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。
新加坡小六的知识点脉络，总结如下图。
总的来说，新加坡政府小学六年级扩展的知识点并不多，因为小六第二学期要进行重要的毕业考试，教学内容会以扩展深度为主。
每个分支包含的知识点分列如下。
分数四则运算
1.1 dividing a proper fraction by a whole number without calculator
1.2 dividing a whole number/proper fraction by a proper fraction without calculator
1.3 solving word problems involving the 4 operations
百分比
1.1 finding the whole given a part and the percentage
1.2 finding percentage increase/decrease
1.3 solving word problems involving percentage
比例关系
1.1 relationship between fraction and ratio
1.2 solving word problems involving ratio including changing ratios
Rate and Speed
1. Distance, Time and Speed
1.1 concepts of speed and average speed
1.2 relationship between distance, time and speed exclude conversion of units e.g. km/h to m/min
1.3 writing speed in different units such as km/h, m/min, m/s and cm/s
1.4 solving up to 3-step word problems involving speed and average speed
代数
1.1 using a letter to represent an unknown number
1.2 notation, representations and interpretation of simple algebraic expressions
1.3 simplifying simple linear expressions excluding brackets
1.4 evaluating simple linear expressions by substitution
1.5 solving simple linear equations involving whole number coefficient only in simple context
几何 - 正方体和立方体体积
2.1 finding one dimension of a cuboid given its volume and the other dimensions
2.2 finding the length of one edge of a cube given its volume
2.3 finding the height of a cuboid given its volume and base area
2.4 finding the area of a face of a cuboid given its volume and one dimension
2.5 use of √ and 3√
几何 - 特殊四边形
1.1 finding unknown angles, without additional construction of lines, in composite geometric figures involving
• square
• rectangle
• triangle
• parallelogram
• rhombus
• trapezium
几何 - Net 立体展开图
2. Nets
2.1 identifying and drawing 2D representations of
• cube
• cuboid
• cone
• cylinder
• prism
• pyramid
2.2 identifying the nets of 3D solids
• cube
• cuboid
• prism
• pyramid
2.3 identifying the solid which can be formed by a given net
统计 - 数据呈现与分析/饼图
1. Pie Charts
1.1 reading and interpreting data from pie charts
1.2 solving 1-step problems using data from tables/graphs