Official Syllabus

Number System

(i) Knowing our Numbers: Integers

• Multiplication and division of integers (through patterns). Division by zero is meaningless

• Properties of integers (including identities for addition & multiplication, commutative, associative, distributive) (through patterns). These would include examples from whole numbers as well. Involve expressing commutative and associative properties in a general form. Construction of counter-examples, including some by children. Counterexamples like subtraction are not commutative.

• Word problems including integers (all operations)

(ii) Fractions and rational numbers:

• Multiplication of fractions

• Fraction as an operator

• Reciprocal of a fraction

• Division of fractions

• Word problems involving mixed fractions

• Introduction to rational numbers (with representation on a number line)

• Operations on rational numbers (all operations) fractions

• Conversion of units (length & mass)

• Word problems (including all operations)

(iii) Powers:

• Exponents only natural numbers.

• Laws of exponents (through observing patterns to arrive at generalisation.)

Algebra

ALGEBRAIC EXPRESSIONS

• Generate algebraic expressions (simple) involving one or two variables

• Identifying constants, coefficients, powers

• Like and unlike terms, degree of expressions e.g., x² y, etc. (exponent less than or equal to 3, number of variables)

• Addition, and subtraction of algebraic expressions (coefficients should be integers).

• Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)

Ratio and Proportion

• Ratio and proportion (revision)

• Unitary method continued consolidation, general expression.

• Percentage- an introduction.

• Understanding percentage as a fraction with denominator 100

• Converting fractions and decimals into percentages and vice-versa.

• Application to profit and loss (single transaction only)

• Application to simple interest (the time period in whole years).

Geometry

(i) Understanding shapes:

• Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)

Official Syllabus

Number System

(i) Knowing our Numbers: Integers

• Multiplication and division of integers (through patterns). Division by zero is meaningless

• Properties of integers (including identities for addition & multiplication, commutative, associative, distributive) (through patterns). These would include examples from whole numbers as well. Involve expressing commutative and associative properties in a general form. Construction of counter-examples, including some by children. Counterexamples like subtraction are not commutative.

• Word problems including integers (all operations)

(ii) Fractions and rational numbers:

• Multiplication of fractions

• Fraction as an operator

• Reciprocal of a fraction

• Division of fractions

• Word problems involving mixed fractions

• Introduction to rational numbers (with representation on a number line)

• Operations on rational numbers (all operations) fractions

• Conversion of units (length & mass)

• Word problems (including all operations)

(iii) Powers:

• Exponents only natural numbers.

• Laws of exponents (through observing patterns to arrive at generalisation.)

Algebra

ALGEBRAIC EXPRESSIONS

• Generate algebraic expressions (simple) involving one or two variables

• Identifying constants, coefficients, powers

• Like and unlike terms, degree of expressions e.g., x² y, etc. (exponent less than or equal to 3, number of variables)

• Addition, and subtraction of algebraic expressions (coefficients should be integers).

• Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)

Ratio and Proportion

• Ratio and proportion (revision)

• Unitary method continued consolidation, general expression.

• Percentage- an introduction.

• Understanding percentage as a fraction with denominator 100

• Converting fractions and decimals into percentages and vice-versa.

• Application to profit and loss (single transaction only)

• Application to simple interest (the time period in whole years).

Geometry

(i) Understanding shapes:

• Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)

• Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles)

(ii) Properties of triangles:

• Angle sum property (with notions of proof & verification through paper folding, proofs using the property of parallel lines, and difference between proof and verification.)

• Exterior angle property

• Sum of two sides of its third side

• Pythagoras Theorem (Verification only)

(iii) Symmetry

• Recalling reflection symmetry

• Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90^o , 120^o , 180^o)

• Operation of rotation through 90^o and 180^o of simple figures.

• Examples of figures with both rotation and reflection symmetry (both operations)

• Examples of figures that have reflection and rotation symmetry and vice-versa

(iv) Representing 3-D in 2-D:

• Drawing 3-D figures in 2-D showing hidden faces.

• Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).

• Matching pictures with objects (Identifying names) proximately through visual estimation.

(v) Congruence

• Congruence through superposition (examples blades, stamps, etc.)

• Extend congruence to simple geometrical shapes e.g. triangles, and circles.

• Criteria of congruence (by verification) SSS, SAS, ASA, RHS

(vi) Construction (Using scale, protractor, compass)

• Construction of a line parallel to a given line from a point outside it. (Simple proof as remark with the reasoning of alternate angles)

• Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.

Mensuration

• Revision of perimeter, Idea of, Circumference of Circle

Area

Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram, and circle, area between two rectangles and two concentric circles.

Data handling

(i) Collection and organization of data – choosing the data to collect for hypothesis testing.

(ii) Mean, median, and mode of ungrouped data – understanding what they represent.

(iii) Constructing bar graphs

(iv) Feel of probability using data through experiments. The notion of chance in events like tossing coins, dice, etc. Tabulating and counting occurrences of 1 through 6 in a number of throws. You are comparing the observation with that for cash. Observing strings of throws, the notion of randomness.

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