Number System (50 hrs)  
(i) Rational Numbers:  
Properties of rational numbers.(including identities). Usinggeneral form of expression to describe properties  
Consolidation of operations on rational numbers.  
Representation of rational numbers on the number line  
Between any two rational numbers there lies another rational number (Making children see that if we take two rational numbers then unlike for whole numbers, in this case you can keep finding more and more numbers that lie between them.)  
Word problem (higher logic, two operations, including ideas like area)  
(ii) Powers  
Integers as exponents.  
Laws of exponents with integral powers  
(iii) a. Squares, Square roots  
Square and Square roots  
Square roots using factor method and division method for numbers containing (a) no more than total 4 digits and (b) no more than 2 decimal places  
(iii) b.Cubes, Cube roots.  
Cubes and cubes roots (only factor method for numbers containing at most 3 digits)  
Estimating square roots and cube roots. Learning the process of moving nearer to the required number.  
(iv)Playing with numbers  
Writing and understanding a^{ 2} and 3 digit number in generalized form (100a + 10b + c , where a, b, c can be only digit 09) and engaging with various puzzles concerning this. (Like finding the missing numerals represented by alphabets in sums involving any of the four operations.) Children to solve and create problems and puzzles.  
Number puzzles and games  
Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or threedigit number expressed in the general form.  
Algebra (20 hrs)  
(i) Algebraic Expressions  
Multiplication and division of algebraic exp.(Coefficient should be integers)  
Some common errors (e.g. 2 + x ≠ 2x, 7x + y ≠ 7xy )  
Identities (a ± b)^{2} = a^{2 }± 2ab + b^{2}, a^{2} – b^{2} = (a – b) (a + b) Factorisation (simple cases only) as examples the following types a(x + y), (x ± y)^{2}, a^{2} – b^{2}, (x + a).(x + b)  
Solving linear equations in one variable in contextual problems involving multiplication and division (word problems) (avoid complex coefficient in the equations)  
Ratio and Proportion (25 hrs)  
Slightly advanced problems involving applications on percentages, profit & loss, overhead expenses, Discount,tax.  
Difference between simple and compound interest (compounded yearly up to 3 years or halfyearly up to 3 steps only), Arriving at the formula for compound interest through patterns and using it for simple problems.  
Direct variation – Simple and direct word problems  
Inverse variation – Simple and direct word problems  
Time & work problems– Simple and direct word problems  
Geometry (40 hrs)  
(i) Understanding shapes:  
Properties of quadrilaterals – Sum of angles of a quadrilateral is equal to 360^{o} (By verification)  
Properties of parallelogram (By verification)  


(ii) Representing 3D in 2D  
Identify and Match pictures with objects [more complicated e.g. nested, joint 2D and 3D shapes (not more than 2)].  
Drawing 2D representation of 3D objects (Continued and extended)  
Counting vertices, edges & faces & verifying Euler’s relation for 3D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids)  
(iii) Construction:  
Construction of Quadrilaterals:  
 Given four sides and one diagonal  
 Three sides and two diagonals  
 Three sides and two included angles  
 Two adjacent sides and three angles  
Mensuration (15 hrs)  
Area of a trapezium and a polygon.  
Concept of volume, measurement of volume using a basic unit, volume of a cube, cuboid and cylinder  
Volume and capacity (measurement of capacity)  
Surface area of a cube, cuboid, cylinder.  
Data handling (15 hrs)  
Reading bargraphs, ungrouped data, arranging it into groups, representation of grouped data through bargraphs, constructing and interpreting bargraphs.  
Simple Pie charts with reasonable data numbers  
Consolidating and generalising the notion of chance in events like tossing coins, dice etc. Relating it to chance in life events. Visual representation of frequency outcomes of repeated throws of the same kind of coins or dice. Throwing a large number of identical dice/coins together and aggregating the result of the throws to get large number of individual events. Observing the aggregating numbers over a large number of repeated events. Comparing with the data for a coin. Observing strings of throws, notion of randomness  
Introduction to graphs (15 hrs)  
PRELIMINARIES:  
Axes (Same units), Cartesian Plane  
Plotting points for different kind of situations (perimeter vs length for squares, area as a function of side of a square, plotting of multiples of different numbers, simple interest vs number of years etc.)  
Reading off from the graphs  
 Reading of linear graphs  
 Reading of distance vs time graph 
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