The abilities by end of Grade 5:
(Calculator is allowed unless otherwise stated.)
1 WHOLE NUMBERS
Numbers up to 10
million Include: • reading and writing numbers in numerals and in words,
• rounding off numbers to the nearest 1000.
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,
• checking reasonableness of answers.
Order of operations
Include: • combined operations involving the 4 operations,
• use of brackets.
2 FRACTIONS
Concept of fraction
as division Include: • association of a fraction with division,
• conversion between fractions and decimals.
Four operations
Include
• addition and subtraction of proper fractions without using
calculators,
• addition and subtraction of mixed numbers,
• multiplication of two proper fractions without using
calculators,
• multiplication of an improper fraction and a proper/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.
(Denominators of given fractions should not exceed 12, for
calculations without using calculators.)
3 DECIMALS
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,
• checking reasonableness of answers.
Exclude multiplication and division by a decimal.
4 PERCENTAGE
Percentage
Include: • expressing a part of a whole as a percentage,
• use of the percentage symbol (%),
• writing fractions and decimals as percentages, and vice versa,
• finding a percentage part of a whole,
• solving up to 2-step word problems involving percentage,
• discount, GST and annual interest.
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.”
5 RATIO
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
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
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.
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 , ml and cm3,
• solving up to 3-step word problems involving the volume of a
cube/ cuboid.
Exclude conversion between cm3 and m3.
7 GEOMETRY
Angles Include use of the following properties to find unknown angles:
∗ angles on a straight line,
∗ angles at a point,
∗ vertically opposite angles.
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 180o,
• 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.
Parallelogram,
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
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.
