 330，因为十位数字0比3小。

Learners also practise rounding to the nearest 10 or 100. 87 rounded to the nearest 10 is 90; 456 rounded to the nearest 100 is 500.

学习者还练习四舍五入到最近的10或100。87四舍五入到最近的10是90；456四舍五入到最近的100是500。

Writing numbers in words is essential. 108 = one hundred and eight, 310 = three hundred and ten, 999 = nine hundred and ninety‑nine.

用文字写数字也很重要。108 = 一百零八，310 = 三百一十，999 = 九百九十九。

---

2. Place Value | 位值

Place value means that a digit’s value depends on where it sits. In 539, the 5 is in the hundreds place (500), the 3 is in the tens place (30), and the 9 is in the ones place (9).

位值表示数字的值取决于它所在的位置。在539中，5在百位上是500，3在十位上是30，9在个位上是9。

Breaking a number into expanded form helps us see its parts: 539 = 500 + 30 + 9. This understanding is crucial for later addition and subtraction with regrouping.

把数字分解成展开式可以看清各部分：539 = 500 + 30 + 9。这种理解对以后学习带进位的加法和减法至关重要。

We can model place value with base‑ten blocks: a flat represents 100, a rod represents 10, and a unit cube represents 1. For 243, we need 2 flats, 4 rods, and 3 units.

我们可以用十进制方块来模拟位值：一块面板表示100，一根长条表示10，一个小方块表示1。对于243，需要2个面板、4根长条和3个小方块。

Number	Hundreds	Tens	Ones	Expanded Form
467	4	6	7	400 + 60 + 7
205	2	0	5	200 + 5
980	9	8	0	900 + 80

Zero acts as a placeholder; without it, 205 would just be 25. Learners must spot its importance in reading and writing numbers.

零起到占位作用；没有它，205就会变成25。学习者必须发现它在读写数字时的重要性。

---

3. Addition and Subtraction within 1000 | 1000以内的加法和减法

Students build solid mental strategies. For 45 + 32, they split the tens and ones: 40 + 30 = 70 and 5 + 2 = 7, so the sum is 77. This method works well without regrouping.

学生们构建扎实的心算策略。对于45 + 32，他们将十位和个位拆分：40 + 30 = 70，5 + 2 = 7，所以和是77。这种方法在无进位时很有效。

Column addition with regrouping is introduced step by step. For 158 + 67, we write the numbers vertically. Add the ones: 8 + 7 = 15, write 5 and carry the 1 ten. Then add the tens: 5 + 6 + 1 = 12, write 2 and carry 1 hundred. Finally add the hundreds: 1 + 1 = 2, giving 225.

带进位的竖式加法逐步引入。对于158 + 67，我们竖着写数字。个位相加：8 + 7 = 15，写5进1个十。然后十位相加：5 + 6 + 1 = 12，写2进1个百。最后百位相加：1 + 1 = 2，得到225。

Subtraction with borrowing (regrouping) is a key skill. In 342 − 175, look at the ones: 2 − 5 is not possible, so borrow 1 ten from the tens column, turning 4 tens into 3 tens and making the ones 12. 12 − 5 = 7. Then tens: 3 − 7 cannot be done, so borrow 1 hundred from 3 hundreds, leaving 2 hundreds and giving 13 tens. 13 − 7 = 6. Finally, hundreds: 2 − 1 = 1. Answer: 167.

带借位的减法是关键技能。在342 − 175中，先看个位：2 − 5不够，从十位借1个十，十位4变成3，个位变成12。12 − 5 = 7。然后十位：3 − 7不够，从百位3借1个百，百位变成2，十位变成13。13 − 7 = 6。最后百位：2 − 1 = 1。答案是167。

Checking by the inverse operation builds confidence: if 342 − 175 = 167, then 167 + 175 should equal 342. Always encourage checking work.

用逆运算检查能建立信心：如果342 − 175 = 167，那么167 + 175应等于342。一定要鼓励检查答案。

• Example: 500 − 236 → borrow from hundreds: 9 tens remain, ones become 10. 10 − 6 = 4, then tens 9 − 3 = 6, hundreds 4 − 2 = 2. Result: 264.

  例子：500 − 236 → 从百位借1，变成9个十，个位变成10。10 − 6 = 4，十位9 − 3 = 6，百位4 − 2 = 2。结果：264。

---

4. Multiplication as Repeated Addition | 乘法：重复加法

Multiplication is first explored as repeated addition. 3 × 4 means 3 groups of 4, which is 4 + 4 + 4 = 12. Arrays give a picture: 3 rows of 4 dots each. Drawing an array helps deepen understanding.

乘法最初作为重复加法来探索。3 × 4表示3组4，即4 + 4 + 4 = 12。阵列给出图像：每行4个点，共3行。画阵列有助于加深理解。

The 2 times table: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. The 5 times table: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. The 10 times table: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Learners chant, sing, and use flashcards to memorise them.

2的乘法表：2、4、6、8、10、12、14、16、18、20。5的乘法表：5、10、15、20、25、30、35、40、45、50。10的乘法表：10、20、30、40、50、60、70、80、90、100。学生通过唱诵和闪卡来熟记。

更多咨询请联系16621398022（同微信）