# Singapore Mathematics - Primary 5 Foundation Mathematics

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,
• comparing and ordering numbers up to 100 000,
• rounding off numbers to the nearest 10, 100 or 1000.
1.2 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,
1.3 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.
1.4 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.)
1.5 Order of operations   Include:
• combined operations involving the 4 operations,
• use of brackets.
2 Fractions
2.1 Concepts of fractions Include:
• fraction of a whole,
• fraction of a set of objects.
2.2 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.)

2.3 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.)

2.4 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
2.1 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 of decimals (up to 2 decimal places)without using calculators,
• estimation of answers in calculations,
• solving up to 2-step word problems involving addition and subtraction (including problems involving money)
4 Percentages
5 Ratios
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 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
6.3 Money
6.4 Area and perimeter
• 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.
6.5 Volume of cube and cuboid
• 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 ( cm^3 )/ cubic metres ( m^3 )
Exclude:
• conversion between cm^3 and m^3
7 Geometry
7.1 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’
7.2 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
7.3 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,
8 DATA ANALYSIS
8.1 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.
8.2 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.
Source: http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf