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Number System (60 hrs)

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(i) Knowing our Numbers:

Consolidating the sense of numberness up to 5 digits, Size, estimation of numbers,
identifying smaller, larger, etc. Place value (recapitulation and extension), connectives:
use of symbols =, <, > and use of brackets, word problems on number operations involving
large numbers up to a maximum of 5 digits in the answer after all operations. This
would include conversions of units of length & mass (from the larger to the smaller
units), estimation of outcome of number operations. Introduction to a sense of the
largeness of, and initial familiarity with, large numbers up to 8 digits and approximation
of large numbers)

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(ii)Playing with Numbers:

Simplification of brackets, Multiples and factors, divisibility rule of 2, 3, 4,
5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped
in deducing some and then asked to derive some that are a combination of the basic
patterns of divisibility.) Even/odd and prime/composite numbers, Co-prime numbers,
prime factorisation, every number can be written as products of prime factors. HCF
and LCM, prime factorization and division method for HCF and LCM, the property LCM
X HCF = product of two numbers. All this is to be embedded in contexts that bring
out the significance and provide motivation to the child for learning these ideas.

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(iii) Whole numbers

Natural numbers, whole numbers, properties of numbers (commutative, associative,
distributive, additive identity, multiplicative identity), number line. Seeing patterns,
identifying and formulating rules to be done by children. (As familiarity with algebra
grows, the child can express the generic pattern.)

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(iv) Negative Numbers and Intergers

How negative numbers arise, models of negative numbers, connection to daily life,
ordering of negative numbers, representation of negative numbers on number line.
Children to see patterns, identify and formulate rules. What are integers, identification
of integers on the number line, operation of addition and subtraction of integers,
showing the operations on the number line (addition of negative integer reduces
the value of the number) comparison of integers, ordering of integers.

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(v) Fractions:

Revision of what a fraction is, Fraction as a part of whole, Representation of fractions
(pictorially and on number line), fraction as a division, proper, improper & mixed
fractions, equivalent fractions, comparison of fractions, addition and subtraction
of fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction
in fractions) Review of the idea of a decimal fraction, place value in the context
of decimal fraction, inter conversion of fractions and decimal fractions (avoid
recurring decimals at this stage), word problems involving addition and subtraction
of decimals (two operations together on money, mass, length and temperature)

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Algebra (15 hrs)

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INTRODUCTION TO ALGEBRA

Introduction to variable through patterns and through appropriate word problems
and generalizations (example 5 X 1 = 5 etc.), Generate such patterns with more examples,
Introduction to unknowns through examples with simple contexts (single perations)

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Ratio and Proportion (15 hrs)

Concept of Ratio, Proportion as equality of two ratios, Unitary method (with only
direct variation implied), Word problems

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Geometry (65 hrs)

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(i) Basic geometrical ideas (2 -D):

Introduction to geometry. Its linkage with and reflection in everyday experience.
Line, line segment, ray. Open and closed figures. Interior and exterior of closed
figures. Curvilinear and linear boundaries. Angle — Vertex, arm, interior and exterior,
Triangle — vertices, sides, angles, interior and exterior, altitude and median,
Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite
sides (only convex quadrilateral are to be discussed), interior and exterior of
a quadrilateral. Circle — Centre, radius, diameter, arc, sector, chord, segment,
semicircle, circumference, interior and exterior.

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(ii) Understanding Elementary Shapes (2-D and 3-D):

Measure of Line segment. Measure of angles. Pair of lines - Intersecting and perpendicular
lines - Parallel lines. Types of angles- acute, obtuse, right, straight, reflex,
complete and zero angle. Classification of triangles (on the basis of sides, and
of angles). Types of quadrilaterals – Trapezium, parallelogram, rectangle, square,
rhombus. Simple polygons (introduction) (Upto octagons regulars as well as non regular).
Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone,prism (triangular),
pyramid (triangular and square) Identification and locating in the surroundings.
Elements of 3-D figures. (Faces, Edges and vertices). Nets for cube, cuboids, cylinders,
cones and tetrahedrons.

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(iii) Symmetry: (reflection)

Observation and identification of 2-D symmetrical objects for reflection symmetry,
Operation of reflection (taking mirror images) of simple 2-D objects, Recognising
reflection symmetry (identifying axes)

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(iv) Constructions (using Straight edge Scale, protractor, compasses)

Drawing of a line segment. Construction of circle. Perpendicular bisector. Construction
of angles (using protractor). Angle 60o, 120o (Using Compasses). Angle bisector-
making angles of 30o, 45o, 90o etc. (using compasses). Angle equal to a given angle
(using compass). Drawing a line perpendicular to a given line from a point a) on
the line b) outside the line.

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Mensuration (15 hrs)

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CONCEPT OF PERIMETER AND INTRODUCTION TO AREA

Introduction and general understanding of perimeter using many shapes. Shapes of
different kinds with the same perimeter. Concept of area, Area of a rectangle and
a square Counter examples to different misconcepts related to perimeter and area.
Perimeter of a rectangle – and its special case – a square. Deducing the formula
of the perimeter for a rectangle and then a square through pattern and generalisation.

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Data handling (10 hrs)

(i) What is data - choosing data to examine a hypothesis?. (ii) Collection and organisation
of data - examples of organising it in tally bars and a table. (iii) Pictograph-
Need for scaling in pictographs interpretation & construction. (iv) Making bar graphs
for given data interpreting bar graphs+.