新加坡政府小学数学大纲及考点（小学四年级G4）

之前我们介绍了新加坡政府小学一年级的教学大纲，今天我们接着来看新加坡政府小学二年级的教学大纲。

回顾一下，整个小学阶段，采用3+1的教学体系，三大模块数学知识和贯穿始终的数学过程思维训练。如下图所示。

数学过程思维这一环节最为关键的是思维技巧和策略思维方法。这部分内容是要求学生在掌握数学知识点的基础上，能活学活用，经过训练，学会常用的思维方法。

比如，从特例推导到一般的思维技巧，发现规律，找出通用模式。将整体拆解成部分，用“分而治之”的方法化整为零突破。从部分整合到全局的能力。猜测+验证的方法，对有些不能采用穷举方法的问题也很管用。具体如下图。

新加坡小四的知识点脉络，总结如下图。

每个分支包含的知识点分列如下。

100,000以内整数知识考查点

1.1 number notation, representations and place values (ten thousands, thousands, hundreds,tens, ones)

1.2 reading and writing numbers in numerals and in words

1.3 comparing and ordering numbers

1.4 patterns in number sequences

1.5 rounding numbers to the nearest 10, 100 or 1000

1.6 use of ≈

因子和倍数

2.1 factors, multiples and their relationship

2.2 determining if a 1-digit number is a factor of a given number within 100

2.3 finding the common factors of two given numbers

2.4 determining if a number is a multiple of a given 1-digit number

2.5 finding the common multiples of two given 1-digit numbers

四则运算

3.1 multiplication algorithm

• up to 4 digits by 1 digit

• up to 3 digits by 2 digits

3.2 division algorithm (up to 4 digits by 1 digit)

3.3 solving up to 3-step word problems involving the 4 operations

分数

1. Mixed Numbers and Improper Fractions

1.1 mixed numbers, improper fractions and their relationships

2. Fraction of a Set of Objects

2.1 fraction as part of a set of objects

3. Addition and Subtraction

3.1 adding and subtracting fractions with denominators of given fractions not exceeding 12 and not more than two different denominators

3.2 solving up to 2-step word problems involving addition and subtraction

小数

1. Decimals up to 3 decimal places

1.1 notation, representations and place values (tenths, hundredths, thousandths)

1.2 comparing and ordering decimals

1.3 dividing a whole number by a whole number with quotient as a decimal

1.4 converting decimals to fractions

1.5 converting fractions to decimals when the denominator is a factor of 10 or 100

1.6 rounding decimals to

• the nearest whole number

• 1 decimal place

• 2 decimal places

2. Addition and Subtraction

2.1 adding and subtracting decimals (up to 2 decimal places)

3. Multiplication and Division

3.1 multiplying and dividing decimals (up to 2 decimal places) by a 1-digit whole number

3.2 solving up to 2-step word problems involving the 4 operations

3.3 rounding off answers to a specified degree of accuracy

度量 - 长度/质量/体积

1. Length, Mass and Volume

1.1 measuring

• length in kilometres (km)

• volume of liquid in millilitres (ml)

1.2 measuring length/mass/volume (of liquid) in compound units

1.3 converting a measurement in compound units to the smaller unit, and vice versa

• kilometres and metres

• metres and centimetres

• kilograms and grams

• litres and millilitres

1.4 solving word problems involving length/mass/volume/capacity excluding fractions and compound units

度量 - 时间

1.1 measuring time in seconds

1.2 24-hour clock

1.3 solving problems involving time in 24-hour clock

几何 - 面积和周长

1.1 finding one dimension of a rectangle given the other dimension and its area/perimeter

1.2 finding the length of one side of a square given its area/perimeter

1.3 finding the area and perimeter of composite figures made up of rectangles and squares

几何 - 角度

1.1 using notation such as ∠ABC and ∠a to name angles

1.2 measuring angles in degrees

1.3 drawing an angle of given size

1.4 relating quarter, half and complete turns to angles in degrees

1.5 8-point compass

几何 - 矩形和正方形

2.1 properties of rectangle and square, excluding diagonal properties

2.2 drawing rectangles and squares on square grid

几何 - 轴线对称

3.1 identifying symmetric figures

3.2 determining whether a straight line is a line of symmetry of a symmetric figure

3.3 completing a symmetric figure with respect to a given line of symmetry on square grid

统计 - 图表和折线图

1.1 completing a table from given data

1.2 reading and interpreting data from tables/line graphs

1.3 solve 1-step problems using data from tables/graphs

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