Multiplication and division of integers (through patterns). Division by zero is meaningless. Properties of integers. subtraction is not commutative. Word problems including integers.
Multiplication of fractions, Fraction as an operator, Reciprocal of a fraction, Division of fractions, Word problems involving mixed fractions, Introduction to rational numbers, Operations on rational numbers, Representation of rational number as a decimal. Word problems on rational numbers ,Multiplication and division of decimal fractions, Conversion of units, Word problems.
Exponents only natural numbers. Laws of exponents (through observing patterns to arrive at generalisation.
Generate algebraic expressions (simple) involving one or two variables. Identifying constants, coefficient, powers. Like and unlike terms, degree of expressions. Addition, subtraction of algebraic expressions (coefficients should be integers). Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients).
Review- variable and constant, Algebraic Expression. Equation- Solution or root of equation, rules of equation, rules for solving an equation- Systematic method, Transposition method. From solution to equation.
Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite). Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles)
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.
Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. Operation of rotation through 90 and 180 degree of simple figures. rotation and reflection symmetry (both operations). Reflection and rotation symmetry and vice-versa.
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.
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).
Revision of perimeter, Circumference of Circle. Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, area between two rectangles and two concentric circles.
Collection and organisation of data, Mean, median and mode of ungrouped data, Constructing bargraphs. Feel of probability using data through experiments. throws. Comparing the observation with that for a coin.
Viewing Different section of solids, object having different shapes(one, two, three Dimensional objects), Faces, edges and vertices of 3-D shapes, nets for building 3-D shapes, Drawing Solids on Flat Surface.
Ratio and proportion. 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.Application to simple interest.
