

1. Food
Sources of food
Plant parts and animal products as sources of food; herbivores,
carnivores, omnivores.
Components of food
Carbohydrates, fats, proteins, vitamins, minerals, fibres, their
sources and significance for human health; balanced diet; diseases
and disabilities due to food deficiencies.
Cleaning food
Threshing, winnowing, hand picking, sedimentation, filtration.
2. Materials
Materials of daily use
Different types of cloth materials –cotton, wool, silk and
synthetics. Development of clothing materials. Plant fibre,
especially cotton and jute; production of cotton, jute and other
locally available plant fibres; types of soil required for the
growth of different fibrous plants.
Different kinds of materials
Grouping things on the basis of common properties.
How things change/ react with one another
Some changes can be reversed and others cannot be
reversed.Solubility, saturated solutions. Amount of substance
dissolving varies with temperature. At the same temperature amounts
of different substances that dissolve varies.
3. The World of the Living
Things around us
Living/nonliving characteristics; habitat; biotic, abiotic (light,
temperature, water, air, soil, fire)
The habitat of the living
Habitat varies aquatic, deserts, mountains etc.plants and animals
show adaptation; other plant part modifications like tendrils,
thorns etc. Animals in deserts and water.
Plants –form and function
Morphological structure and function of root, stem and leaves.
Structure of the flower, differences.
Animals –form and function
Structure and functions of the animal body; Human skeletal system,
some other animals e.g. fish, bird, cockroach, snail.
4. Moving Things, People and Ideas
Moving
Need to measure distance (length). Measurement of length. Motion as
change in position with time.
5. How things work
Electric current and circuits
Electric current: Electric circuit (current flows only when a cell
and other components are connected in an unbroken loop) Conductor,
Insulator.
Magnets
Magnet. Poles of a magnet. A freely suspended magnet always aligns
in a particular direction. North and South poles. Like poles repel
and unlike poles attract each other.
6. Natural Phenomena
Rain, thunder and lightning
Evaporation and condensation, water in different states. Water
cycle.
Light
Classification of various materials in terms of transparent,
translucent and opaque. A shadow is formed only when there is a
source of light and an opaque material obstructs a source it. A
shadow is black irrespective of the colour of the object. Reflecting
surfaces; images are different from shadows.
7. Natural Resources
Importance of water
Importance of water, dependence of the living on water. Droughts and
floods.
Importance of air
Some animals and plants live in water; some live on land and some
live in upper layers of soil; but all need air to breath/to respire.
Waste
Waste; recycling of waste products; things that rot and things that
don’. Rotting is supported by animals/animal and plant products.
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Number System
(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)
(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, Coprime
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.
(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.)
(iv)
Negative Numbers and Integers
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.
(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)
Algebra
Introduction to Algebra
•Introduction to variable through patterns and through appropriate
word problems and generalisations (example 5 X 1 = 5 etc.)
•Generate such patterns with more examples.
•Introduction to unknowns through examples with simple contexts
(single perations)
Ratio and Proportion
•Concept of Ratio
•Proportion as equality of two ratios
•Unitary method (with only direct variation implied)
•Word problems
Geometry
(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.
(ii)
Understanding Elementary Shapes (2D and 3D):
•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 3D shapes: Cubes, Cuboids, cylinder, sphere,
cone,prism (triangular), pyramid (triangular and square)
Identification and locating in the surroundings
•Elements of 3D figures. (Faces, Edges and vertices)
•Nets for cube, cuboids, cylinders, cones and tetrahedrons.
(iii)
Symmetry: (reflection)
•Observation and identification of 2D symmetrical objects for
reflection symmetry
•Operation of reflection (taking mirror images) of simple 2D
objects
•Recognising reflection symmetry (identifying axes)
(iv)
Constructions (using Straight edge Scale, protractor,
compasses)
•Drawing of a line segment
•Construction of circle
•Perpendicular bisector
•Construction of angles (using protractor)
•Angle 60 degree, 120 degree (Using Compasses)
•Angle bisector making angles of 30 degree, 45 degree, 90 degree
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.
Mensuration
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.
Data handling
(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.
Top

1.Food
Food sources
Autotrophic and heterotrophic nutrition; parasites, saprophytes;
photosynthesis.
Utilisation of food
Types of nutrition, nutrition in amoeba and human beings, Digestive
system human, ruminants; types of teeth; link with transport and
respiration.
2. Materials
Materials of daily use
Wool, silk  animal fibres. Process of extraction of silk;
associated health problems. Heat flow; temperature.
Different kinds of materials
Classification of substances into acidic, basic and neutral;
indicators.
How things change/react with one another
Chemical substances; in a chemical reaction a new substance is
formed. Substances can be separated by crystallisation.
3. The World of the Living
Surroundings affect the living
Climate, soil types, soil profile, absorption of water in soil,
suitability for crops, adaptation of animals to different climates.
The breath of life
Respiration in plants and animals.
Movement of substances
Herbs, shrubs, trees; Transport of food and water in plants;
circulatory and excretion system in animals; sweating.
Multiplication in plants
Vegetative, asexual and sexual reproduction in plants, pollination 
cross, self pollination; pollinators, fertilisation, fruit, seed.
4. Moving Things,People and Ideas
Moving objects
Appreciation of idea of time and need to measure it. Measurement of
time using periodic events. Idea of speed of moving objects – slow
and fast motion along a straight line.
5. How Things Work
Electric current and circuits
Electric circuit symbols for different elements of circuit. Heating
effect of current. Principle of fuse. A currentcarrying wire has an
effect on a magnet. A currentcarrying coil behaves like a magnet.
Working of an electric bell.
6. Natural Phenomena
Rain, thunder and lightning
Highspeed winds and heavy rainfall have disastrous consequences for
human and other life.
Light
Rectilinear propagation of light. Reflection, certain surfaces
reflect light. Real and virtual images. White light is composed of
many colours.
7. Natural Resources
Scarcity of water
Water exists in various forms in nature. Scarcity of water and its
effect on life.
Forest products
Interdependence of plants and animals in forests. Forests contribute
to purification of air and water.
Waste Management
Sewage; need for drainage/sewer systems that are closed.
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Number System
(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 oper • 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) am an am+n
(ii) (am)n =amn
(iii) am/an = amn, where m  n
Algebra
Algebraic Expressions
• Generate algebraic expressions (simple) involving one or two
variables
• Identifying constants, coefficient, powers
• Like and unlike terms, degree of expressions e.g., x²y etc.
• 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
• 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 viceversa.
• Application to profit and loss (single transaction only)
• Application to simple interest (time period in complete years).
Geometry
(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 2D objects. (90 degree, 120 degree, 180 degree)
• Operation of rotation through 90 degree and 180 degree of simple
figures.
• Examples of figures with both rotation and reflection symmetry
(both operations)
• Examples of figures that have reflection and rotation symmetry and
viceversa
(iv)
Representing 3D in 2D:
• Drawing 3D figures in 2D 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 (examples blades, 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
• 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
(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.
Top

1. Food
Crop production
Crop production: Soil preparation, selection of seeds, sowing,
applying fertilizers, irrigation, weeding, harvesting and storage;
nitrogen fixation, nitrogen cycle.
Microorganisms
Micro organisms – useful and harmful.
2. Materials
Materials in daily life
Synthetic clothing materials. Other synthetic materials, especially
plastics; usefulness of plastics and problems associated with their
excessive use.There are a variety of fibrous materials in use. A
material is chosen based on desired property.
Different kinds of materials and their reactions
Metals and nonmetals.
How things change/ react with one another
Combustion, flame All fuels release heat on burning. Fuels differ in
efficiency, cost etc. Natural resources are limited. Burning of
fuels leads to harmful by products.
3. The World of the Living
Why conserve
Conservation of biodiversity/wild life/ plants; zoos, sanctuaries,
forest reserves etc. flora, fauna endangered species, red data book;
endemic species, migration.
The cell
Cell structure, plant and animal cells, use of stain to observe,
cell organelles – nucleus, vacuole, chloroplast, cell membrane, cell
wall.
How babies are formed
Sexual reproduction and endocrine system in animals, secondary
sexual characters, reproductive health; internal and external
fertilisation.
4. Moving Things, People and Ideas
Idea of force
Idea of forcepush or pull; change in speed, direction of moving
objects and shape of objects by applying force; contact and
noncontact forces.
Friction
Friction – factors affecting friction, sliding and rolling friction,
moving; advantages and disadvantages of friction for the movement of
automobiles, airplanes and boats/ships; increasing and reducing
friction.
Pressure
Idea of pressure; pressure exerted by air/liquid; atmospheric
pressure.
Sound
Various types of sound; sources of sound; vibration as a cause of
sound; frequency; medium for propagation of sound; idea of noise as
unpleasant and unwanted sound and need to minimise noise.
5. How Things Work
Electric current and circuits
Water conducts electricity depending on presence/ absence of salt in
it. Other liquids may or may not conduct electricity.
Chemical effects of current. Basic idea of electroplating.
6. Natural Phenomena
Rain, thunder and lightning
Clouds carry electric charge. Positive and negative charges,
attraction and repulsion. Principle of lightning conductor.
Light
Laws of reflection. Characteristics of image formed with a plane
mirror. Regular and diffused reflection. Reflection of light from an
object to the eye. Multiple reflection. Dispersion of light.
Structure of the eye. Lens becomes opaque, light not reaching the
eye. Visually challenged use other senses to make sense of the world
around. Alternative technology available. Role of nutrition in
relation to blindness
Night sky
Idea about heavenly bodies/celestial objects and their
classification – moon, planets, stars, constellations. Motion of
celestial objects in space; the solar system.
Earthquakes
Phenomena related to earthquakes.
7. Natural Resources
Man’s intervention in phenomena of nature
Consequences of deforestation: scarcity of products for humans and
other living beings, change in physical properties of soil, reduced
rainfall. Reforestation; recycling of paper. Formation of coal and
petroleum in nature. (fossil fuels). Consequences of over extraction
of coal and petroleum.
Pollution of air and water
Water and air are increasingly getting polluted and therefore become
scarce for use. Biological and chemical contamination of water;
effect of impure water on soil and living beings; effect of soil
containing excess of fertilisers and insecticides on water
resources. Potable water.
Top

Number System
(i)
Rational Numbers:
Properties of rational numbers.(including identities). Usinggeneral
form of expression to describe properties
Consolidation of operations on rational numbers.
Representation of rational numbers on the number line
Between any two rational numbers there lies another rational number
(Making children see that if we take two rational numbers then
unlike for whole numbers, in this case you can keep finding more and
more numbers that lie between them.)
Word problem (higher logic, two operations, including ideas like
area)
(ii)
Powers
Integers as exponents.
Laws of exponents with integral powers
(iii)
Squares, Square roots, Cubes, Cube roots.
Square and Square roots
Square roots using factor method and division method for numbers
containing (a) no more than total 4 digits and (b) no more than 2
decimal places
Cubes and cubes roots (only factor method for numbers containing at
most 3 digits)
Estimating square roots and cube roots. Learning the process of
moving nearer to the required number.
(iv)
Playing with numbers
Writing and understanding a² and 3 digit number in generalized form
(100a + 10b + c , where a, b, c can be only digit 09) and engaging
with various puzzles concerning this. (Like finding the missing
numerals represented by alphabets in sums involving any of the four
operations.)
Number puzzles and games
Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or
threedigit number expressed in the general form.
Algebra
(i)
Algebraic Expressions
Multiplication and division of algebraic exp.(Coefficient should be
integers)
Some common errors (e.g. 2 + x is not equal to 2x, 7x + y is not
equal to 7xy )
Identities (a ± b)² = a² ± 2ab + b², a²  b² = (a  b) (a + b)
Factorisation (simple cases only) as examples the following types
a(x + y), (x ± y)², a²  b², (x + a).(x + b)
Solving linear equations in one variable in contextual problems
involving multiplication and division (word problems) (avoid complex
coefficient in the equations)
Ratio and Proportion
Slightly advanced problems involving applications on percentages,
profit; loss, overhead expenses, Discount,tax.
Difference between simple and compound interest (compounded yearly
up to 3 years or halfyearly up to 3 steps only), Arriving at the
formula for compound interest through patterns and using it for
simple problems.
Direct variation – Simple and direct word problems
Inverse variation – Simple and direct word problems
Time; work problems– Simple and direct word problems
Geometry
(i)
Understanding shapes:
Properties of quadrilaterals – Sum of angles of a quadrilateral is
equal to 360 degrees (By verification)
Properties of parallelogram (By verification)
* Opposite sides of a parallelogram are equal,
* Opposite angles of a parallelogram are equal,
* Diagonals of a parallelogram bisect each other. [Why (iv), (v) and
(vi) follow from (ii)]
* Diagonals of a rectangle areequal and bisect each other.
* Diagonals of a rhombus bisect each other at right angles.
* Diagonals of a square are equal and bisect each other at right
angles.
(ii)
Representing 3D in 2D
Identify and Match pictures with objects [more complicated e.g.
nested, joint 2D and 3D shapes (not more than 2)].
Drawing 2D representation of 3D objects (Continued and extended)
Counting vertices, edges; faces ; verifying Euler’s relation for 3D
figures with flat faces (cubes, cuboids, tetrahedrons, prisms and
pyramids)
(iii)
Construction:
Construction of Quadrilaterals:
 Given four sides and one diagonal
 Three sides and two diagonals
 Three sides and two included angles
 Two adjacent sides and three angles
Mensuration
Area of a trapezium and a polygon.
Concept of volume, measurement of volume using a basic unit, volume
of a cube, cuboid and cylinder
Volume and capacity (measurement of capacity)
Surface area of a cube, cuboid, cylinder.
Data handling
Reading bargraphs, ungrouped data, arranging it into groups,
representation of grouped data through bargraphs, constructing and
interpreting bargraphs.
Simple Pie charts with reasonable data numbers
Consolidating and generalising the notion of chance in events like
tossing coins, dice etc. Relating it to chance in life events.
Visual representation of frequency outcomes of repeated throws of
the same kind of coins or dice. Throwing a large number of identical
dice/coins together and aggregating the result of the throws to get
large number of individual events. Observing the aggregating numbers
over a large number of repeated events. Comparing with the data for
a coin. Observing strings of throws, notion of randomness
Introduction to graphs
Preliminaries:
Axes (Same units), Cartesian Plane
Plotting points for different kind of situations (perimeter vs
length for squares, area as a function of side of a square, plotting
of multiples of different numbers, simple interest vs number of
years etc.)
Reading off from the graphs
 Reading of linear graphs
 Reading of distance vs time graph
Top

UNITS 

MARKS 
I 
FOOD 
05 
II 
MATTER ITS NATURE AND BEHAVIOUR 
15 
III 
ORGANISATION IN LIVING WORLD 
13 
IV 
MOTION, FORCE & WORK 
20 
V 
OUR ENVIRONMENT 
07 

TOTAL 
60 

Theme : Food
UNIT I : FOOD (10) Periods
Plant and animal breeding and selection for quality improvement and
management ; use of fertilizers, manures; protection from pests and
diseases; organic farming.
Theme : Materials
UNIT 2 : MATTER  NATURE AND BEHAVIOUR (50) Periods
Definition of matter; solid, liquid and gas; characteristics 
shape, volume, density; change of statemelting (absorption of
heat), freezing, evaporation (Cooling by evaporation), condensation,
sublimation.
Nature of matter :
Elements, compounds and mixtures. Heterogenous and homogenous
mixtures, colloids and suspensions.
Particle nature, basic units :
atoms and molecules. Law of constant proportions. Atomic and
molecular masses.
Mole Concept :
Relationship of mole to mass of the particles and numbers. Valency.
Chemical formula of common compounds.
Structure of atom :
Electrons, protons and neutrons; Isotopes and isobars.
Theme : The World of the living
UNIT 3 : ORGANIZATION IN THE LIVING WORLD (45) Periods
BiologicalDiversity :
Diversity of plants and animals  basic issues in scientific naming,
basis of classification. Hierarchy of categories / groups, Major
groups of plants (salient features) (Bacteria, Thalophyta, Bryo
phyta, Pteridophyta, gymnosperms and Angiosperms). Major groups of
animals (salient features) (Nonchordates upto phyla and chordates
upto classes).
Cell Basic Unit of life :
Cell as a basic unit of life; prokaryotic and eukaryotic cells,
multicellular organisms; cell membrane and cell wall, cell
organelles; chloroplast, mitochondria, vacuoles, ER, golgi
apparatus; nucleus, chromosomes  basic structure, number. Tissues,
organs, organ systems, organism. Structure and functions of animal
and plant tissues (four types in animals; merismatic and permanent
tissues in plants).
Health and diseases :
Health and its failure. Disease and its causes. Diseases caused by
microbes and their prevention  Typhoid, diarrhoea, malaria,
hepatitis, rabies, AIDS, TB, polio; pulse polio programme.
Transport of materials in the living systems :
Diffusion / exchange of substances between cells and their
environment and between the cells themselves in the living system;
role in nutrition, water and food transport, excretion, gaseous
exchange.
Theme : Moving things, people and ideas
UNIT 4 : MOTION, FORCE AND WORK (60) Periods
Motion:
displacement, velocity; uniform and nonuniform motion along a
straight line; acceleration, distance  time and velocitytime
graphs for uniform and uniformly accelerated motion, equations of
motion by graphical method; elementary idea of uniform circular
motion.
Force and Newton's laws :
Force and motion, Newton's laws of motion, inertia of a body,
inertia and mass, momentum, force and acceleration. Elementary idea
of conservation of momentum, action and reaction forces.
Gravitation:
Gravitation; universal law of gravitation, force of gravitation of
the earth (gravity), acceleration due to gravity; mass and weight;
free fall.
Work,Energy and Power :
Work done by a force, energy, power; kinetic and potential energy;
law of conservation of energy.
Floatation:
Thrust and pressure. Archimedes' principle, buoyancy, elementary
idea of relative density.
Sound:
Nature of sound and its propagation in various media, speed of
sound, range of hearing in humans; ultrasound; reflection of sound;
echo and SONAR.
Structure of the human ear (auditory aspect only).
Theme : Natural Resources
UNIT 5 : OUR ENVIRONMENT (15) Periods
Physical resources :
Air, Water, Soil. Air for respiration, for combustion, for
moderating temperatures, movements of air and its role in bringing
rains across India.
Air, water and soil pollution ( brief introduction). Holes in ozone
layer and the probable damages.
Biogeo chemical cycles in nature :
water, oxygen, carbon, nitrogen
Top

UNITS 

MARKS 
I 
NUMBER SYSTEMS 
06 
II 
ALGEBRA 
20 
III 
COORDINATE GEOMETRY 
06 
IV 
GEOMETRY 
22 
V 
MENSURATION 
14 
VI 
STATISTICS AND PROBABILITY 
12 

TOTAL 
80 

UNIT I : NUMBER SYSTEMS (20) Periods
1.
REAL NUMBERS
Review of representation of natural numbers, integers, rational
numbers on the number line. Representation of terminating /
nonterminating recurring decimals, on the number line through
successive magnification. Rational numbers as recurring/terminating
decimals.
Examples of nonrecurring / non terminating decimals such as v2, v3,
v5 etc. Existence of nonrational numbers (irrational numbers) such
as v2, v3 and their representation on the number line.
Explaining that every real number is represented by a unique point
on the number line and conversely, every point on the number line
represents a unique real number.
Existence of vx for a given positive real number x (visual proof to
be emphasized).
Definition of nth root of a real number.
Recall of laws of exponents with integral powers. Rational exponents
with positive real bases (to be done by particular cases, allowing
learner to arrive at the general laws.)
Rationalization (with precise meaning) of real numbers of the type
(& their combinations)
UNIT II : ALGEBRA
1.
POLYNOMIALS
(25) Periods
Definition of a polynomial in one variable, its coefficients, with
examples and counter examples, its terms, zero polynomial. Degree of
a polynomial. Constant, linear, quadratic, cubic polynomials;
monomials, binomials, trinomials. Factors and multiples. Zeros/roots
of a polynomial / equation. State and motivate the Remainder Theorem
with examples and analogy to integers. Statement and proof of the
Factor Theorem.
Factorization of ax² + bx + c, a1 0 where a, b, c are real numbers,
and of cubic polynomials using the Factor Theorem.
Recall of algebraic expressions and identities. Further identities
of the type (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx, (x y)3 =
x3 y3 3xy (x y).
x³ + y³ + z³  3xyz = (x + y + z) (x² + y² + z²xy  yz  zx) and
their use in factorization of. polymonials. Simple expressions
reducible to these polynomials.
2.
LINEAR EQUATIONS IN TWO VARIABLES
(12) Periods
Recall of linear equations in one variable. Introduction to the
equation in two variables. Prove that a linear equation in two
variables has infinitely many solutions and justify their being
written as ordered pairs of real numbers, plotting them and showing
that they seem to lie on a line. Examples, problems from real life,
including problems on Ratio and Proportion and with algebraic and
graphical solutions being done simultaneously.
UNIT III : COORDINATE GEOMETRY
1.
COORDINATE GEOMETRY
(9) Periods
The Cartesian plane, coordinates of a point, names and terms
associated with the coordinate plane, notations, plotting points in
the plane, graph of linear equations as examples; focus on linear
equations of the type ax + by + c = 0 by writing it as y = mx + c
and linking with the chapter on linear equations in two variables.
UNIT IV : GEOMETRY
1.
INTRODUCTION TO EUCLID'S GEOMETRY
(6) Periods
History  Euclid and geometry in India. Euclid's method of
formalizing observed phenomenon into rigorous mathematics with
definitions, common/obvious notions, axioms/postulates and theorems.
The five postulates of Euclid. Equivalent versions of the fifth
postulate. Showing the relationship between axiom and theorem.
1. Given two distinct points, there exists one and only one line
through them.
2. (Prove) two distinct lines cannot have more than one point in
common.
2.
LINES AND ANGLES
(10) Periods
1. (Motivate) If a ray stands on a line, then the sum of the two
adjacent angles so formed is 180 degrees and the converse.
2. (Prove) If two lines intersect, the vertically opposite angles
are equal.
3. (Motivate) Results on corresponding angles, alternate angles,
interior angles when a transversal intersects two parallel lines.
4. (Motivate) Lines, which are parallel to a given line, are
parallel.
5. (Prove) The sum of the angles of a triangle is 180 degrees.
6. (Motivate) If a side of a triangle is produced, the exterior
angle so formed is equal to the sum of the two interiors opposite
angles.
3.
TRIANGLES
(20) Periods
1. (Motivate) Two triangles are congruent if any two sides and the
included angle of one triangle is equal to any two sides and the
included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the
included side of one triangle is equal to any two angles and the
included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one
triangle are equal to three sides of the other triangle (SSS
Congruene).
4. (Motivate) Two right triangles are congruent if the hypotenuse
and a side of one triangle are equal (respectively) to the
hypotenuse and a side of the other triangle.
5. (Prove) The angles opposite to equal sides of a triangle are
equal.
6. (Motivate) The sides opposite to equal angles of a triangle are
equal.
7. (Motivate) Triangle inequalities and relation between 'angle and
facing side' inequalities in triangles.
4.
QUADRILATERALS
(10) Periods
1. (Prove) The diagonal divides a parallelogram into two congruent
triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and
conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and
conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its
opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other
and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points
of any two sides is parallel to the third side and (motivate) its
converse.
5.
AREA
Review concept of area, recall area of a rectangle.
1. (Prove) Parallelograms on the same base and between the same
parallels have the same area.
2. (Motivate) Triangles on the same base and between the same
parallels are equal in area and its converse.
6.
CIRCLES
(15) Periods
Through examples, arrive at definitions of circle related concepts,
radius, circumference, diameter, chord, arc, subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the
center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a
chord bisects the chord and conversely, the line drawn through the
center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three
given noncollinear points.
4. (Motivate) Equal chords of a circle (or of congruent circles) are
equidistant from the center(s) and conversely.
5. (Prove) The angle subtended by an arc at the center is double the
angle subtended by it at any point on the remaining part of the
circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (Motivate) If a line segment joining two points subtendes equal
angle at two other points lying on the same side of the line
containing the segment, the four points lie on a circle.
8. (Motivate) The sum of the either pair of the opposite angles of a
cyclic quadrilateral is 180o and its converse
7.
CONSTRUCTIONS
(10) Periods
1. Construction of bisectors of line segments & angles, 60 degree,
90 degree, 45 degree angles etc., equilateral triangles.
2. Construction of a trangle given its base, sum/difference of the
other two sides and one base angle.
3. Construction of a triangle of given perimeter and base angles.
UNIT V :MENSURATION
1.
AREAS
(4) Periods
Area of a triangle using Heros formula(without proof) and its
application in finding the area of a quadrilateral
2.
SURFACE AREAS AND VOLUMES
(10) Periods
Surface areas and volumes of cubes, cuboids, spheres)including
hemispheres) and right circular and right circular cylinders/cones.
UNIT VI : STATISTICS AND PROBABILITY
1.
STATISTICS
(13) Periods
Introduction to statistics: Collection of data, Presentation of
data tabular form, ungrouped / grouped, bar graphs, histograms(with
varying base lengths), frequency polygons, qualitative analysis of
data to choose the correct form of presentation for the collected
data. Mean, median, mode of ungrouped data.
2.
PROBABILITY
(12) Periods
History, Repeated experiments and observed frequency approach to
probability. Focus is on empirical probability.(A large amount of
time to be developed to group and to individual activities to
motivate the concept; the experiment to be drawn from real  life
situations, and from example used in the chapter on statistics).
Top
INTERNAL ASSESSMENT 
(20 MARKS) 
Evaluation of activities 
10 Marks 
Project Work 
05 Marks 
Continuous Evaluation 
05 Marks 


UNITS 

MARKS 
I 
CHEMICAL SUBSTANCE 
18 
II 
WORLD OF LIVING 
16 
III 
EFFECTS OF CURRENT 
10 
IV 
LIGHT 
08 
V 
NATURAL RESOURCES 
08 

TOTAL 
60 

Theme : Materials
UNIT 1 : CHEMICAL SUBSTANCES  NATURE AND BEHAVIOUR (55) Periods
Acids,bases and salts :
General properties, examples and uses.
Chemical reactions :
Types of chemical reactions : combination, decomposition,
displacement, double displacement, precipitation, neutralization,
oxidation and reduction in terms of gain and loss of oxygen and
hydrogen.
Metals and non metals :
Brief discussion of basic metallurgical processes. Properties of
common metals. Elementary idea about bonding.
Carbon Compounds :
Carbon compounds, elementary idea about bonding. Saturated
hydrocarbons, alcohols, carboxylic acids (no preparation, only
properties).
Some Important chemical compounds :
Soapcleansing action of soap.
Periodic classification of elements :
Gradations in properties : Mendeleev periodic table.
Theme : The world of the living
UNIT 2 : OUR ENVIRONMENT (50) Periods
Our environment :
Environmental problems, their solutions. Biodegradable, non
biodegradable, ozone depletion.
Life Processes :
"living" things; Basic concept of nutrition, respiration, transport
and excretion in plants and animals.
Control and Coordination in plants and animals :
Tropic movements in plants; Introduction to plant hormones; control
and coordination in animals : voluntary, involuntary and reflex
action, nervous system; chemical coordination : animal hormones.
Reproduction:
Reproduction in plants and animals. Need for and methods of family
planning. Safe sex vs HIV/AIDS. Child bearing and women's health.
Heridity and evolution :
Heridity; Origin of life : brief introduction; Basic concepts of
evolution.
Theme : How things work.
UNIT 3 :EFFECTS OF CURRENT (35) Periods
Potential, Potential difference, Ohm's law; Series combination of
resistors, parallel combination of resistors; Power dissipation due
to current; Inter relation between P, V, I and R.
Magnets:
Magnetic field, field lines, field due to a current carrying wire,
field due to current carrying coil or solenoid; Force on current
carrying conductor, Fleming's left hand rule. Electro magnetic
induction. Induced potential difference, Induced current. Direct
current. Alternating current; frequency of AC. Advantage of AC over
DC. Domestic electric circuits.
Theme : Natural Phenomena
UNIT 4 :LIGHT (20) Periods
Convergence and divergence of light. Images formed by a concave
mirror; related concepts; centre of curvature; principal axis. Optic
centre, focus, focal length. Refraction; laws of refraction. Image
formed by a convex lens; functioning of a lens in human eye;
problems of vision and remedies. Applications of spherical mirrors
and lenses. Appreciations of concept of refraction; velocity of
light; refractive index; twinkling of stars; dispersion of light.
Scattering of light.
Theme : Natural Resources
UNIT 5 :NATURAL RESOURCES (20) Periods
Conservation of natural resources :
Management of natural resources. Conservation and judicious use of
natural resources. Forest and wild life, coal and petroleum
conservation. People's participation. Chipko movement. Legal
perspectives in conservation and international scenario.
The Regional environment :
Big dams : advantages and limitations; alternatives if any. Water
harvesting. Sustainability of natural resources.
Sources of energy :
Different forms of energy, leading to different sources for human
use : fossil fuels, solar energy; biogas; wind, water and tidal
energy; nuclear energy. Renewable versus non  renewable sources.
Top

UNITS 

MARKS 
I 
NUMBER SYSTEM 
04 
II 
ALGEBRA 
20 
III 
TRIGONOMETRY 
12 
IV 
COORDINATE GEOMETRY 
08 
V 
GEOMETRY 
16 
VI 
MENSURATION 
10 
VII 
STATISTICS AND PROBABILITY 
10 

TOTAL 
80 

UNIT I : NUMBER SYSTEMS
1.
REAL NUMBERS
(15) Periods
Euclid's division lemma, Fundamental Theorem of Arithmetic 
statements after reviewing work done earlier and after illustrating
and motivating through examples, Proofs of results  irrationality
of root 2, root 3, root 5, decimal expansions of rational numbers in
terms of terminating/nonterminating recurring decimals.
UNIT II : ALGEBRA
1.
POLYNOMIALS
(6) Periods
Zeros of a polynomial. Relationship between zeros and coefficients
of a polynomial with particular reference to quadratic polynomials.
Statement and simple problems on division algorithm for polynomials
with real coefficients.
2.
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
(15) Periods
Pair of linear equations in two variables. Geometric representation
of different possibilities of solutions inconsistency. Algebraic
conditions for number of solutions. Solution of pair of linear
equations in two variables algebraically by substitution, by
elimination and by cross multiplication. Simple situational problems
must be included.
Simple problems on equations reducible to linear equations may be
included.
3.
QUADRATIC EQUATIONS
(15) Periods
Standard form of a quadratic equation ax² + bx + c = 0, (a1 0).
Solution of the quadratic equations (only real roots) by
factorization and by completing the square, i.e. by using quadratic
formula. Relationship between discriminant and nature of roots.
Problems related today to day activities to be incorporated.
4.
ARITHMETIC PROGRESSIONS
(8) Periods
Motivation for studying AP. Derivation of standard results of
finding the nth term and sum of first n terms.
UNIT III : TRIGONOMETRY
1.
INTRODUCTION TO TRIGONOMETRIY
(12) Periods
Trigonometric ratios of an acute angle of a rightangled triangle.
Proof of their existence (well defined); motivate the ratios,
whichever are defined at 0 degree & 90 degree. Values (with proofs)
of the trigonometric ratios of 30 degree, 45 degree & 60 degree.
Relationships between the ratios.
2.
TRIGONOMETRIC IDENTITIES
(16) Periods
Proof and applications of the identity sin² A + cos² A = 1. Only
simple identities to be given. Trigonometric ratios of complementary
angles.
3.
HEIGHTS AND DISTANCES
(8) Periods Simple and believable problems on heights and distances.
Problems should not involve more than two right triangles. Angles of
elevation / depression should be only 30 degree, 45 degree, 60
degree.
UNIT IV : COORDINATE GEOMETRY
1.
LINES (In twodimensions)
(15) Periods
Review the concepts of coordinate geometry done earlier including
graphs of linear equations. Awareness of geometrical representation
of quadratic polynomials. Distance between two points and section
formula (internal). Area of a triangle.
UNIT V : GEOMETRY
1.
TRIANGLES
(15) Periods
Definitions, examples, counter examples of similar triangles.
1. (Prove) If a line is drawn parallel to one side of a triangle to
intersect the other two sides in distinct points, the other two
sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same
ratio, the line is parallel to the third side.
3. (Motivate) If in two triangles, the corresponding angles are
equal, their corresponding sides are proportional and the triangles
are similar.
4. (Motivate) If the corresponding sides of two triangles are
proportional, their corresponding angles are equal and the two
triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of
another triangle and the sides including these angles are
proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the
right angle of a right triangle to the hypotenuse, the triangles on
each side of the perpendicular are similar to the whole triangle and
to each other.
7. (Prove) The ratio of the areas of two similar triangles is equal
to the ratio of the squares on their corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is
equal to the sum of the squares on the other two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum
of the squares on the other two sides, the angles opposite to the
first side is a right traingle.
2.
CIRCLES
(8) Periods
Tangents to a circle motivated by chords drawn from points coming
closer and closer and closer to the point.
1. (Prove) The tangent at any point of a circle is perpendicular to
the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to
circle are equal.
3.
CONSTRUCTIONS
(8) Periods
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.
UNIT VI :MENSURATION
1.
AREAS RELATED TO CIRCLES
(12) Periods
Motivate the area of a circle; area of sectors and segments of a
circle. Problems based on areas and perimeter / circumference of the
above said plane figures. (In calculating area of segment of a
circle, problems should be restricted to central angle of 60 degree,
90 degree & 120 degrees only. Plane figures involving triangles,
simple quadrilaterals and circle should be taken.)
2.
SURFACE AREAS AND VOLUMES
(12) Periods
(i) Problem on finding surface areas and volumes of combinations of
any two of the following: cubes, cuboids, spheres, hemispheres and
right circular cylinder/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into
another and other mixed problem.(Problems with combination of not
more than two different solids be taken.)
UNIT VII : STATISTICS AND PROBABILITY
1.
STATISTICS
(15) Periods
Mean, median and mode of grouped data(bimodal situation to be
avoided). Cumulative frequency graph.
2.
PROBABILITY
(10) Periods
Classical definition of probability. Connection with probability as
given in class IX. Simple problem on single events, not using set
notation.
Top
INTERNAL ASSESSMENT 
20 MARKS 
Evaluation of activities 
10 Marks 
Project Work 
05 Marks 
Continuous Evaluation 
05 Marks 


