新加坡政府小学数学大纲及考点（小学五年级G5）

之前我们介绍了新加坡政府小学一至四年级的教学大纲，今天我们接着来看新加坡政府小学五年级的教学大纲。

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。

新加坡小五的知识点脉络，总结如下图。

每个分支包含的知识点分列如下。

1千万以内整数知识考查点

1.1 reading and writing numbers in numerals and in words

整数四则运算

2.1 multiplying and dividing by 10, 100, 1000 and their multiples without calculator

2.2 order of operations without calculator

2.3 use of brackets without calculator

2.4 solving word problems involving the 4 operations

分数除法

1.1 dividing a whole number by a whole number with quotient as a fraction

1.2 converting fractions to decimals

分数四则运算

2.1 adding and subtracting mixed numbers

2.2 multiplying a proper/improper fraction and a whole number without calculator

2.3 multiplying a proper fraction and a proper/improper fractions without calculator

2.4 multiplying two improper fractions

2.5 multiplying a mixed number and a whole number

2.6 solving word problems involving addition, subtraction and multiplication

小数四则运算

1.1 multiplying and dividing decimals (up to 3 decimal places) by 10, 100, 1000 and their multiples without calculator

1.2 converting a measurement from a smaller unit to a larger unit in decimal form, and vice versa

• kilometres and metres

• metres and centimetres

• kilograms and grams

• litres and millilitres

1.3 solving word problems involving the 4 operations

百分比

expressing a part of a whole as a percentage

use of %

finding a percentage part of a whole

finding discount, GST and annual interest

solving up to 2-step word problems involving percentage

比例关系

1.1 notation, representations and interpretation of a:b and a:b:c, where a, b and c are whole numbers, excluding ratios involving fractions and decimals

1.2 equivalent ratios

1.3 dividing a quantity in a given ratio

1.4 expressing a ratio in its simplest form

1.5 finding the ratio of two or three given quantities

1.6 finding the missing term in a pair of equivalent ratios

1.7 solving up to 2-step word problems involving ratio

Rate

1.1 rate as the amount of a quantity per unit of another quantity

1.2 finding rate, total amount or number of units given the other two quantities

1.3 solving word problems involving rate

几何 - 三角形面积

1.1 concepts of base and height of a triangle

1.2 area of triangle

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

几何 - 正方体和立方体体积

2.1 building solids with unit cubes

2.2 measuring volume in cubic units, cm2 and m3 ,excluding conversion between cm2 and m3

2.3 drawing cubes and cuboids on isometric grid

2.4 volume of a cube/cuboid

2.5 finding the volume of liquid in a rectangular tank

2.6 relationship between l (or ml) and cm3

几何 - 角度

angles on a straight line

angles at a point

vertically opposite angles

finding unknown angles

几何 - 三角形

2.1 properties of

• isosceles triangle

• equilateral triangle

• right-angled triangle

2.2 angle sum of a triangle

2.3 finding unknown angles without additional construction of lines

几何 - 平行四边形/菱形/梯形

3.1 properties of

• parallelogram

• rhombus

• trapezium

3.2 finding unknown angles without additional construction of lines

统计 - 数据分析/平均值

1.1 average as ‘total value  number of data’

1.2 relationship between average, total value and number of data

参加新加坡PLSE或AEIS考试的孩子可以参照大纲复习，扫除知识盲点。