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Key stage
KS1(P.1-P.3)
Strand > Learning Unit
- KS1-N2-1 -Perform addition (with numbers up to 3 digits, not involving carrying in three steps but involving the commutative and associative properties of addition).
- KS1-N2-2 -Perform subtraction (with numbers up to 3 digits).
- KS1-N2-3 -Perform multiplication (with numbers up to 1 digit by 3 digits, involving the commutative property of multiplication).
- KS1-N2-4 -Perform division (with divisor 1 digit and dividend 3 digits).
- KS1-N2-5 -Perform mixed operations of:
(a) Addition and subtraction (with numbers up to 3 digits, involving small brackets); (b) Multiplication and addition; } (Multiplication with numbers not greater than 10; no brackets involved) (c) Multiplication and subtraction. - KS1-N2-6 -Solve problems involving mixed operations.
- KS1-N2-7 -Solve problems involving addition, subtraction, multiplication and division in the calculation of money (not involving mixed operations).
- KS1-M2-1 -Compare the length of objects and the distance between objects directly.
- KS1-M2-2 -Compare the length of objects and the distance between objects using improvised units (e.g. a paper clip, an eraser, a book, etc.)
- KS1-M2-3 -Measure and compare the length of objects and the distance between objects using 'millimetre' (mm), 'centimetre' (cm) or 'metre' (m).
- KS1-M2-4 -Express and compare the length of objects and the distance between objects using 'kilometre' (km).
- KS1-M2-5 -Measure the length of objects and the distance between objects with finger width, arm length, foot span, finger span, stride length, etc., as 'ever-ready rulers'.
- KS1-M2-6 -Measure with appropriate measuring tools.
- KS1-M2-7 -Record the length of objects and the distance between objects with an appropriate single unit.
- KS1-M3-1 -Tell the dates and days of a week.
- KS1-M3-2 -Tell time from a clock face and a digital clock.
- KS1-M3-3 -Record the duration of time for different activities using 'hours and minutes', 'minutes and seconds' or 'seconds' (not involving changing units).
- KS1-M3-4 -Recognize and apply the '24-hour time'.
- KS1-M4-1 -Compare the weight of objects directly.
- KS1-M4-2 -Measure and compare the weight of objects using improvised units.
- KS1-M4-3 -Measure and compare the weight of objects using 'gram' (g) or 'kilogram' (kg).
- KS1-M4-4 -Measure with appropriate tools.
- KS1-M4-5 -Record the weight of objects with appropriate units.
- KS1-S2-1 -Identify 2-D shapes intuitively: triangles, quadrilaterals, trapeziums, parallelograms, pentagons, hexagons, squares, rectangles, rhombuses and circles.
- KS1-S2-2 -Recognize the simple characteristics of triangles (e.g. 3 sides, 3 angles), including right-angled triangles, isosceles triangles and equilateral triangles.
- KS1-S2-3 -Group 2-D shapes.
- KS1-S2-4 -Describe the relative positions of two 2-D shapes using 'left', 'right', 'above' and 'under'.
KS2(P.4-P.6)
Strand > Learning Unit
- KS2-N2-1 -Understand the concepts of multiples and factors.
- KS2-N2-2 -Use the listing method to find all the factors of a number.
- KS2-N2-3 -Understand the concepts of common multiples and common factors.
- KS2-N2-4 -Use the listing method to find common multiples and common factors of two numbers.
- KS2-N2-5 -Use the listing method to find the least common multiple and the highest common factor of two numbers.
- KS2-N3-1 -Understand the concept of fractions as a part of one whole.
- KS2-N3-2 -Recognize the relationship between fractions and the whole.
- KS2-N3-3 -Convert improper fractions into mixed fractions and vice versa.
- KS2-N3-4 -Understand the concept of equivalent fractions.
- KS2-N3-5 -Compare fractions.
- KS2-N5-1 -Perform the four operations on whole numbers and fractions (with denominators not exceeding ten for addition and subtraction.)
- KS2-N5-2 -Perform the four operations involving whole numbers and decimals.
- KS2-N5-3 -Solve problems involving whole numbers and fractions.
- KS2-N5-4 -Solve problems involving whole numbers and decimals.
- KS2-N5-5 -Solve problems involving whole numbers and decimals in the calculation of money.
- KS2-N5-6 -Estimate the answers.
- KS2-N6-1 -Understand the concept of percentages.
- KS2-N6-2 -Convert percentages into fractions, and vice versa.
- KS2-N6-3 -Convert percentages into decimals, and vice versa.
- KS2-N6-4 -Solve simple problems on percentages, including:
(a) Finding percentages;
(b) Expressing the value of a percentage of a quantity;
(c) Discount.
- KS2-M2-1 -Tell the dates and days of a week.
- KS2-M2-2 -Tell time from a clock face and a digital clock.
- KS2-M2-3 -Record the duration of time for different activities using'hours and minutes, 'minutes and seconds' or 'seconds' (not involving changing units).
- KS2-M2-4 -Recognize and apply the ' 24-hour time '.
- KS2-M3-1 -Compare the length of objects and the distance between objects directly.
- KS2-M3-2 -Compare the length of objects and the distance between objects using improvised units (e.g. a paper clip, an eraser, a book, etc.)
- KS2-M3-3 -Measure and compare the length of objects and the distance between objects using 'millimetre' (mm), 'centimetre' (cm) or 'metre' (m).
- KS2-M3-4 -Express and compare the length of objects and the distance between objects using 'kilometre' (km).
- KS2-M3-5 -Measure the length of objects and the distance between objects with finger width, arm length, foot span, finger span, stride length, etc., as 'ever-ready rulers'.
- KS2-M3-6 -Measure with appropriate measuring tools.
- KS2-M3-7 -Record the length of objects and the distance between objects with an appropriate single unit.
- KS2-M4-1 -Compare the weight of objects directly.
- KS2-M4-2 -Measure and compare the weight of objects using improvised units.
- KS2-M4-3 -Measure and compare the weight of objects using 'gram'(g) or 'kilogram' (kg).
- KS2-M4-4 -Measure with appropriate tools.
- KS2-M4-5 -Record the weight of objects with appropriate units.
- KS2-M5-1 -Compare the capacity of containers directly.
- KS2-M5-2 -Measure and compare the capacity of containers using improvised units.
- KS2-M5-3 -Measure and compare the capacity of containers using 'Litre' (L) or 'millilitre' (mL).
- KS2-M5-4 -Measure with appropriate tools.
- KS2-M5-5 -Record the capacity of containers with an appropriate single unit.
- KS2-M8-1 -Measure and compare the volume of solids using 'cubic centimetre' (cm3) or 'cubic metre' (m3).
- KS2-M8-2 -Find the volume of cubes and cuboids.
- KS2-M8-3 -Understand the relationship between capacity and volume (the relationship between litre / millilitre and cubic centimetre).
- KS2-M8-4 -Find the volume of irregular solids by displacement of water or other methods.
- KS2-S2-1 -Recognize the characteristics of 2-D shapes: triangles (e.g. 3 sides, 3 angles, including right-angled triangles, isosceles triangles and equilateral triangles), quadrilaterals, pentagons, hexagons, squares, rectangles, rhombuses, parallelograms, trapeziums and circles.
- KS2-S2-2 -Group 2-D shapes.
KS3(S.1-S.3)
Strand > Learning Unit
- KS3-NA1-1 -use positive numbers, negative numbers and zero to describe situations like profit and loss, floor levels relative to the ground level
- KS3-NA1-2 -demonstrate recognition of the ordering of integers on the number line
- KS3-NA1-3 -add, subtract, multiply and divide directed numbers (with at most 3 operations in each expression)
- KS3-NA5-1 -solve simple selling problems
- KS3-NA5-2 -solve problems on simple interest
- KS3-NA5-3 -solve simple problems on compound interest, compounded yearly (confined to calculations for at most 3 years when not using the compound interest formula; excluding problems to find the number of years and the interest rate)
- KS3-NA5-4 -solve simple problems on growths and depreciations (confined to calculations of new values for at most 3 repeated growths/depreciations)
- KS3-NA7-1 -demonstrate recognition of the difference between rate and ratio
- KS3-NA7-2 -represent a ratio in the form a : b (or
), a: b: c - KS3-NA7-3 -find the other quantity from a given ratio a : b and the value of either a or b (including similar calculations for the case of a : b : c)
- KS3-NA7-4 -use rate and ratio to solve simple real-life problems including mensuration problems
- KS3-NA8-1 -distinguish the difference between 2x and 2 + x; (–2)n and –2n; x2 and 2x, etc.
- KS3-NA8-2 -translate word phrases/contexts into algebraic languages
- KS3-NA8-3 -substitute values into some common and simple formulas and find the value of a specified variable
- KS3-NA8-4 -formulate simple equations/inequalities from simple contexts
- KS3-NA8-5 -describe patterns by writing the next few terms in arithmetic sequences, geometric sequences, Fibonacci sequence or sequences of polygonal numbers from several consecutive terms of integral values
- KS3-NA8-6 -find intuitively the nth term of a simple number sequence from the first few given terms (the terms given should be non-negative integers and the nth term is limited to the forms kn, n + k, nk and kn)
- KS3-NA8-7 -find the terms of the sequence from a given nth term
- KS3-NA9-1 -distinguish polynomials from algebraic expressions
- KS3-NA9-2 -demonstrate recognition of terminologies such as degree, ascending/descending orders, coefficients, number of terms, unlike terms and like terms, constants and variables
- KS3-NA9-3 -add or subtract polynomials of at most 4 terms
- KS3-NA9-4 -multiply
(a) a monomial by a monomial
(b) a binomial by a monomial
(c) a trinomial by a monomial - KS3-NA9-5 -multiply a binomial by a binomial
- KS3-NA11-1 -demonstrate recognition of factorization as a reverse process of expansion
- KS3-NA11-2 -factorize simple polynomials of not more than 4 terms by taking out common factors and/or grouping terms
- KS3-NA11-3 -factorize simple polynomials by using the difference of two squares or the perfect square expressions once
- KS3-NA11-4 -use the cross method to factorize expressions of the form ax2 + bx + c, where a is 1, 2 or 3 and c is an integer numerically not greater than 20
- KS3-NA13-1 -plot graphs of linear equations in 2 unknowns
- KS3-NA13-2 -demonstrate recognition that graphs of equations of the form ax + by + c = 0 are straight lines
- KS3-NA13-3 -determine whether a point lies on a straight line with a given equation
- KS3-NA13-4 -formulate simultaneous equations from simple contexts
- KS3-NA13-5 -solve a system of simple linear simultaneous equations (with integral coefficients and constants) which has a unique solution
(a) by algebraic methods (students can choose either the method of elimination or the method of substitution)
(b) by the graphical method - KS3-NA13-6 -be aware that the root obtained by the graphical method may not be exact
- KS3-NA14-1 -tell whether an equality is an equation or an identity
- KS3-NA14-2 -expand simple algebraic expressions by using the difference of two squares and the perfect square expressions
- KS3-NA15-1 -manipulate algebraic fractions with only one term in both the numerator and denominator such as
, 
, etc. - KS3-NA15-2 -substitute values of formulas (in which all exponents are positive integers) and find the value of a specified variable
- KS3-NA15-3 -perform change of subject in simple formulas but not including radical sign
- KS3-NA16-1 -use inequality signs >, > ,< and < to compare numbers
- KS3-NA16-2 -demonstrate recognition of and apply the following properties of inequalities:
For x > y,
(a) x + c > y+c
(b) cx > cy ( c > 0 ); cx < cy ( c < 0 ) - KS3-NA16-3 -formulate linear inequalities in one unknown from simple contexts
- KS3-NA16-4 -solve simple linear inequalities in one unknown with integral coefficients and constants
- KS3-NA16-5 -represent inequalities, such as x < –2, x > 3, etc., on the number line and vice versa
- KS3-MS1-1 -find the range of measures from a measurement of a given degree of accuracy
- KS3-MS1-2 -choose an appropriate measuring tool and technique for real-life measurements
- KS3-MS1-3 -choose an appropriate unit and the degree of accuracy for real-life measurements
- KS3-MS1-4 -estimate measures with justification
- KS3-MS1-5 -reduce errors in measurements
- KS3-MS3-1 -calculate arc lengths
- KS3-MS3-2 -calculate areas of sectors
- KS3-MS3-3 -calculate volumes of pyramids, circular cones and spheres
- KS3-MS3-4 -calculate surface areas of right pyramids, right circular cones and spheres
- KS3-MS3-5 -use the relationships between sides and surface areas/volumes of similar figures to solve related problems (calculations related to frusta are not expected)
- KS3-MS3-6 -distinguish among formulas for lengths, areas, volumes by considering dimensions
- KS3-MS4-1 -demonstrate recognition of common terms in geometry such as line segments, angles, polygons, regular polygons, cubes, cuboids and regular polyhedra (Platonic solids)
- KS3-MS4-2 -use common notations to represent points, line segments, angles and polygons
- KS3-MS4-3 -identify types of angles with respect to their sizes
- KS3-MS4-4 -determine whether a polygon is regular, convex, concave, equilateral or equiangular
- KS3-MS4-5 -make 3-D solids from given nets
- KS3-MS4-6 -sketch simple solids
- KS3-MS4-7 -sketch cross-sections of simple solids
- KS3-MS5-1 -determine the number of axes of symmetry from a figure and draw the axes of symmetry
- KS3-MS5-2 -determine the order of rotational symmetry from a figure and locate the centre of rotation
- KS3-MS5-3 -name the single transformation involved in comparing the object and its image
- KS3-MS5-4 -identify the image of a figure after a single transformation
- KS3-MS5-5 -demonstrate recognition of the effect on the size and shape of a figure under a single transformation
- KS3-MS7-1 -demonstrate recognition of the following terminologies on angles with respect to their positions relative to lines and polygons:
(a) adjacent angles
(b) angles at a point
(c) vertically opposite angles
(d) interior angles and exterior angles of polygons
(e) angles associated with lines and their transversals - KS3-MS7-2 -use the angle properties associated with intersecting lines/parallel lines to solve simple geometric problems (related converse theorems are to be treated in the learning unit 'Learning Geometry through a Deductive Approach')
- KS3-MS7-3 -use the properties of angles of triangles to solve simple geometric problems
- KS3-MS7-4 -use the relations between sides and angles associated with isosceles/equilateral triangles to solve simple geometric problems
- KS3-MS7-5 -use the formulas for the sums of the interior angles and exterior angles of convex polygons
- KS3-MS8-1 -name planes of reflectional symmetries of cubes
- KS3-MS8-2 -name axes of rotational symmetries of cubes
- KS3-MS8-3 -identify the nets of cubes, regular tetrahedra and right prisms with equilateral triangles as bases
- KS3-MS8-4 -match 3-D objects built up of cubes (not more than 10) from 2-D representations from various views
- KS3-MS8-5 -name
(a) the projection of an edge on a horizontal/vertical plane
(b) the angle between a line and a horizontal/vertical plane
(c) the angle between 2 planes, one of the planes being horizontal/vertical
- KS3-MS12-1 -use polar coordinates to describe positions of points in a plane
- KS3-MS12-2 -use an ordered pair to describe the position of a point in the rectangular coordinate plane and locate a point of given rectangular coordinates
- KS3-MS12-3 -match a point under a single transformation with its image in the rectangular coordinate plane (the transformation includes only translation, reflection with respect to lines parallel to the x-axis, y-axis and rotation about the origin through 90°, 180° and 270°)
- KS3-MS12-4 -calculate areas of simple figures that can be cut into or formed by common 2-D rectilinear figures
- KS3-MS14-1 -find the sine, cosine and tangent ratios for angles between 0° to 90° and vice versa
- KS3-MS14-2 -solve right-angled triangles
- KS3-MS14-3 -demonstrate recognition of the ideas of bearing, gradient, the angle of elevation and the angle of depression
- KS3-MS14-4 -solve simple 2-D problems involving one right-angled triangle
- KS3-DH1-1 -demonstrate recognition of various stages of Statistics including collection, organization, representation and analysis of data
- KS3-DH1-2 -use simple methods to collect data
- KS3-DH1-3 -distinguish discrete and continuous data
- KS3-DH1-4 -organize the same set of data by different grouping methods
- KS3-DH2-1 -construct simple statistical charts including stem-and-leaf diagrams, pie charts, histograms, scatter diagrams, broken line graphs, frequency polygons and curves, cumulative frequency polygons and curves
- KS3-DH2-2 -interpret simple statistical charts including stem-and-leaf diagrams, pie charts, histograms, scatter diagrams, broken line graphs, frequency polygons and curves, cumulative frequency polygons and curves
- KS3-DH2-3 -choose appropriate diagrams/graphs to present a set of data
- KS3-DH2-4 -compare the presentations of the same set of data by using statistical charts (statistical charts including various types of charts or the same type of charts but in different scales)
- KS3-DH2-5 -read information (including percentiles, quartiles, median) and frequencies from diagrams/graphs
- KS3-DH2-6 -identify sources of deception in misleading graphs/accompanying statements
- KS3-DH3-1 -find mean, median and mode from a set of ungrouped data
- KS3-DH3-2 -find median (from cumulative frequency polygons/curves only), mean and modal class from a set of grouped data
- KS3-DH3-3 -calculate the weighted mean of a set of data
- KS3-DH3-4 -identify sources of deception in cases of misuse of averages
, where 
(calculations on inclinations are not required)