Available for CBSE, ICSE and State Board syllabus.
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Install Now1. Number System (50 hrs) |
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(i) Knowing our Numbers:Integers |
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| • 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: |
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| • 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) |
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(iii) Powers: |
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| • Exponents only natural
numbers. • Laws of exponents (through observing patterns to arrive at generalisation.) |
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| (i) am an am+n (ii) (am)n =amn (iii) am/an = am-n, where m - n ∈ Ν |
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2. Algebra (20 hrs) |
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(i) Algebraic Expressions |
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| • Generate algebraic expressions
(simple) involving one or two
variables • 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) |
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(ii) Ratio and Proportion (20 hrs) |
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| •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). |
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3. Geometry (60 hrs) |
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(i) Understanding shapes: |
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| • Pairs of angles (linear,
supplementary, complementary,
adjacent, vertically opposite)
(verification and simple proof
of vertically opposite angles) |
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| • Properties of parallel lines with transversal (alternate,corresponding, interior, exterior angles) | |
(ii) Properties of triangles: |
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| • 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) |
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(iii) Symmetry |
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| • 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 |
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(iv) Representing 3-D in 2-D: |
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| • 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. |
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(v) Congruence |
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| • 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 |
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(vi) Construction (Using scale, protractor, compass) |
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| • 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. |
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4. Mensuration (15 hrs) |
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| • 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. | |
5. Data handling (15 hrs) |
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| (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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