|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)
|• Exponents only natural
• Laws of exponents (through observing patterns to arrive at generalisation.)
|(i) am an am+n
(ii) (am)n =amn
(iii) am/an = am-n, where m - n ∈ Ν
|Algebra (20 hrs)|
|• Generate algebraic expressions
(simple) involving one or two
• 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)
|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,
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
• Exterior angle property
• Sum of two sides of a it's third side
• Pythagoras Theorem (Verification only)
|• 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
|(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.
|• Congruence through
• 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.