## Sg.Sec1 History

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[ colspan=3]1 Whole numbers

[ colspan=3]1 Numbers and Algebra

[]1.1 Numbers up to 100

[]1.1 Numbers and the four operations

- 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 <.

- primes and prime factorisation
- finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation
- negative numbers, integers, rational numbers, real numbers and their four operations
- calculations with the use of a calculator
- representation and ordering of numbers on the number line
- use of the symbols <, >, ≤, ≥
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors)

[]

[]1.2 Addition and subtraction

[]1.2 Ratio, rate and proportion

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

- ratios involving rational numbers
- writing a ratio in its simplest form
- average rate
- problems involving ratio and rate

[]1.3 Mental calculation

[]1.3 Percentage

- addition and subtraction within 20,
- addition and subtraction involving
- ∗ a 2-digit number and ones without renaming,
- ∗ a 2-digit number and tens

- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- increasing/decreasing a quantity by a given percentage
- reverse percentages
- problems involving percentages

[ colspan=3]1 Numbers and Algebra

[ colspan=3]1 Whole numbers

[]1.1 Numbers and the four operations

[]1.1 Numbers up to 100

- primes and prime factorisation
- finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation
- negative numbers, integers, rational numbers, real numbers and their four operations
- calculations with the use of a calculator
- representation and ordering of numbers on the number line
- use of the symbols <, >, ≤, ≥
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors)

[]

- 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 <.

[]1.2 Ratio, rate and proportion

[]1.2 Addition and subtraction

- ratios involving rational numbers
- writing a ratio in its simplest form
- average rate
- problems involving ratio and rate

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

[]1.3 Percentage

[]1.3 Mental calculation

- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- increasing/decreasing a quantity by a given percentage
- reverse percentages
- problems involving percentages

- addition and subtraction within 20,
- addition and subtraction involving
- ∗ a 2-digit number and ones without renaming,
- ∗ a 2-digit number and tens

- solving simple inequality (e.g. 3x \le 5 )

- concepts of speed, uniform speed and average speed

- area of parallelogram and trapezium

- area of parallelogram and trapezium

- primes and prime factorisation

- the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

- cartesian coordinates in two dimensions

Excludes:

Exclude:

[ colspan=3]1 Numbers and Algebra

[ colspan=3]1 Numbers and Algebra

[]1.1 Numbers and the four operations

[]1.1 Numbers and the four operations

• primes and prime factorisation

• finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation

• negative numbers, integers, rational numbers, real numbers and their four operations

• calculations with the use of a calculator

• representation and ordering of numbers on the number line

• use of the symbols <, >, ≤, ≥

• approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors)

- primes and prime factorisation
- finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation
- negative numbers, integers, rational numbers, real numbers and their four operations
- calculations with the use of a calculator
- representation and ordering of numbers on the number line
- use of the symbols <, >, ≤, ≥
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors)

[]1.2 Ratio, rate and proportion

[]1.2 Ratio, rate and proportion

• ratios involving rational numbers

• writing a ratio in its simplest form

• average rate

• problems involving ratio and rate

- ratios involving rational numbers
- writing a ratio in its simplest form
- average rate
- problems involving ratio and rate

[]1.3 Percentage

[]1.3 Percentage

• expressing one quantity as a percentage of another

• comparing two quantities by percentage

• percentages greater than 100%

• increasing/decreasing a quantity by a given percentage

• reverse percentages

• problems involving percentages

- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- increasing/decreasing a quantity by a given percentage
- reverse percentages
- problems involving percentages

[]1.4 Speed

[]1.4 Speed

• concepts of speed, uniform speed and average speed

• conversion of units (e.g. km/h to m/s)

• problems involving speed, uniform speed and average speed

- concepts of speed, uniform speed and average speed
- conversion of units (e.g. km/h to m/s)
- problems involving speed, uniform speed and average speed

[]1.5 Algebraic representation and formulae

[]1.5 Algebraic representation and formulae

• using letters to represent numbers

• interpreting notations:

- using letters to represent numbers
- interpreting notations:

• evaluation of algebraic expressions and formulae

• translation of simple real-world situations into algebraic expressions

• recognising and representing number patterns (including finding an algebraic expression for the nth term)

- evaluation of algebraic expressions and formulae
- translation of simple real-world situations into algebraic expressions
- recognising and representing number patterns (including finding an algebraic expression for the nth term)

[]1.6 Algebraic manipulation

[]1.6 Algebraic manipulation

• addition and subtraction of linear algebraic expressions

• simplification of linear algebraic expressions, e.g.

- addition and subtraction of linear algebraic expressions
- simplification of linear algebraic expressions, e.g.

• factorisation of linear algebraic expressions of the form

∗ ax + ay (where a is a constant)

∗ ax + bx + kay + kby (where a , b and k are constants)

- factorisation of linear algebraic expressions of the form
- ax + ay (where a is a constant)
- ax + bx + kay + kby (where a , b and k are constants)

[]1.7 Functions and graphs

[]1.7 Functions and graphs

• cartesian coordinates in two dimensions

• graph of a set of ordered pairs

• linear relationships between two variables (linear functions)

• the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

- cartesian coordinates in two dimensions
- graph of a set of ordered pairs
- linear relationships between two variables (linear functions)
- the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

[]1.8 Solutions of equations and inequalities

[]1.8 Solutions of equations and inequalities

• solving linear equations in one unknown (including fractional coefficients)

• solving simple inequality (e.g. 3x \le 5 )

• solving simple fractional equations that can be reduced to linear equations, e.g.

- solving linear equations in one unknown (including fractional coefficients)
- solving simple inequality (e.g. 3x \le 5 )
- solving simple fractional equations that can be reduced to linear equations, e.g.

• formulating a linear equation in one unknown to solve problems

- formulating a linear equation in one unknown to solve problems

[ colspan=3]2 Geometry and Measurement

[ colspan=3]2 Geometry and Measurement

[]2.1 Angles, triangles and polygons

[]2.1 Angles, triangles and polygons

• right, acute, obtuse and reflex angles, complementary and supplementary angles, vertically opposite angles, adjacent angles on a straight line, adjacent angles at a point, interior and exterior angles

• angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles

• properties of triangles and special quadrilaterals

• classifying special quadrilaterals on the basis of their properties

• angle sum of interior and exterior angles of any convex polygon

• properties of regular pentagon, hexagon, octagon and decagon

• properties of perpendicular bisectors of line segments and angle bisectors

• construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate

- right, acute, obtuse and reflex angles, complementary and supplementary angles, vertically opposite angles, adjacent angles on a straight line, adjacent angles at a point, interior and exterior angles
- angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- properties of triangles and special quadrilaterals
- classifying special quadrilaterals on the basis of their properties
- angle sum of interior and exterior angles of any convex polygon
- properties of regular pentagon, hexagon, octagon and decagon
- properties of perpendicular bisectors of line segments and angle bisectors
- construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate

[]2.2 Mensuration

[]2.2 Mensuration

• area of parallelogram and trapezium

• problems involving perimeter and area of composite plane figures (including triangle and circle)

• volume and surface area of cube, cuboid, prism and cylinder

• conversion between cm2 and m2 , and between cm3 and m3

• problems involving volume and surface area of composite solids

- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures (including triangle and circle)
- volume and surface area of cube, cuboid, prism and cylinder
- conversion between cm2 and m2 , and between cm3 and m3
- problems involving volume and surface area of composite solids

[ colspan=3]3 Statistics and Probability

[ colspan=3]3 Statistics and Probability

[]3.1 Data handling

[]3.1 Data handling

• data collection methods such as:

∗ taking measurements

∗ conducting surveys

∗ classifying data

∗ reading results of observations/outcomes of events

• construction and interpretation of:

∗ tables

∗ bar graphs

∗ pictograms

∗ line graphs

∗ pie charts

∗ histograms

• purposes and use, advantages and disadvantages of the different forms of statistical representations

• drawing simple inference from statistical diagrams

Exclude histograms with unequal intervals.

- data collection methods such as:
- taking measurements, conducting surveys, classifying data, reading results of observations/outcomes of events

- construction and interpretation of:
- tables, bar graphs, pictograms, line graphs, pie charts, histograms

- purposes and use, advantages and disadvantages of the different forms of statistical representations
- drawing simple inference from statistical diagrams

Excludes:

- histograms with unequal intervals.

[row]

- {x \over 3}+{x-2 \over 4}=3 3

- {x \over 3}+{x-2 \over 4}=3

[tableend]

[table width=100% border=0]

[ colspan=3]2 Geometry and Measurement

[]2.1 Angles, triangles and polygons

[]Include:

• right, acute, obtuse and reflex angles, complementary and supplementary angles, vertically opposite angles, adjacent angles on a straight line, adjacent angles at a point, interior and exterior angles

• angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles

• properties of triangles and special quadrilaterals

• classifying special quadrilaterals on the basis of their properties

• angle sum of interior and exterior angles of any convex polygon

• properties of regular pentagon, hexagon, octagon and decagon

• properties of perpendicular bisectors of line segments and angle bisectors

• construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate

[row]

[]2.2 Mensuration

[]Include:

• area of parallelogram and trapezium

• problems involving perimeter and area of composite plane figures (including triangle and circle)

• volume and surface area of cube, cuboid, prism and cylinder

• conversion between cm2 and m2 , and between cm3 and m3

• problems involving volume and surface area of composite solids

[]

[row]

[ colspan=3]3 Statistics and Probability

[row]

[]3.1 Data handling

[]Include:

• data collection methods such as:

∗ taking measurements

∗ conducting surveys

∗ classifying data

∗ reading results of observations/outcomes of events

• construction and interpretation of:

∗ tables

∗ bar graphs

∗ pictograms

∗ line graphs

∗ pie charts

∗ histograms

• purposes and use, advantages and disadvantages of the different forms of statistical representations

• drawing simple inference from statistical diagrams

Exclude histograms with unequal intervals.

[]

[tableend]

[table width=100% border=0]

[row]

∗ − 2(3x − 5) + 4x

∗

2

3( 5)

3

2 −

x − x

- − 2(3x − 5) + 4x
- {2x \over 3}-{3(x-5) \over 2}

∗ ax + ay (where a is a constant)

∗ ax + bx + kay + kby (where a, b and k are constants)

∗ ax + ay (where a is a constant)

∗ ax + bx + kay + kby (where a , b and k are constants)

• solving simple inequality (e.g. 3x ≤ 5 )

• solving simple inequality (e.g. 3x \le 5 )

∗ 3

4

2

3

=

−

x + x

∗ 6

2

3 =

x −

- {x \over 3}+{x-2 \over 4}=3 3
- {3 \over x-2}=6

Include:

[]Include:

1.5 Algebraic representation and formulae

Include:

[]

[row]

[]1.5 Algebraic representation and formulae

[]Include:

∗ ab as a × b

- ab as a \times b
- {a \over b} as a \div b
- a^2 as a \times a , a^3 as a \times a \times a , a^2b as a \times a \times b...
- 3y as y + y + y or 3 /times y
- {{3 \pm y} \over 5} as {{(3 \pm y)} \div 5} or {1 \over 5}\times {(3 \pm y)}

• evaluation of algebraic expressions and formulae

• translation of simple real-world situations into algebraic expressions

• recognising and representing number patterns (including finding an algebraic expression for the nth term)

[]

[row]

[]1.6 Algebraic manipulation

[]Include:

• addition and subtraction of linear algebraic expressions

• simplification of linear algebraic expressions, e.g.

∗ − 2(3x − 5) + 4x

b

a

as a ÷ b

∗ a2 as a × a, a3 as a × a × a, a2b as a × a × b, . . .

∗ 3y as y + y + y or 3 × y

∗

5

3 ± y

as (3 ± y) ÷ 5 or (3 )

5

1× ± y

• evaluation of algebraic expressions and formulae

• translation of simple real-world situations into algebraic expressions

• recognising and representing number patterns (including finding an algebraic expression for the nth term)

1.6 Algebraic manipulation

Include:

• addition and subtraction of linear algebraic expressions

• simplification of linear algebraic expressions, e.g.

∗ − 2(3x − 5) + 4x

∗

1.7 Functions and graphs

Include:

[]

[row]

[]1.7 Functions and graphs

[]Include:

1.8 Solutions of equations and inequalities

Include:

[]

[row]

[]1.8 Solutions of equations and inequalities

[]Include:

[]

[table width=100% border=0]

[table border=1 width=100% cellpadding=3]

[!]Topic/Sub-topic

[!]Content

[!]Learning Outcomes

[row]

[ colspan=3]1 Numbers and Algebra

[row]

[]1.1 Numbers and the four operations

[]Include:

• primes and prime factorisation

• finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation

• negative numbers, integers, rational numbers, real numbers and their four operations

• calculations with the use of a calculator

• representation and ordering of numbers on the number line

• use of the symbols <, >, ≤, ≥

• approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures, estimating the results of computation, and concepts of rounding and truncation errors)

[]

[row]

[]1.2 Ratio, rate and proportion

[]Include:

• ratios involving rational numbers

• writing a ratio in its simplest form

• average rate

• problems involving ratio and rate

[]

[row]

[]1.3 Percentage

[]Include:

• expressing one quantity as a percentage of another

• comparing two quantities by percentage

• percentages greater than 100%

• increasing/decreasing a quantity by a given percentage

• reverse percentages

• problems involving percentages

[]

[row]

[]1.4 Speed

Include:

• concepts of speed, uniform speed and average speed

• conversion of units (e.g. km/h to m/s)

• problems involving speed, uniform speed and average speed

1.5 Algebraic representation and formulae

Include:

• using letters to represent numbers

• interpreting notations:

∗ ab as a × b

∗

b

a

as a ÷ b

∗ a2 as a × a, a3 as a × a × a, a2b as a × a × b, . . .

∗ 3y as y + y + y or 3 × y

∗

5

3 ± y

as (3 ± y) ÷ 5 or (3 )

5

1× ± y

• evaluation of algebraic expressions and formulae

• translation of simple real-world situations into algebraic expressions

• recognising and representing number patterns (including finding an algebraic expression for the nth term)

1.6 Algebraic manipulation

Include:

• addition and subtraction of linear algebraic expressions

• simplification of linear algebraic expressions, e.g.

∗ − 2(3x − 5) + 4x

∗

2

3( 5)

3

2 −

x − x

• factorisation of linear algebraic expressions of the form

∗ ax + ay (where a is a constant)

∗ ax + bx + kay + kby (where a, b and k are constants)

1.7 Functions and graphs

Include:

• cartesian coordinates in two dimensions

• graph of a set of ordered pairs

• linear relationships between two variables (linear functions)

• the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

1.8 Solutions of equations and inequalities

Include:

• solving linear equations in one unknown (including fractional coefficients)

• solving simple inequality (e.g. 3x ≤ 5 )

• solving simple fractional equations that can be reduced to linear equations, e.g.

∗ 3

4

2

3

=

−

x + x

∗ 6

2

3 =

x −

• formulating a linear equation in one unknown to solve problems

[tableend]

[table width=100% border=0]

[row]