Singapore · MOE Syllabus Outcomes
Primary 6 Mathematics
A comprehensive final year primary course focusing on preparing students for secondary transition through deep conceptual understanding. Students master complex ratios, algebraic foundations, and spatial visualization to solve multi-step real world problems.
01Algebraic Foundations
Introduction to using letters to represent unknown numbers and expressing relationships through algebraic expressions.
Understanding how variables represent unknown quantities and constructing simple algebraic expressions.
Substituting numerical values for variables to evaluate the value of algebraic expressions.
Combining like terms and applying the distributive property to simplify linear algebraic expressions.
Translating word problems into simple linear equations with one unknown.
Using inverse operations to solve basic linear equations involving addition, subtraction, multiplication, and division.
Applying multiple inverse operations to solve linear equations with two steps.
02Proportional Reasoning with Fractions
Extending fractional concepts to division and complex multi-step word problems involving remainders.
Visualizing and understanding the concept of dividing a fraction by a whole number or another fraction.
Calculating the division of fractions using the reciprocal method and simplifying results.
Solving complex word problems involving all four operations with fractions, decimals, and whole numbers.
Solving problems where a fraction of a remaining amount is taken, often using model drawing.
Converting between fractions, decimals, and percentages to solve problems efficiently.
03Advanced Ratio and Percentage
Analyzing relationships between quantities and applying percentage increases or decreases to financial contexts.
Exploring the connection between ratio notation, fractional representation, and proportional relationships.
Solving problems involving direct proportional relationships using various methods, including unitary method and ratio.
Calculating percentage increase and decrease in various real-world contexts, including profit/loss.
Applying percentage concepts to real-world financial transactions, including taxes, discounts, and commissions.
Solving problems involving two successive percentage changes, focusing on understanding the base for each change.
04Circles and Area
Investigating the properties of circles and calculating area and perimeter of composite figures.
Identifying radius, diameter, circumference, and understanding the constant pi (π) as a ratio.
Calculating the circumference of circles and semi-circles using the formula C = πd or C = 2πr.
Deriving and applying the formula for the area of a circle (A = πr²).
Finding the area and perimeter of complex shapes made of rectangles, triangles, and circles/semi-circles.
Calculating the perimeter of complex shapes involving straight lines and curved arcs.
05Volume and Rate
Measuring space in three dimensions and calculating the speed of change over time.
Calculating the volume of cuboids and other right prisms, and understanding capacity.
Calculating the volume of liquids and solving problems involving the rate of flow into or out of containers.
Defining speed as a rate and solving basic problems involving distance, time, and speed.
Calculating average speed for journeys involving varying speeds and durations.
Interpreting and drawing distance-time graphs to represent journeys and calculate speed.
Solving more complex problems involving speed, distance, and time, including scenarios with varying speeds or multiple segments.
06Data Interpretation and Pie Charts
Analyzing and representing data sets using pie charts and calculating averages.
Understanding different methods of data collection and types of data (qualitative/quantitative).
Using frequency tables, tally charts, and simple bar graphs to organize and present data.
Interpreting data presented in circular graphs using fractions, percentages, and angles.
Converting raw data into angles or percentages to accurately construct pie charts.
Calculating the mean of a data set and using it to find unknown values.
Calculating the weighted mean for data sets where different values have different frequencies or importance.
Using statistical information to make predictions or informed choices, considering data reliability.
07Integers and Rational Numbers
Extending number systems to include negative numbers and performing operations with them.
Understanding positive and negative numbers, their representation on a number line, and real-world applications.
Performing addition and subtraction with positive and negative integers using number lines and rules.
Applying rules for multiplication and division of positive and negative integers.
Applying the order of operations (BODMAS/PEMDAS) to expressions involving integers.
Defining rational numbers and performing operations with fractions and decimals (including negative).
08Angles and Polygons
Exploring properties of angles, parallel lines, and various polygons.
Identifying and classifying different types of angles (acute, obtuse, reflex, complementary, supplementary).
Applying properties of angles at a point, angles on a straight line, and vertically opposite angles to solve problems.
Investigating the sum of angles in a triangle and properties of isosceles and equilateral triangles.
Understanding the sum of angles in a quadrilateral and properties of special quadrilaterals (squares, rectangles, parallelograms).
Deepening understanding of the properties of various triangles and quadrilaterals, including their sides, angles, and diagonals.
09Introduction to Coordinate Geometry
Plotting points, finding distances, and understanding basic transformations on a coordinate plane.
Understanding the Cartesian coordinate system, plotting points, and identifying quadrants.
Calculating the horizontal and vertical distances between points on a coordinate plane.
Calculating the area of simple polygons (e.g., triangles, rectangles) when their vertices are given on a coordinate plane.
Understanding the concept of congruence and identifying congruent figures in various orientations.
Identifying and drawing lines of symmetry and understanding rotational symmetry in 2D shapes.
10Number Patterns and Sequences
Identifying patterns, generating terms, and finding the nth term of linear sequences.
Recognizing and describing simple arithmetic and geometric number patterns.
Using a given rule or formula to generate terms of a number sequence.
Deriving the general formula (nth term) for linear (arithmetic) sequences.
Solving problems involving number patterns and sequences in practical contexts.