# Singapore Mathematics - Primary 5

Topic/Sub-topic Content Learning Outcomes
1 Whole numbers
1.1 Numbers up to 10 million Include:
• reading and writing numbers in numerals and in words,
• rounding off numbers to the nearest 1000.

1.2 Four operations   Include:
• multiplication and division by tens, hundreds and thousands without using calculators,
• solving word problems involving the 4 operations,
• estimation of answers in calculations,
1.3 Order of operations Include:
• combined operations involving the 4 operations,
• use of brackets.
2 Fractions
2.1 Concepts of fraction as division Include:
• association of a fraction with division,
• conversion between fractions and decimals.
2.2 Four operations Include:
• addition and subtraction of proper fractions without using calculators,
• addition and subtraction of mixed numbers,
• multiplication of a proper fractions and a proper/ improper fraction without using calculators,
• multiplication of an improper fraction and an improper fraction,
• multiplication of a mixed number and a whole number,
• division of a proper fraction by a whole number without using calculators,
• solving word problems involving the 4 operations.
Exclude:
• calculations involving more than 2 different denominators,
• multiplication of a mixed number by a proper fraction/improper fraction/mixed number,
• division of an improper fraction/mixed number by a whole number/ proper fraction.
• division by an improper fraction/ mixed number

(Denominators of given fractions should not exceed 12, for calculations without using calculators)

3 Decimals
3.1 Four operations   Include:
• multiplication and division of decimals (up to 3 decimal places) by tens, hundreds and thousands without using calculators,
• solving word problems involving the 4 operations,
• rounding off answers to a specified degree of accuracy,
• estimation of answers in calculations,
Exclude:
• expressing one quantity as a percentage of another, e.g. “A is 60% of B”.
• comparison of two quantities by percentage, e.g. “ A is 20% more than B.”
4 Percentages
5 Ratios
5.1 Ratio   Include:
• interpretation of a : b and a : b : c, where a, b and c are whole numbers,
• writing equivalent ratios,
• expressing a ratio in its simplest form,
• finding the ratio of two or three given quantities,
• finding the missing term in a pair of equivalent ratios,
• finding one quantity given the other quantity and their ratio,
• solving up to 2-step word problems involving ratio.
Exclude:
• ratios involving fractions and decimals.
6 Measurement
6.1 Length, mass and volume Include:
• conversion of 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
6.2 Area of triangle Include:
• identifying the base of a triangle and its corresponding height,
• use of formula to calculate the area of a triangle.
Exclude:
• finding the base/ height of a triangle given its area.
6.3 Volume of cube and cuboid Include:
• building solids with unit cubes,
• measurement of volume in cubic units,
• drawing cubes and cuboids on an isometric grid,
• measurement of volume in cubic centimetres (cm3)/ cubic metres (m3),
• use of formula to calculate the volume of a cube/ cuboid,
• finding the volume of liquid in a rectangular tank,
• conversion between l, ml and cm^3 ,
• solving up to 3-step word problems involving the volume of a cube/ cuboid.
Exclude:
• conversion between cm^3 and m^3
7 Geometry
7.1 Angles Include:
• using notation such as ∠ABC and ∠x to name angles,
• estimation and measurement of angles in degrees,
• drawing an angle using a protractor,
• use of the following properties to find unknown angles
• angles on a straight line,
• angles at a point,
• vertically opposite angles
7.2 Triangle Include:
• identifying and naming the following types of triangles
• isosceles triangle,
• equilateral triangle,
• right-angled triangle,
• use of the property that the angle sum of a triangle is 180°,
• finding unknown angles,
• drawing a triangle from given dimensions using ruler, protractor and set squares
Exclude:
• geometrical construction where the use of compasses is required,
• finding angles involving additional construction of lines,
• exterior angles
7.3 Paralelogram, rhombus and trapezium Include:
• identifying and naming parallelogram, rhombus and trapezium,
• properties of parallelogram, rhombus and trapezium,
• finding unknown angles,
• drawing a square/rectangle/parallelogram/rhombus/trapezium from given dimensions using ruler, protractor and set squares.
Exclude:
• the term ‘diagonal’ and its related properties,
• geometrical construction where the use of compasses is required,
• finding angles involving additional construction of lines.
8 DATA ANALYSIS
8.1 Average of a set of data Include:
• interpretation of average as "total amount ÷ number of items",
• calculation of the average number/quantity,
• finding the total amount given the average and the number of items,
• solving word problems involving average.
Source: http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf