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) a^{m} a^{n} a^{m+n} (ii) (a^{m})^{n} =a^{mn} (iii) a^{m}/a^{n} = a^{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^{2}y 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. (90^{o}, 120^{o}, 180^{o}) • Operation of rotation through 90^{o} and 180^{o} 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. |