Students attending Ministry of Education’s (MOE) Primary Schools in Singapore follow a well-defined Mathematics syllabus. We provide a complementary tuition programme.
The learning journey can be divided into a Lower Block (Primary Three and Primary Four) and an Upper Block (Primary Five and Primary Six).
The Upper Block builds upon the foundation established in the Lower Block. Most topics introduced in Primary Three and Four are revisited in greater depth. Concepts learnt become assumed knowledge, and they are built upon like a Mille-feuille. In addition, some new topics are introduced.
Overall, there is broader content, greater depth, more inter-connections between topics and the pace of learning is faster.
Here is a simple overview.
Primary Five |
Theme: Number and Algebra |
1. Numbers up to 10 million |
2. Four orders of operations (without calculator) – × and ÷ by 10, 100, 100 – BODMAS – estimation and checking reasonableness of calculated answer – word problems (part-whole, comparison models) |
3. Fractions (without calculator) – understand conceptual relation between fraction and division (part-whole model) – + and – mixed numbers: + and – whole-number and fractional parts – fraction of a set: fraction x whole number – proper/improper fraction x proper/improper fraction, “cancellation”, simplify – mixed number x whole number – word problems (+, -, x) (part-whole, comparison, guess-and-check, working backwards, grouping/simplifying models) (single-, multi-step) |
4. Decimals (without calculator) – x and ÷ decimals (to 3 d.p.) by 10/100/1000 – unit conversion and equivalence for length (cm-m, m-km), weight (g-kg), volume (ml-l) – relationship b/w smaller and larger units on linear scale (e.g. ruler, weighing scale, measuring cylinder) – estimation and checking reasonableness of calculated answer – word problems (+, -, x, ÷, everyday examples, e.g. prices) |
5. Percentages – understand part of a whole concept in terms of % – find percentage part of a whole; writing asnwer as % – use linear scale to visualize part-whole concept, equivalence / relationship between %, fraction and decimal – word problems (discount, GST, service charge, savings/loan annual interest) |
6. Ratio – interpretation of a:b and a:b:c – equivalent ratios, simplifying ratios – dividing a quantity in a given ratio – word problems (2 sets of ratios with common term, part-whole, comparison models) |
7. Rate – interpretation: quantity A per unit quantity B – triangle relation between rate, quantity A and quantity B – word problems (everyday examples – postage, parking, water bill, electricity bill; proportion) |
Theme: Measurement and Geometry |
1. Area of Triangle – concept of base (b), height (h), their perpendicular relationship; identification of b and h – formula for area – concept: area of triangle is ½ area of rectangle, relation of b and h to length and breadth of rectangle – word problems (Δ on square grids; composite figures with squares, rectangles and triangles) |
2. Volume of Cube and Cuboid – unit cubes, volume of 3-D figures in cubic units, cm^{3}, m^{3}. – drawing on isometric grid – drawing top/front/side view of 3-D figure on square grid – volume formula – relate area to volume – volume of liquid in tank – to know and apply 1ml = 1cm^{3}, 1L = 1000cm^{3} |
3. Angles – angles on a straight line – angles at a point – vertically opposite angles – finding unknown angles |
4. Angles in Triangles – acute- and obture-angle triangles – properties of equilateral, isoceles and right-angle triangles – sum of angles in triangle = 180^{o} – finding unknown angles in triangle – draw triangles with given angles and lengths using protractor, ruler and set squares |
5. Rhombus, Parallelogram and Trapezium -their properties – find unknown angles in these quadrilaterals |
Theme: Statistics |
1. Average of a set of data – understand average = total / number of data – triangle relationship; calculate third unknown given two quantities – word problems (average height / weight, average temperature etc) |
Primary Six |
Theme: Number and Algebra |
1. Fraction – division * proper fraction divide by whole number * whole number / proper fraction divide by proper fraction – word problems * BODMAS combinations * proper/improper/mixed * part-whole, comparison models, multi-steps, combination with other topics (e.g. area, volume, ratio) |
2. Percentage – find whole given percentage of a part – increase and decrease in percent, before and after concept in terms of %, identifying the original 100% – model relationship between “fraction of fraction” and “percent of percent” – word problems (everyday examples) |
3. Ratio – convert fraction of a set to ratio – proportions and ratios – word problems involving equivalent ratios, before-after concept |
4. Rate and speed – difference between speed and average speed – speed = distance / time; triangle relationship – calculate and write speed in different units, e.g. km/h, m/s, m/min, cm/s. – word problems * everyday examples: vehicles, animals, 100m sprint time, fan speed * journey question with speed, distance, time; given two variable, find the third variable * Two vehicles moving (1) in same direction; (2) away from a point in opposite directions; (3) towards a common point from opposite directions * appreciate that distance and time can add; not speed * constant speed = no change in speed |
5. Algebra – concept of variable – link algebra (unknown variable) to model drawing – write simple linear algebraic expressions and solving equations, BODMAS – simplify linear equations (no brackets); solving – simultaneous equations, substitution, elimination |
Theme: Measurement and Geometry |
1. Area and circumference of circle – identify radius, diameter; know their properties – to know π = circumference / diameter, 22/7 or 3.14 – formula for circles, semi-circles and quadrants – composite figures with squares, rectangles, triangles, semi-circles, quandrants – estimate area of circle on square grid paper – to understand circumference of wheel = distance travelled in one complete turn – circle drawn in square: relate diameter of circle to length of square |
2. Volume of cube and cuboid – find length, given volume of a cube – find length, given volume, breadth and height of cuboid – find height, given volume and base area of cuboid – find area, given volume and height of cuboid – identify perfect squares and relationship of square root (√) to length of a face of cuboid – identify perfect cubes and relationship of cube root to length of a cube |
3. Special Quadrilaterals – Solve for unknown angles in square, rectangle, triangle, rhombus, parallelogram, trapezium. |
4. Nets – Identify and draw 2-D representations of a cube, cuboid, cone, cylinder, prism, pyramid – identify the nets of a 3-D figure: cube, cuboid, prism, pyramid – identify an object from it’s net drawing |
Theme: Statistics |
1. Pie charts – interpret data in terms of fraction and percentage (concept of proportionality) – 1-step word problems |
Many students view topics in isolation. They compartmentalize content knowledge into silos in their mind. Rote learning is common – memorization of formulas and method steps, followed by repetition of laborious computations on numerous similar practice questions. Many parents subscribe to the methodology of grinding through endless problem sums from past-year papers. The more, the merrier.
The difficulty level is raised for the Upper Block. The problem sums encountered in the Lower Block are elementary. In Primary 5 and Primary 6, some topics require content knowledge from topics learnt in the Lower Block and earlier in the Upper Block. Some problem sums test understanding of concepts from multiple topics (e.g. fraction plus ratio). Some require multiple heuristic approaches to solve. All these add up to increase the difficulty level for Upper Block students.
Our Math tuition emphasis a fundamental understanding of mathematical concepts. Each problem sum is approached as a novel challenge. The student is taught careful analysis and deconstruction of information, agile thinking, and identification of heuristic approaches for solution. Clear and neat presentation of the method used is always encouraged.