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Number System (50 hrs)

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(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 counterexamples, including some by
children. Counter examples like subtraction is not commutative, Word problems including
integers (all operations)

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(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 number line), Operations on rational numbers
(all operations), Representation of rational number as a decimal, Word problems
on rational numbers (all operations), Multiplication and division of decimal fractions,
Conversion of units (length & mass), Word problems (including all operations)

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(iii) Powers:

Exponents only natural numbers, Laws of exponents (through observing patterns to
arrive at generalization.), (i) am an am+n (ii), (am)n =amn, (iii) am/an = am-n,
where m - n ∈ Ν

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Algebra (20 hrs)

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ALGEBRAIC EXPRESSIONS

Generate algebraic expressions (simple) involving one or two variables, Identifying
constants, coefficient, powers, Like and unlike terms, degree of expressions e.g.,
x2y etc. (exponent ≤ 3, number of variables, Addition, subtraction of algebraic
expressions (coefficients should be integers), Simple linear equations in one variable
(in contextual problems) with two operations (avoid complicated coefficients)

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Ratio and Proportion (20 hrs)

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 percentage and vice-versa.
, Application to profit and loss (single transaction only), Application to simple
interest (time period in complete years).

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Geometry (60 hrs)

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(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)

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(ii) Properties of triangles:

Angle sum property (with notions of proof & verification through paper folding,
proofs using property of parallel lines, difference between proof and verification.),
Exterior angle property, Sum of two sides of a it's third side, Pythagoras Theorem
(Verification only)

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(iii) Symmetry

Recalling reflection symmetry, Idea of rotational symmetry, observations of rotational
symmetry of 2-D objects. (90o, 120o, 180o), Operation of rotation through 90o and
180o 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

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(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), Mapping the space around approximately
through visual estimation.

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(v) Congruence

Congruence through superposition (examples blades, stamps, etc.), Extend congruence
to simple geometrical shapes e.g. triangles, circles, Criteria of congruence (by
verification) SSS, SAS, ASA, RHS

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(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.

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Mensuration (15 hrs)

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.

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Data handling (15 hrs)

(i) Collection and organisation of data – choosing the data to collect for a hypothesis
testing, (ii) Mean, median and mode of ungrouped data – understanding what they
represent, (iii) Constructing bargraphs, (iv) Feel of probability using data through
experiments. Notion of chance in events like tossing coins, dice etc. Tabulating
and counting occurrences of 1 through 6 in a number of throws. Comparing the observation
with that for a coin.Observing strings of throws, notion of randomness.