Topics/ Sub-topics

Content

1   WHOLE NUMBERS

Numbers up to 100

Include:

•       counting to tell the number of objects in a given set,

•       comparing the number of objects in two or more sets,

•       use of ordinal numbers (first, second, up to tenth) and symbols (1st, 2nd, 3rd, etc.),

•       number notation and place values (tens, ones), 

•       reading and writing numbers in numerals and in words,

•       comparing and ordering numbers, 

•       number patterns.

Exclude:

•       use of the terms ‘cardinal number’ and ‘ordinal number’,

•       use of the symbols > and <.

Addition and subtraction

Include:

•       concepts of addition and subtraction,

•       use of the addition symbol (+) or subtraction symbol (−) to write a mathematical statement for a given situation,

•       comparing two numbers within 20 to tell how much one number is greater (or smaller) than the other,

•       recognising the relationship between addition and subtraction,

•       building up the addition bonds up to 9 + 9 and committing to memory,

•       solving 1-step word problems involving addition and subtraction within 20,

•       addition of more than two 1-digit numbers,

•       addition and subtraction within 100 involving

∗ a 2-digit number and ones,

∗ a 2-digit number and tens,

∗ two 2-digit numbers,

•       addition and subtraction using formal algorithms.

Mental calculation 

Include:

•       addition and subtraction within 20,

•       addition and subtraction involving

∗ a 2-digit number and ones without renaming,

∗ a 2-digit number and tens.

Multiplication and division

Include:

•       multiplication as repeated addition (within 40),

•       use of the multiplication symbol (×) to write a mathematical statement for a given situation,

•       division of a quantity (not greater than 20) into equal sets:

∗ given the number of objects in each set,

∗   given the number of sets,

•       solving 1-step word problems with pictorial representation.

Exclude: 

•       use of multiplication tables,

•       use of the division symbol (÷).

2   MEASUREMENT 

Length and mass

Include:

•       measurement and comparison of the lengths/ masses of two or more objects in non-standard units,

•       use of the following terms: long, longer, longest short, shorter, shortest tall, taller, tallest

high, higher, highest heavy, heavier, heaviest light, lighter, lightest

Exclude finding the difference in length/ mass.

Time

Include telling and writing time to the hour/ half hour.

Exclude 24-hour clock.

Money

Include:

•       identifying coins and notes of different denomination,

•       matching a coin/ note of one denomination to an equivalent set of coins/ notes of another denomination,

•       telling the amount of money ∗ in cents up to $1, ∗ in dollars up to $100.

•       use of the symbols $ and ¢,

•       solving word problems involving addition and subtraction of money in dollars only (or in cents only).

Exclude combinations of dollars and cents.

3   GEOMETRY

Basic shapes:

•       rectangle

•       square

•       circle 

•       triangle

Include:

•       identifying and naming the 4 basic shapes from 2-D and 3-D objects,

•       describing and classifying shapes.

Patterns 

Include:

•       making/ completing patterns with 2-D cut-outs according to one or two of the following attributes

∗ shape ∗ size

∗ colour

•       making / completing patterns with 3-D models:

∗ cube

∗ cuboid (rectangular block) 

∗ cone

∗ cylinder

4   DATA ANALYSIS

Picture graphs 

Include:

•       collecting and organising data,

•       making picture graphs,

•       use of a symbol/picture to represent one object,

•       reading and interpreting picture graphs in both horizontal and vertical forms.

Exclude picture graphs with scales.

Topics/ Sub-topics

Content

1   WHOLE NUMBERS

Numbers up to 1000

Include:

•        counting in tens/ hundreds,

•        number notation and place values (hundreds, tens, ones), 

•        reading and writing numbers in numerals and in words,

•        comparing and ordering numbers,

•        number patterns.

Addition and

subtraction 

Include:            

•       addition and subtraction of numbers up to 3 digits,

•       solving up to 2-step word problems involving addition and subtraction.

Multiplication and division

Include:

•       building up the multiplication tables of 2, 3, 4, 5 and 10 and committing to memory,

•       use of the division symbol (÷) to write a mathematical statement for a given situation,

•       recognising the relationship between multiplication and division,

•       multiplication and division within the multiplication tables,

•       solving 1-step word problems involving multiplication and division within the multiplication tables.

Exclude division with remainder.

Mental calculation  

Include 

•       addition and subtraction involving

∗ a 3-digit number and ones,

∗ a 3-digit number and tens,

∗ a 3-digit number and hundreds.

•       multiplication and division within the multiplication tables of 2, 3, 4, 5 and 10.

2   FRACTIONS

Fraction of a whole

Include:

•        interpretation of fraction as part of a whole,

•        reading and writing fractions,

•        comparing and ordering

∗ unit fractions,

∗ like fractions.

(Denominators of given fractions should not exceed 12.) Exclude fraction of a set of objects.

Addition and subtraction

Include addition and subtraction of like fractions within one whole. 

(Denominators of given fractions should not exceed 12.)

3   MEASUREMENT

Length, mass and volume 

Include:

•       estimation and measurement of

       ∗     length in metres/ centimetres,

       ∗     mass in kilograms/ grams,

       ∗     volume of liquid in litres,

•       drawing a straight line of given length,

•       use of the appropriate measures and their abbreviations cm, m,

g, kg, A,

•       comparing ∗ lengths,

∗ masses,

∗ volumes,

•       solving word problems involving length/ mass/ volume.

Exclude:

•       conversion of units,

•       measurement in compound units,

•       capacity of container,

•       volume of solid.

Time

Include:

•       telling and writing time to 5 minutes,

•       use of ‘a.m.’ and ‘p.m.’,

•       use of abbreviations h and min,

•       drawing hands on the clock face to show time,

•       duration of one hour/ half hour from an o’clock time.

Exclude finding the duration of a time interval.

Money

Include:

•       counting the amount of money in a given set of notes and coins,

•       reading and writing money in decimal notation,

•       comparing two or three amounts of money,

•       converting an amount of money in decimal notation to cents only, and vice versa,

•       solving word problems involving money in dollars only (or in cents only).   

4   GEOMETRY

2-D and 3-D figures

Include:

•      identifying, naming and describing 

∗ semicircle 

∗ quarter circle,

•      identifying the basic shapes that make up a given figure,

•      forming different 2-D figures with cut-outs of 

∗ rectangle

∗ square

∗ triangle

∗ semicircle

∗ quarter circle,

•      forming different 3-D figures with concrete models of 

∗ cube

∗ cuboid

∗ cone

∗ cylinder,

•      copying figures on dot grid or square grid.

Patterns 

Include making/ completing patterns with 2-D cut-outs according to one or two of the following attributes

∗   shape

∗   size

∗    orientation

∗    colour

Line, curve and surface

Include:

• identifying lines (straight lines) and curves,

• identifying flat faces of a 3-D object.

5   DATA ANALYSIS 

Picture graphs

Include:

•       making picture graphs with scales,

•       reading and interpreting picture graphs with scales,

•       solving problems using information presented in picture graphs.

Exclude use of an incomplete symbol/picture.

Topics/ Sub-topics

Content

1   WHOLE NUMBERS 

Numbers up to          10 000

Include:

•       number notation and place values (thousands, hundreds, tens, ones), 

•       reading and writing numbers in numerals and in words,

•       comparing and ordering numbers,

•       odd and even numbers,

•       number patterns.

Addition and

subtraction 

Include:

•      addition and subtraction of numbers up to 4 digits, 

•      use of the terms ‘sum’ and ‘difference’,

•      solving up to 2-step word problems involving addition and subtraction.

Multiplication and division

Include:

•       building up the multiplication tables of 6, 7, 8 and 9 and committing to memory,

•       use of the terms ‘product’, ‘quotient’ and ‘remainder’,

•       multiplication and division within the multiplication tables,

•       division with remainder,

•       multiplication and division of numbers up to 3 digits by 1 digit,

•       solving up to 2-step word problems involving the 4 operations.

Mental calculation  

Include:

•     addition and subtraction involving two 2-digit numbers,

•     multiplication and division within the multiplication tables.

2  FRACTIONS

Equivalent fractions

Include:

•       recognising and naming equivalent fractions,

•       listing the first 8 equivalent fractions of a given fraction,

•       writing the equivalent fraction of a fraction given the denominator or the numerator,

•       expressing a fraction in its simplest form,

•       comparing fractions with respect to half,

•       comparing and ordering unlike fractions.

(Denominators of given fractions should not exceed 12.)

Addition and subtraction

Include addition and subtraction of two related fractions within one whole. 

(Denominators of given fractions should not exceed 12.)

3   MEASUREMENT

Length, mass and volume 

Include:

•       measurement of

∗ length in kilometres (km),

∗ volume of liquid in millilitres (ml),

•       measurement of length/ mass/ volume (of liquid) in compound

units,

•       conversion of a measurement in compound units to the smaller unit, and vice versa,

        ∗     kilometres and metres,

        ∗     metres and centimetres,

        ∗     kilograms and grams,

  ∗     litres and millilitres. 

•       solving word problems involving length/ mass/ volume/ capacity.

Exclude the 4 operations and word problems involving compound units.

Time

Include:

•       telling and writing time to 1 minute,

•       use of the terms ‘past’ and ‘to’, e.g. ’10 minutes past 5’ and ’15 minutes to 12’,

•       measurement of time in hours and minutes,

•       conversion of time in hours and minutes to minutes only, and vice versa,

•       finding the duration of a time interval,

•       finding the starting time/ finishing time,

•       solving word problems involving addition and subtraction of time given in hours and minutes.

Money

Include:

•       addition and subtraction of money in decimal notation,

•       solving word problems involving addition and subtraction of money in decimal notation.

Area and perimeter

Include:

•       concepts of area and perimeter of a plane figure,

•       measurement of area in square units,

•       measurement of area in square centimetres (cm²) / square metres (m²),

•       calculation of the perimeter of 

∗ rectilinear figure

∗ rectangle

∗ square

•       use of formula to calculate the area of a rectangle/ square,

•       solving word problems involving the area/ perimeter of squares and rectangles.

Exclude conversion between cm² and m².

4  GEOMETRY

Perpendicular and parallel lines

Include:

•      identifying and naming perpendicular and parallel lines,

•      drawing perpendicular and parallel lines on square grids.

Angles

Include:

•       angle as an amount of turning,

•       identifying angles in 2-D and 3-D objects,

•       identifying angles in 2-D figures,

•       identifying right angles, angles greater than/ smaller than a right angle.

Exclude use of the terms ‘acute’, ‘obtuse’ and 'reflex’ angles.

5   DATA ANALYSIS

Bar graphs

Include:

•       reading and interpreting bar graphs in both horizontal and vertical forms,

•       reading scales,

•       completing a bar graph from given data,

•       solving problems using information presented in bar graphs.

Topics/ Sub-topics

Content

1   Whole Numbers

Numbers up to           100 000

Include:

•       number notation and place values (ten thousands, thousands, hundreds, tens, ones), 

•       reading and writing numbers in numerals and in words,

•       comparing and ordering numbers,

•       number patterns,

•       rounding off numbers to the nearest 10 or 100,

•       use of the approximation symbol (≈).

Multiplication and division

Include:

•        multiplication of a 4-digit number by a 1-digit number,

•        multiplication of a 3-digit number by a 2-digit number,

•        division of a 4-digit number by a 1-digit number,

•        solving up to 3-step word problems involving the 4 operations,

•        estimation of answers in calculations involving the 4 operations,

•        checking reasonableness of answers.

Factors and

multiples

Include:

•       determining if a 1-digit number is a factor of a given number,

•       listing all factors of a given number up to 100,

•       finding the common factors of two given numbers,

•       recognising the relationship between factor and multiple,

•       determining if a number is a multiple of a given 1-digit number,

•       listing the first 12 multiples of a given 1-digit number,

•       finding the common multiples of two given 1-digit numbers.

Exclude 'highest common factor' (H.C.F.) and 'lowest common multiple’ (L.C.M.).

2   FRACTIONS 

Mixed numbers and

improper fractions

Include:

•        concepts of mixed numbers and improper fractions,

•        expressing an improper fraction as a mixed number, and vice versa,

•        expressing an improper fraction/mixed number in its simplest form.

(Denominators of given fractions should not exceed 12.)

Addition and

subtraction 

Include addition and subtraction of ∗ like fractions,

∗    related fractions.

(Denominators of given fractions should not exceed 12.)

Exclude calculations involving more than 2 different denominators.

Fraction of a set of objects

Include interpretation of fraction as part of a set of objects.

Multiplication 

Include:

•       multiplication of a proper/improper fraction and a whole number,

•       solving up to 2-step word problems involving addition, subtraction and multiplication,

•       using unitary method to find the whole given a fractional part.

3   DECIMALS

Decimals up to 3 decimal places

Include:

•       notation and place values (tenths, hundredths, thousandths),

•       identifying the values of the digits in a decimal,

•       use of the number line to display decimals,

•       comparing and ordering decimals,

•       conversion of a decimal to a fraction,

•       conversion of a fraction whose denominator is a factor of 10 or 100 to a decimal,

•       rounding off decimals to

     ∗     the nearest whole number,

∗     1 decimal place,

∗     2 decimal places.

Addition and subtraction

Include:

•        addition and subtraction of decimals (up to 2 decimal places),

•        estimation of answers in calculations,

•        checking reasonableness of answers.

Multiplication and division

Include:

•       division of a whole number by a whole number with answer in decimal form,

•       multiplication and division of decimals (up to 2 decimal places) by a 1-digit whole number,

•       solving up to 2-step word problems involving the 4 operations,

•       rounding off answers to a specified degree of accuracy,

•       estimation of answers in calculations,

•       checking reasonableness of answers.

4   MEASUREMENT

Time

Include:

•       measurement of time in seconds (s),

•       24-hour clock,

•       solving word problems involving time in 24-hour clock.

Money

Include:

•       multiplication and division of money in decimal notation,

•       solving word problems involving the 4 operations of money in decimal notation.

Area and perimeter

Include:

•       finding the area of a composite figure made up of rectangles and squares,

•       finding one dimension of a rectangle given the other dimension and its area/ perimeter,

•       finding the length of one side of a square given its area/ perimeter,

•       solving word problems involving the area/ perimeter of squares and rectangles.

Exclude use of the symbol  .

5   GEOMETRY

Perpendicular and parallel lines

Include:

•        drawing of perpendicular and parallel lines using ruler and set squares,

•       use of the terms ‘vertical’ and ‘horizontal’.

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,

•       associating  turn/ right angle with 90^o  turn with 180^o  turn with 270^o

a complete turn with 360 ^o  

•       8-point compass.

Exclude:

•       drawing and measuring reflex angles,

•       use of the notation x°.

Rectangle and square

Include:

•        properties of rectangle and square,

•        finding unknown angles.

Exclude:

•        the term ‘diagonal’ and its related properties,

•        finding angles involving additional construction of lines.

Symmetry

Include:

•        identifying symmetric figures, 

•        determining whether a straight line is a line of symmetry of a symmetric figure, 

•        completing a symmetric figure with respect to a given horizontal/vertical line of symmetry, 

•        designing and making patterns. 

Exclude:

•        finding the number of lines of symmetry of a symmetric figure,

•        rotational symmetry. 

Tessellation

Include:

•        recognising shapes that can tessellate,

•        identifying the unit shape in a tessellation,

•        making different tessellations with a given shape,

•        drawing a tessellation on dot paper,

•        designing and making patterns.

6   DATA ANALYSIS

Tables

Include:

•       completing a table from given data,

•       reading and interpreting tables,

•       solving problems using information presented in tables.

Line graphs

Include:

•       reading and interpreting line graphs,

•       solving problems using information presented in line graphs.

Exclude the distance-time graph.

Topics/ Sub-topics

Content

Primary 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 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

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 A, 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 180^o,

•      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.

Topics/ Sub-topics

Content

Primary 6  (Calculator is allowed unless otherwise stated.)

1   FRACTIONS

Four operations

Include division of a whole number/proper fraction by a proper fraction without using calculators.

Exclude: 

•       division of an improper fraction/mixed number by a proper fraction,

•       division by an improper fraction/mixed number.

2   PERCENTAGE

Percentage

Include:

•       finding the whole given a part and the percentage,

•       finding percentage increase/decrease,

•       solving word problems involving percentage.

Exclude finding percentage profit/loss.

3   RATIO  

Ratio 

Include:

•       expressing one quantity as a fraction of another, given their ratio, and vice versa,

•       finding how many times one quantity is as large as another, given their ratio, and vice versa,

•       expressing one quantity as a fraction of another given the two quantities,

•       finding the whole/ one part when a whole is divided into parts in a given ratio,

•       solving word problems involving 2 pairs of ratios. 

4   SPEED

Distance, time and

speed

Include:

•       concepts of speed and average speed,

•       relationship between distance, time and speed

       ∗     Distance = Speed × Time,

       ∗     Speed = Distance ÷ Time,

       ∗     Time = Distance ÷ Speed,

•       calculation of speed, distance or time given the other two quantities,

•       writing speed in different units such as km/h, m/min, m/s and cm/s,

•       solving up to 3-step word problems involving speed and average speed.

Exclude conversion of units, e.g. km/h to m/min.

5   MEASUREMENT

Area and circumference of

circle

Include:

•       use of formulae to calculate the area and circumference of a

circle,

•       finding the area and perimeter of

∗ semicircle (half circle)

∗ quarter circle

•       solving word problems involving area and perimeter.

Exclude finding the radius/ diameter of a circle given its area or circumference.

Area and perimeter of composite figure

Include finding the area and perimeter of a figure made up of some of the following shapes: square, rectangle, triangle, semicircle and quarter circle.

Volume of cube and cuboid

Include:

•         finding one dimension of a cuboid given its volume and the other dimensions,

•         finding the length of one edge of a cube given its volume,

•         finding the height of a cuboid given its volume and base area,

•         finding the area of a face of a cuboid given its volume and one dimension,

•         use of the symbols          and ³     ,

•         solving word problems involving volume of a cube/ cuboid.

6   GEOMETRY

Geometrical figures

Include finding unknown angles in geometrical figures involving square, rectangle, parallelogram, rhombus, trapezium and triangle.

Nets

Include:

•       2-D representation of cube, cuboid, cone, cylinder, prism and pyramid,

•       identifying nets of the following solids

∗ cube,

∗ cuboid,

∗ prism,

∗ pyramid,

•       identifying the solid which can be formed by a given net,

•       making 3-D solids from given nets.

Exclude nets of cylinder and cone.

  7   DATA ANALYSIS 

Pie charts

Include:

•       reading and interpreting pie charts,

•       solving 1-step problems using information presented in pie charts.

Exclude use of degrees for calculation.

8   ALGEBRA

Algebraic expressions in one

variable

Include:

•       representation of an unknown number using a letter,

•       simple algebraic expressions such as

y ± 2, 6 ± y

y + y

3 y

^y₂

^{3 ± y}₅

•       interpreting

∗      3y as y + y + y  or 3 × y

∗       ^y₂ as y ÷ 2 or ¹₂ × y

∗       ^{( 3±y)}₅ as (3 ± y) ÷ 5 or ¹₅ × (3 ± y)

•       simplification of algebraic expressions,

•       evaluation of simple algebraic expressions by substitution,

•       solving word problems involving algebraic expressions.

Exclude:

•       evaluation of expressions involving variable in the denominator

such as ¹_x

•       simplification of expressions involving

        ∗     fractional coefficients

        ∗     brackets

Topics/ Sub-topics

Content 

Primary 5 Foundation Mathematics  (Calculator is allowed unless otherwise stated)

1   Whole Numbers 

Numbers up to            

10 million

 Include:

•            reading and writing numbers in numerals and in words,

•            comparing and ordering numbers up to 100 000,

•            rounding off numbers to the nearest 10, 100 or 1000.

Four operations

Include: 

•       addition and subtraction involving two 3-digit numbers

without using calculators,

•       multiplication and division of a 2-digit number by a 1-digit number without using calculators,

•       solving up to 3-step word problems involving the 4 operations,

•       estimation of answers in calculations,

•       checking reasonableness of answers.

Mental calculation  

Include 

•      addition and subtraction involving a 3-digit number and ones, tens or hundreds without using calculators,

•      multiplication and division within the multiplication tables without using calculators.

Factors and multiples

Include:

•       determining if a 1-digit number is a factor of a given number,

•       listing all factors of a given number up to 100,

•       finding the common factors of two given numbers,

•       recognising the relationship between factor and multiple,

•       determining if a number is a multiple of a given 1-digit number,

•       listing the first 12 multiples of a given 1-digit number,

•       finding the common multiples of two given numbers up to 12.

Exclude 'highest common factor' (H.C.F.) and 'lowest common multiple’ (L.C.M.).

Order of operations

Include:

•      combined operations involving the 4 operations,

•      use of brackets.

 2   FRACTIONS

Concepts of fractions

Include: 

•      fraction of a whole,

•      fraction of a set of objects.

Equivalent fractions

Include:

•       recognising and naming equivalent fractions,

•       listing the first 8 equivalent fractions of a given fraction,

•       writing the equivalent fraction of a fraction given the denominator or the numerator,

•       expressing a fraction in its simplest form,

•       comparing fractions with respect to half,

•       comparing and ordering unlike fractions.

(Denominators of given fractions should not exceed 12.)

Mixed numbers and

improper fractions

Include:

•       expressing an improper fraction as a mixed number, and vice versa,

•       expressing an improper fraction/mixed number in its simplest form.

(Denominators of given fractions should not exceed 12.)

Four operations

Include: 

•         addition and subtraction of proper fractions without

using calculators,

•         addition and subtraction of mixed numbers,

•         multiplication of a proper/improper fraction and a whole number without using calculators,

•         multiplication of two proper/improper fractions,

•         solving up to 2-step word problems involving addition, subtraction and multiplication,

•         using unitary method to find the whole given a fractional part.

Exclude:

•         calculations involving more than 2 different denominators

•         multiplication involving mixed numbers.

       * (Denominators of given fractions should not exceed 12,

           for calculations without using calculators)

3   DECIMALS

Decimals up to 3 decimal places

Include:

•       notation and place values (tenths, hundredths, thousandths),

•       identifying the values of the digits in a decimal,

•       use of the number line to display decimals,

•       comparing and ordering decimals, conversion of a decimal to a fraction,

•       conversion of a fraction whose denominator is a factor of 10 or 100 to a decimal,

•       rounding off decimals to

∗  the nearest whole number,

∗  1 decimal place,

∗  2 decimal places.

Addition and

subtraction

Include:

•       addition and subtraction of decimals (up to 2 decimal places) without using calculators,

•       estimation of answers in calculations,

•       checking reasonableness of answers,

•       solving up to 2-step word problems involving addition and subtraction (including problems involving money).

4    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

Time

Include:

•       finding the duration of a time interval,

•       24-hour clock,

•       solving up to 3-step word problems involving addition and subtraction of time given in hours and minutes.

Area and perimeter

Include:

•       finding the perimeter of a rectilinear figure,

•       finding the area of a figure made up of rectangles and squares,

•       finding one dimension of a rectangle given the other dimension and its area/ perimeter,

•       finding the length of one side of a square given its area/ perimeter,

•       solving up to 3-step word problems involving the area/ perimeter of squares and rectangles. 

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),

Exclude conversion between cm³ and m³.

5    GEOMETRY

Perpendicular and parallel lines

Include:

•      identifying and naming perpendicular and parallel lines

•      drawing of perpendicular and parallel lines using ruler and set squares,

•      use of the terms ‘vertical’ and ‘horizontal’.

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.

Exclude:

•       drawing and measuring reflex angles,

•       use of the notation x°.

Rectangle and square

Include:

•       properties of rectangle and square,

•       drawing a rectangle/square from given dimensions using ruler, protractor and set squares,

Exclude the term ‘diagonal’ and its related properties.

6    DATA ANALYSIS

Tables,  bar graphs, 

line graphs

Include:

•       reading and interpreting tables, bar graphs and line graphs,

•       completing a table/ bar graph from given data, 

•       solving problems using information presented in tables/ bar graphs/ line graphs.

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 up to 3-step word problems involving average.

Topics/ Sub-topics

Content 

Primary 6 Foundation Mathematics  (Calculator is allowed unless otherwise stated)

1   FRACTIONS

Concept of fraction as

division

Include:

•       association of a fraction with division,

•       conversion between fractions and decimals.

Division 

Include: 

•       division of a whole number/proper fraction by a whole number/proper fraction,

•       solving up to 3-step word problems involving the 4 operations.

Exclude:

•       division of an improper fraction/mixed number by a whole number/proper fraction,

•       division by an improper fraction/mixed number.

2   DECIMALS

Multiplication and division

Include:

•       multiplication and division of decimals (up to 2 decimal places) by a

1-digit whole number without using calculators,

•       division of  a whole number by a whole number with answer in decimal form,

•       solving up to 3-step word problems involving the 4 operations

(including problems involving money),

•       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.

 3    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:

•       finding percentage profit/loss,

•       finding percentage increase/ decrease,

•       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    MEASUREMENT

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.

Area and perimeter of composite figure

Include finding the area and perimeter of a figure made up of some of the following shapes: square, rectangle and triangle.

Volume of cube and cuboid

Include:

•      use of formula to calculate the volume of a cube/ cuboid,

•      finding the volume of liquid in a rectangular tank,

•      conversion between A, ml and cm³,

•      solving up to 3-step word problems involving the volume of a cube/ cuboid.

 5    GEOMETRY

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^o,

•      drawing a triangle from given dimensions using ruler, protractor and set squares. 

Exclude:

•      geometrical construction where the use of compasses is required,

•      exterior angles.

Angles in geometric figures

Include finding unknown angles in geometrical figures using the properties of: 

*    angles on a straight line,

*    angles at a point,

*    vertically opposite angles,

*    a square, a rectangle and a triangle.

Exclude:

•      properties related to diagonals of square and rectangle,

•      finding angles involving additional construction of lines.

6    DATA ANALYSIS

Pie charts

Include:

•       reading and interpreting pie charts,

•       solving 1-step problems using information presented in pie charts.

Exclude use of degrees for calculation.