📚 Cambridge Primary Mathematics Learner's Book 1 (2nd Edition): Complete Topic Guide | 《剑桥小学数学学生用书1》第二版全考点指南
Cambridge Primary Mathematics Learner's Book 1, 2nd Edition by Cherri Moseley and Janet Rees is the first step in the Cambridge Primary Maths series. It builds the essential number, geometry, measurement and data skills that learners need before moving to more formal arithmetic. This guide explains every main topic in the book with clear examples, common misconceptions and practice ideas for classroom or home use.
《Cambridge Primary Mathematics Learner's Book 1》第二版由 Cherri Moseley 与 Janet Rees 编写，是剑桥小学数学系列的第一步。它帮助学习者建立数感、几何、测量与数据处理的核心技能，为后续更正式的算术学习打下基础。本指南逐一解析书中的主要专题，配有清晰示例、常见误区以及适合课堂或家庭的练习建议。
1. Book Overview and How to Use This Guide | 教材概览与使用指南
Learner's Book 1 is designed for the first year of primary schooling, usually ages 5-6. It follows the Cambridge Primary Mathematics curriculum framework and presents learning through visual prompts, practical tasks and short activities. Each unit focuses on one key concept, such as counting, addition, shapes or time, and repeats it in varied contexts to build confidence.
《Learner's Book 1》面向小学第一学年，通常是 5-6 岁的学生。它遵循剑桥小学数学课程框架，通过视觉提示、动手操作和短活动展开学习。每个单元聚焦一个核心概念，例如数数、加法、图形或时间，并在不同情境中反复出现，以帮助学生建立信心。
To use this guide effectively, read the English explanation first, then check the Chinese version. Use the worked examples to try similar questions at home. The section headings match the main topics in the course, so you can use this guide as a revision checklist before any assessment.
为了有效使用本指南，请先阅读英文解释，再核对中文版本。使用文中的示例在家尝试类似问题。各小节标题与教材中的主要专题对应，因此你可以把本指南当作任何测验前的复习清单。
2. Number Recognition and Counting to 20 | 20 以内数的认识与数数
Learners begin by recognising numerals 0 to 10, then extend to 20. They count forwards and backwards from any starting point, match quantities to numerals, and use one-to-one correspondence. Key skills include saying which number is one more or one less, and placing numbers in the correct order on a number track.
学生先认识 0 到 10 的数字，再扩展到 20。他们能从任意起点正数或倒数，将数量与数字对应，并建立一一对应关系。核心技能包括说出比一个数大 1 或小 1 的数，以及把数字按正确顺序放在数字轨道上。
- Number names: zero, one, two, three ... twenty | 数字名称：zero、one、two、three……twenty
- Number sequence: 14, 15, 16, 17, 18 | 数字顺序：14、15、16、17、18
- One more / one less: 12 → 13, 12 → 11 | 大 1 / 小 1：12 → 13，12 → 11
- Missing numbers: 7, __, 9, 10 | 填缺数：7、__、9、10
A number track from 1 to 20 is a useful tool. Learners place counters or point to each number as they count. This strengthens both forward and backward counting and helps them see that 15 comes before 16 and after 14.
1 到 20 的数字轨道是非常有用的工具。学生边数边放计数器或指着数字。这能强化正数和倒数，并帮助他们理解 15 在 16 之前、在 14 之后。
3. Place Value: Tens and Ones | 位值：十位与个位
For numbers up to 20, children begin to see a two-digit number as made of tens and ones. Using base ten blocks, bead strings or ten frames, they partition 15 into 10 + 5. This is the foundation for later column addition and subtraction.
对于 20 以内的数，孩子开始把一个两位数看成几个十与几个一。借助十格框、穿珠串或小棒，他们把 15 拆成 10 + 5。这是今后竖式加减法的基础。
15 = 10 + 5
Place value language should be precise. Say 'one ten and five ones', not 'one and five'. Consistent language prevents confusion when comparing or ordering numbers. For example, 12 is not 'ten two' but one ten and two ones.
位值表述应当准确。要说“1 个十和 5 个一”，而不是“1 和 5”。统一的语言有助于在比较或排序时避免混淆。例如，12 不是“十和二”，而是 1 个十和 2 个一。
Ten frames are especially useful for showing numbers 11 to 20. One full ten frame shows 10, and a second frame shows the extra ones. This visual model makes the meaning of each digit clear.
十格框对表示 11 到 20 的数特别有用。一个满十格框表示 10，另一个十格框表示多出来的几个一。这种视觉模型使每个数字的含义更加清晰。
4. Addition Within 20 | 20 以内加法
s to 10 and then use them to add beyond 10, for example 7 + 5 = 12 by bridging through 10.
本书的加法重点是把两个集合合并并继续数。学生使用数线、手指、十格框和计数器。他们先学习 10 的组成，再利用凑十法计算超过 10 的加法，例如 7 + 5 = 12。
7 + 5 = 12 (把 5 拆成 3 + 2: 7 + 3 = 10, 10 + 2 = 12)
Number bonds to 10 are the building blocks of mental calculation. Learners should know pairs such as 6 + 4, 7 + 3, 8 + 2 and 9 + 1 instantly. These facts allow them to solve larger additions by making ten first.
10 的组成是心算的基础。学生应快速掌握 6 + 4、7 + 3、8 + 2 和 9 + 1 等组合。这些事实使他们能够先凑十，再解决更大的加法问题。
| Number bond | 组合 | Fact | 算式 | Making ten | 凑十 |
|---|---|---|
| 6 + 4 | 10 | 6 + 4 = 10 |
| 7 + 3 | 10 | 7 + 3 = 10 |
| 8 + 5 | 13 | 8 + 2 = 10, 10 + 3 = 13 |
| 9 + 4 | 13 | 9 + 1 = 10, 10 + 3 = 13 |
When using a number line, learners start at the larger number and jump forward the smaller number. This is more efficient than counting from 1 every time.
使用数线时，学生从较大的数开始，向前跳较小的数。这比每次都从 1 数起更高效。
5. Subtraction Within 20 | 20 以内减法
lated addition facts to see inverse operations, for example 13 − 6 = 7 because 7 + 6 = 13.
减法以“拿走”“求差”和“倒数”三种方式引入。学生先使用实物操作，再过渡到数线。他们通过相关加法事实理解逆运算，例如 13 − 6 = 7，因为 7 + 6 = 13。
13 − 6 = 7 ↔ 6 + 7 = 13
- Take away: 9 − 4 = 5 | 拿走：9 − 4 = 5
- Difference: 9 and 4 differ by 5 | 差值：9 与 4 相差 5
- Count back: start at 7, then 6, 5, 4 | 倒数：从 7 开始，然后 6、5、4
- Missing number: 12 − __ = 8 | 缺数：12 − __ = 8
irm it by adding 7 + 8 = 15. This connection reduces reliance on counting back one by one.
把减法理解为加法的逆运算有助于学生检查答案。如果 15 − 7 = 8，他们可以通过 7 + 8 = 15 来验证。这种联系减少了对逐个倒数的依赖。
Word problems in Book 1 often use words like 'left', 'gave away', 'fewer' and 'how many more'. Learners should identify whether the problem asks for a take away or a difference before calculating.Published by TutorHao | IB Mathematics Revision Series | aleveler.com
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