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Learn maths in fun way, enjoy your every class

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Number System (50 hrs) (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) (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) (iii) Powers: • Exponents only natural numbers. • Laws of exponents (through observing patterns to arrive at generalisation.) (i) m n m n a a a + ⋅ = (ii) ( ) a a m n mn = (iii) a a a m n m n = − , where m n − ∈Ν

Algebra (20 hrs) ALGEBRAIC EXPRESSIONS • Generate algebraic expressions (simple) involving one or two variables • Identifying constants, coefficient, powers • Like and unlike terms, degree of expressions e.g., x y 2 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) 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)

Geometry (60 hrs) (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 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) (iii) Symmetry • Recalling reflection symmetry • Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (900 , 1200 , 1800 ) • Operation of rotation through 900 and 1800 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) • Mapping the space around approximately through visual estimation. (v) Congruence • Congruence through superposition (examplesblades, stamps, etc.) • Extend congruence to simple geometrical shapes e.g. triangles, 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 (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. 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

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