📚 Math G2 Student Book | 数学 G2 学生用书
This student book builds core mathematical skills for Grade 2 learners. It focuses on number sense, addition and subtraction within 1000, early multiplication and division, fractions, measurement, money, time, shapes, and data. Each section provides clear explanations, worked examples, and practice ideas.
本书为二年级学生构建核心数学技能。内容聚焦数感、1000 以内加减法、乘除法入门、分数、测量、货币、时间、图形与数据。每一节提供清晰的讲解、示例与练习建议。
1. Place Value to 1000 | 千以内位值
In Grade 2, students learn that a three-digit number is made of hundreds, tens, and ones. For example, in 426, the digit 4 means 4 hundreds, 2 means 2 tens, and 6 means 6 ones.
在二年级，学生认识到三位数由百位、十位和个位组成。例如，在 426 中，数字 4 表示 4 个百，2 表示 2 个十，6 表示 6 个一。
We can break a number into expanded form to show the value of each digit. This helps students understand why 507 is different from 570.
我们可以把一个数写成展开式来表示每一位的值。这有助于学生理解 507 与 570 为何不同。
426 = 400 + 20 + 6
507 = 500 + 0 + 7
- Read and write numbers up to 1000 in words and digits. | 读写 1000 以内的数字与文字。
- Identify the value of a digit in hundreds, tens, and ones. | 辨认百位、十位、个位上数字的值。
- Use base-ten blocks or place value charts to model numbers. | 使用十进制积木或位值表表示数。
2. Comparing and Ordering Numbers | 比较与排序数
To compare three-digit numbers, start with the hundreds place. If the hundreds are the same, compare the tens, then the ones.
比较三位数时，先看百位。如果百位相同，就比较十位，再比较个位。
relationship between two numbers. For example, 382 < 418 because 3 hundreds are less than 4 hundreds.
符号 >、< 和 = 表示两个数之间的关系。例如，382 < 418，因为 3 个百小于 4 个百。
725 > 719, 263 = 263, 580 < 805
- Arrange a set of numbers from smallest to largest. | 将一组数从小到大排列。
- Use a number line to locate and compare numbers. | 使用数轴定位并比较数。
- Explain comparison using place value language. | 用位值语言解释比较。
3. Addition within 1000 | 千以内加法
Grade 2 addition focuses on adding two- and three-digit numbers with and without regrouping. Students learn to add ones, tens, and hundreds in columns.
二年级加法重点是两位数和三位数的进位与不进位加法。学生学习按列相加个位、十位和百位。
Regrouping happens when a column total is 10 or more. For example, 7 ones + 5 ones gives 12 ones, so we write 2 ones and carry 1 ten.
当某一列相加结果等于或超过 10 时，就需要进位。例如，7 个一加 5 个一得到 12 个一，因此写 2 个一，并向十位进 1。
276 + 158 = 434
| Hundreds 百位 | Tens 十位 | Ones 个位 |
| 2 + 1 + 1 = 4 | 7 + 5 = 12, carry 1 | 6 + 8 = 14, carry 1 |
- Use mental strategies such as adding tens first. | 使用先加十位等心算策略。
- Solve one-step and two-step word problems. | 解决一步和两步应用题。
- Check answers by using the inverse operation. | 用逆运算检查答案。
4. Subtraction within 1000 | 千以内减法
Subtraction in Grade 2 includes taking away two- and three-digit numbers, with and without borrowing. Borrowing is used when the top digit is smaller than the bottom digit in a column.
二年级减法包括两位数和三位数的退位与不退位减法。当某一列上方的数字小于下方的数字时，就需要借位。
For example, to subtract 156 from 432, we cannot take 6 ones from 2 ones, so we borrow 1 ten from the tens place, making 12 ones.
例如，计算 432 − 156 时，个位 2 不能减 6，因此从十位借 1 个十，变成 12 个一。
432 − 156 = 276
- Subtract using a place value chart or number line. | 使用位值表或数轴进行减法。
- Understand subtraction as taking away, comparing, and finding the difference. | 理解减法表示拿走、比较和求差。
- Practice word problems involving change and comparison. | 练习涉及找零和比较的应用题。
5. Introduction to Multiplication | 乘法入门
as repeated addition. For example, 4 × 3 means 4 groups of 3, which is 3 + 3 + 3 + 3 = 12.
乘法以重复加法引入。例如，4 × 3 表示 4 组 3，即 3 + 3 + 3 + 3 = 12。
skip counting to find products. An array with 3 rows and 5 columns shows that 3 × 5 = 15.
学生通过排列方阵和跳数来求积。3 行 5 列的方阵表示 3 × 5 = 15。
5 × 2 = 10, 3 × 4 = 12, 2 × 6 = 12
- Relate multiplication to equal groups. | 将乘法与等组联系起来。
- Use skip counting by 2s, 5s, and 10s. | 使用 2、5、10 的跳数。
- Recognise the multiplication sign ×. | 认识乘号 ×。
6. Introduction to Division | 除法入门
Division is introduced as sharing into equal groups. For example, 12 ÷ 4 means sharing 12 objects into 4 equal groups, giving 3 in each group.
除法以平均分组引入。例如，12 ÷ 4 表示把 12 个物体平均分成 4 组，每组 3 个。
g how many groups can be made. If 12 apples are packed in bags of 3, then 12 ÷ 3 = 4 bags.
除法也可以理解为求能分成多少组。如果 12 个苹果每 3 个装一袋，那么 12 ÷ 3 = 4 袋。
12 ÷ 4 = 3, 20 ÷ 5 = 4, 18 ÷ 3 = 6
- Use drawings or counters to model equal sharing. | 使用图画或计数片表示平均分配。
- Connect division to multiplication facts. | 将除法与乘法口诀联系起来。
- Solve simple sharing and grouping word problems. | 解决简单的分配与分组应用题。
7. Fractions: Halves, Thirds, Quarters | 分数：二分之一、三分之一、四分之一
Grade 2 students learn fractions as equal parts of a whole. A half is one of two equal parts, a third is one of three equal parts, and a quarter is one of four equal parts.
二年级学生将分数理解为整体的等份。二分之一是两个等份中的一份，三分之一是三个等份中的一份，四分之一是四个等份中的一份。
Fractions can describe parts of a shape or parts of a set. If a rectangle is divided into 4 equal parts and 1 part is shaded, the shaded fraction is 1/4.
分数可以描述图形的一部分或集合的一部分。如果一个长方形被分成 4 等份，其中 1 份涂色，则涂色部分为 1/4。
1/2, 1/3, 1/4, 2/4 = 1/2
- Recognise halves, thirds, and quarters of shapes. | 辨认图形的二分之一、三分之一和四分之一。
- Compare unit fractions using visual models. | 用图示比较单位分数。
- Understand that equal parts must be the same size. | 理解等份必须大小相同。
8. Money and Shopping | 货币与购物
Students learn to recognise coins and notes, count money, and make simple change. Common denominations include 1p, 2p, 5p, 10p, 20p, 50p, £1, and £2.
学生认识硬币和纸币，计算金额并进行简单找零。常见面额包括 1 便士、2 便士、5 便士、10 便士、20 便士、50 便士、1 英镑和 2 英镑。
roblems combine addition and subtraction. For example, if a toy costs 65p and you pay with £1, the change is 100p − 65p = 35p.
货币问题综合运用加减法。例如，一个玩具 65 便士，你付 1 英镑，找零为 100p − 65p = 35p。
£1 = 100p, 50p + 20p + 10p = 80p
- Count a mixed set of coins and notes. | 计算混合硬币和纸币的总金额。
- Add and subtract money amounts. | 对金额进行加减。
- Solve shopping word problems involving change. | 解决涉及找零的购物应用题。
9. Time and Calendar | 时间与日历
Grade 2 students read time to the nearest five minutes on analogue and digital clocks. They know that 60 minutes make 1 hour and 24 hours make 1 day.
二年级学生能读出模拟钟和数字钟上接近五分钟的时间。他们知道 60 分钟等于 1 小时，24 小时等于 1 天。
Calendar skills include naming days of the week, months of the year, and reading dates. Students also compare durations such as hours and half hours.
日历技能包括说出星期和月份的名称，并读出日期。学生还能比较小时和半小时等时间长度。
1 hour = 60 minutes, 1 day = 24 hours, 1 week = 7 days
- Match analogue times to digital times. | 将模拟时间与数字时间对应。
- Solve simple problems about elapsed time. | 解决简单的经过时间问题。
- Use a calendar to find dates and days. | 使用日历查找日期和星期。
10. Length and Measurement | 长度与测量
Students measure length using non-standard units and standard units such as centimetres and metres. They learn to estimate, compare, and order lengths.
学生使用非标准单位和标准单位（如厘米和米）测量长度。他们学习估计、比较和排序长度。
A ruler is used to measure to the nearest centimetre. Longer distances can be measured in metres, and 100 centimetres equal 1 metre.
使用尺子测量到最接近的厘米。较长距离可用米测量，100 厘米等于 1 米。
1 m = 100 cm
- Choose the correct unit for measuring objects. | 为测量物体选择合适的单位。
- Compare lengths using >, <, and =. | 使用 >、< 和 = 比较长度。
- Solve measurement word problems. | 解决测量应用题。
11. 2D and 3D Shapes | 平面与立体图形
Grade 2 geometry covers common two-dimensional shapes such as triangles, squares, rectangles, circles, pentagons, and hexagons. Students count sides and vertices.
二年级几何包括常见的平面图形，如三角形、正方形、长方形、圆形、五边形和六边形。学生数边和顶点。
Three-dimensional shapes include cubes, cuboids, spheres, cylinders, cones, and pyramids. Students identify faces, edges, and vertices.
立体图形包括正方体、长方体、球体、圆柱体、圆锥体和棱锥体。学生辨认面、棱和顶点。
A cube has 6 faces, 12 edges, and 8 vertices.
正方体有 6 个面、12 条棱和 8 个顶点。
- Sort shapes by their properties. | 根据属性对图形分类。
- Identify shapes in everyday objects. | 辨认日常物品中的图形。
- Draw and describe simple 2D shapes. | 画出并描述简单平面图形。
12. Data and Picture Graphs | 数据与象形图
Students collect, organise, and represent data using tally charts and picture graphs. Each picture or symbol represents one item or a given number of items.
学生收集、整理数据，并使用记数表和象形图表示数据。每个图形或符号代表一个项目或指定数量的项目。
They answer questions by reading and interpreting data. For example, a picture graph of favourite fruits shows which fruit is most popular.
他们通过读取和解释数据回答问题。例如，最喜爱水果的象形图可以显示哪种水果最受欢迎。
苹果 🍎 = 2 个, 香蕉 🍌 = 1 个
- Create tally charts and picture graphs. | 制作记数表和象形图。
- Compare data using words like more, fewer, and same. | 使用“更多”“更少”“相同”等词语比较数据。
- Solve simple problems based on graph data. | 根据图表数据解决简单问题。
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