Kendriya Vidyalaya, Lesson Plan€¦ · and make the children understand how to use algebraic...

Kendriya Vidyalaya, Lesson Plan

Date :-………………………..

Class : IX ( NINTH ) Section :………….

Subject:- Maths

Lesson : a) Rational Numbers

Periods :_ ………………19

Gist Of The lesson

(Focused skills / Competencies)

Targeted Learning

Outcome (TLO)

• A number r is called a Rational Numbers, if it can be

written in the form of �� ,where p and q are integers

and q ≠ 0

• A number r is called a Irrational Numbers, if it can not

be written in the form of �� ,where p and q are

integers and q ≠ 0. E.g.,1.01001000100001.,√2, √3, √5

• The decimal expansion of a Rational Number is

either terminating or non-terminating recurring .

• The decimal expansion of an Irrational Number is

non - terminating non- recurring .

• All the Rational Numbers and Irrational Numbers make

up a collection of Real Numbers.

• There is a Real Numbers corresponding to every point

on the number line .

• If r is a Rational Number and s is called an Irrational

Number , then r + s and r – s are Irrational Numbers ,

and r s and � are Irrational Numbers , r ≠ 0

Laws of exponents for real numbers. Let a > 0 be a real

number and m and n be rational numbers.Then,

• (a)�� x� = �� ; (b) �� ÷÷÷÷� =�� ;(c) (��) =��

• ( d) ��x �� =(��)� (e) �� = (��)� (f) �� = 1

• To rationalize the denominator of �

�√�� , we multiply

by �√��√�� , where a and are integers.

• To understand the

form of a rational

number and an

irrational number

and its decimal

expansion

• To understand how

to locate √2, √3, √5

etc. on a number line

by using Pythagoras

theorem.

• To locate any real

number on a number

line using successive

magnification

• For positive real

numbers a and How

to operate identities

like ;

• √�� = √� √�

• �� = √�√�

• �√� + √�� √� − √�� = a – b.

• �√� + √��² = a + 2√�� + b

• �� + √�� − √�� = �" - b

REMARKS/ SUGGESTIONS……………………………………………………………………………………….

……………………………………………………………………………………………………………………………….


Date of Commencement ……………………………..

Expected date of completion ………………………...

Actual date of Completion… ………………………….

[A] Planning Format Annexure – 1

Lesson : a) Rational Numbers

Teaching learning activities planned for achieving the TLO

using suitable resources and classroom management

strategies

Assessment

Strategies Planned

• Show the terminating and non- terminating recurring

decimal expansion of a given #$ form.

• Make the children understand how to insert rational

numbers between given rationals

• Show the non- terminating non-recurring decimal

expansion of a given irrational number.

• Make the children understand how to insert rational

numbers between given irrationals. Sow the egs. Like

1.01001000100001….., 3.25225222522225…….

• Demonstrate the method to locate √2, √3, √5 etc, and a

poisitive real number ( say 9.3) on a number line on the

black board.

• Make the children understand the magnification to locate

a decimal expansion having more number of digits in the

decimal part (Visualization)

• Demonstrate the operations using different examples

and make the children understand how to use algebraic

identities in real numbers

• Demonstrate the simplifications using the conversions

√% � %&'( , √%) � %

&*( , √%+ =%

&,( etc.

• Sub. Erichment

Lab Activity-

Square Root

Spiral

• Portfolio

CW & HW (Qns

from exercises)

• Revising problems

from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests/QUIZ

MCQs

CLASS TESTS

Cross Word Puzzle

Sign. of the Teacher _____________ Sign. of the PRINCIPAL / VP _____________

Name of the Teacher:

Designation :- TGT(MATH) Date: _________


Date :-………………………..


Subject:- Maths

Lesson : a) Polynomials

Periods :_ ………………19

Gist Of The lesson

(Focused skills / Competencies)

Targeted Learning

Outcome (TLO)

• A polynomialpolynomialpolynomialpolynomial p(x) in one variable x is an algebraic

expression in x of the form

p(x) = �- .- + �-��.-�� + ……+�"." +��.� + �/, where a₀ , a₁ , a₂ ,…………….� are constants and � ≠ 0 .

a₀ , a₁ , a₂ ,…………….� are respectively the coefficientscoefficientscoefficientscoefficients of

%� ,%& , %', ……………% , and n is called the degree of the degree of the degree of the degree of the

polynomial.polynomial.polynomial.polynomial.. Each of �- .-, �-��.-��, …,�".", ��.� , �/, with � ≠ 0 is called a term of the polynomial p(x) .

• Every linear polynomial in one variable has a unique zero

, a non –zero constant polynomial has no zero , and every

real number is a zero of a zero polynomial .

• The value of a polynomial for a given value of the variable.

• A real number ‘a’ is a zero of a polynomial zero of a polynomial zero of a polynomial zero of a polynomial p(x),if p(a) = 0. In

this case , a is also called a root of the equation p(x) = 0.

• Remainder theorem : If p(x) is any polynomialpolynomialpolynomialpolynomial of degree

greater than or equal to 1 and p(x) is divided by the

linear polynomial x – a , then the remainder is p(a) .

• Factor theorem : x – a is a factor of the polynomial p(x) if

p(a) = 0 .Also , if x – a is a factor of p(x), then p(a) = 0.

• Factorisation of polynomials.

• The zero of a polynomial

• Algebraic Identities

(. + 0 + 1)" = ." +0" +1" + 2xy + 2yz + 2xz

(. + 0)2 = .2 + 02 + 3xy( x + y)

(. − 0)2 = .2 - 02 - 3xy ( x - y)

.2 +02 +12 – 3xyz = (x + y + z) (." +0" +1"- xy - yz – xz)

• Understand the

definition of

polynomial, no. of

terms, degree of

polynomial and the

different t ypes

of polynomials

• Finding the value of

a polynomial 3(4) for a given value

4 = 5 as 3(5)by

substituting 4 = 5.

• Understand 4 = 5

is a zero of 3(4) if 3(5) = /

• Understand when

3(4) is divided by

4 − 5 the

remainder is 3(4) 4 − 5 is a factor

of 3(4) ⟺

3(5) = /

REMARKS/

SUGGESTIONS……………………………………………………………………………………………………….

……………………………………………………………………………………………………………………………….






Lesson : a) Polynomials



strategies

Assessment

Strategies Planned

• Show different egs to explain monomial binomial,

trinomial Etc. Also make the children understand the

degree of a polynomial by taking different polynomials.

• Make the children understand how to substitute 4 = 5

in 3(4) and simplify to get the value of 3(4) by doing

different problems.

• Verify the zeroes for different polynomials

• Verify the Remainder theorem and Factor theorem in

various polynomials. Make the children understand the

exercise problems.

• Make the children understand the factorization of

54" + 74 + 8 by splitting the middle term.

• To factorise 542 + 74" + 84 + 9 find by trial method

one zero 4 = 5 and divide the polynomial by 4 − 5 and

find the other quadratic factor to get the other two

zeroes. Apply the identities in various problems to

make understand the children the use of identities.

• Demonstrate the application in finding the value of

(�/:)2, (;;)2 etc.

• To factorise quadratic polynomial and a cubic

polynomial by factor theorem

• Understand the identities

• (i) (4 ± =)2 ; (ii) (4 + = + >)" and

• (iii) (4 + = + >)2 − 24=> = (4 + = + >)(4" + =" + >" −4= − 4> − =>)

• Sub. Erichment

Lab Activity:-

Verify the

factorization 4" + (5 + 7)4 + 57 =(4 + 5)(4 + 7)

• Portfolio

CW & HW (Qns

from exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests/QUIZ

MCQs

CLASS TESTS

Work Sheet

Chart/ Table





Date :-………………………..


Subject:- Maths

Lesson : a) Co-ordinate Geometry

Periods :_ ………………10

Gist Of The lesson

(Focused skills/Competencies)

Targeted Learning

Outcome (TLO)

• To locate the position of an object or a point in a

plane , we require two perpendicular lines. One

of them is horizontal, and the other is vertical.

• The plane is called the Cartesian or coordinate

plane and the lines are called the coordinate

axes.

• The horizontal line is called the x- axis , and the

vertical line is called the y-axis.

• The coordinate axes divide the plane into four

parts called quadrants.

• The point of intersection of the axes is called the

origin.

• The distance of a point from the y-axis is called its

x- coordinate ,or abscissa , and the distance of

the point from the x-axis is called its y-

coordinate , or ordinate.

• If the abscissa of a point is x and the

ordinate is y, the( x, y ) is called the

coordinates of the point. It is called an

ordered pair.

• The coordinates of the are ( 0,0).

• The coordinates of a point are of the form

(+, +) in the first quadrant, ( - .+) in the

second quadrant , ( - , - ) in the third

quadrant and ( + ,- ) in the fourth quadrant,

where + denotes a positive real number

and – denotes a negative real number.

• To know the Cartesian

system: XY-plane,

Quadrants, Origin etc.

• To plot a point on an XY-

plane whose coordinates

are given


……………………………………………………………………………………………………………………………….






Lesson : a) Co-ordinate Geometry

Teaching learning activities planned for achieving the TLO using

suitable resources and classroom management strategies

Assessment

Strategies

Planned

• Make the children understand Cartesian system by

drawing XY-plane on the grid sheet and explain how to

number the axes, what are quadrants?, what is origin?

• Demonstrate the method of plotting on the black board

and make the children understand in (4, =�, x represents

the horizontal movement and = represent the vertical

movement of a point starting from the origin.

• Practice with problems.

• CW & HW

Portfolio

(Qns from

exercises)

• Revising

problems

from R D

Sharma

• MULTIPLE

ASSESSMENT

Oral Tests/

Quiz

MCQs

CLASS TESTS





Date :-………………………..


Subject:- Maths

Lesson : a) Linear Equations In Two Variables

Periods :_ ………………8

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• An equation of the form ax + by + c = 0 , where a, b, c are real

numbers , such that a and are not both zero, is called a linear

equation in two variables.

• A linear equation in two variables has infinitely many

solutions.

• The graph of every linear equation in two variables is a

straight line.

• X = 0 is the equation of the y-axis and y = 0 is the equation of

the x – axis.

• The graph of x = a is a straight line parallel to the y = axis.

• The graph of y = a is a straight line parallel to the x = axis.

• An equation of the the type y= mx represents a line passing

through the origin.

• Every point on the graph of a linear equation in two variables is a

solution of the linear equation . Moreover, every solution of the

linear equation is a point on the graph of the linear equation.

• Standard form of a linear equation

• Frame a linear equation from a given situation.

• Graph of linear equation.

• Equations of lines parallel to the x-axis and y-axis.

• Geometrical representation of solution linear equation in

(i) one variable E.G. 2X + 5 =0

(ii) two variables

Solution of equation in two variable on Number Line

2X + 5 = 0

• To write a linear equation

in the form ax+by+c=0 and

indicate the values of a,b

and c.

• To identify the variables

in the given situation and

make the relation

numerically as a linear

equation.

• Understand that a linear

equation in two variables

has infinite solutions.

• How to find the solutions

of a given linear equation

in two variables.

• To draw the graph of a

given linear equation.

• Understand that the

graph of linear equation

in two variables is always

a straight line.


equation of a line parallel

to x-axis is y=band the

equation of line parallel

to y-axis is x=a.

• A solution of a linear

equation in one variable

form can be represented

as a point on number line

and the solution of linear

equation in two variables

form can be represented

as a line in Cartesian

plane.


……………………………………………………………………………………………………………………………….






Lesson : a) Linear Equations In Two

Variables

Teaching learning activities planned for achieving

the TLO using suitable resources and classroom

management strategies

Assessment

Strategies Planned

• Illustrate with examples how to write the

equations in the form �% + �? + @ = 0 and

how to write the values of �, ��BC@. e.g.,

". � !20 :. ". 20 ! : � /,Then � � ", � � 2, E � !:

‘ The length of a rectangle is 4 more than

thrice its breadth.’

Let length=% and breadth=? then the equation

is . � 20 F → . ! 20 ! F � /

• Solution of linear equations in two variables

x + 2y = 6

• Portfolio CW & HW

(Qns from exercises)

• Revising problems from R D

Sharma

• MULTIPLE ASSESSMENT

Oral Tests

MCQs

CLASS TESTS

Draw a Graph of the Linear

Equation in two

variables x + 2y = 6





Date :-………………………..


Subject:- Maths

Lesson : a) Introduction to Euclid’s Geometry

Periods :_ ………………06

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• Euclid defined a point, a line and a plane, the definitions are not

accepted by mathematicians. Therefore , these times are known as

undefined.

• Axioms or postulates are the assumptions which are obvious

universal truths. They are not proved.

• Theorems are statements which are proved , using definitions ,

axioms, previously proved statements and deductive reasoning.

• Some of Euclid’s Axioms are : (1) Things which are equal to the same thing are equal to one

another.

(2) If equals are added to equals , the wholes are equal.

(3) If equals are subtracted from equals , the remainders are equal.

(4) Things which coincide with one another are equal to one another.

(5) The whole is greater than the part .

(6) Things which are double of the same things are equal to one

another.

(7) Things which are halves of the same things are equal to one

another.

• Euclid’s postulates were Postulate 1: A straight line may be drawn from any one point

to any other point.

Postulate 2: A terminated line can be produced indefinitely.

Postulate 3: A circle can be drawn with any Centre and any radius.

Postulate 4: All right angles are equal to one another.

Postulate5: if a straight line falling on two straight lines makes

the interior angles on the same side of it taken together less than

two right angles, then the two straight lines, if produced

indefinitely, meet on that side on which the sum of angles is less

than two right angles.

• All the attempts to prove Euclid’s fifth postulate using the first 4

postulates failed. But they led to the discovery of several other

geometries, called non-Euclidean geometries.

• To know the

history of

Geometry and

the

mathematicians

who developed

the results in

Geometry.

• To know which

are the

definitions

given by Euclid,

what are

axioms and

postulates and

how to

distinguish

them

• Understand the

five postulates

and their

applications

• Understand the

different

versions of 5th

postulate and

definition of

parallel lines.

REMARKS/

SUGGESTIONS………………………………………………………………………………………………………..

……………………………………………………………………………………………………………………………….






Lesson : a) Introduction to Euclid’s

Geometry

Teaching learning activities planned for achieving the

TLO using suitable resources and classroom

management strategies

Assessment

Strategies Planned

• Let the children read the introduction given in NCERT

book. Explain works and discoveries of different

mathematicians like Pythagoras, Thales, Euclid etc.

• Explain the seven definitions given in the chapter in

simple manner.

• Make the children understand the terms ‘Axioms’

and ‘Postulates’. Postulates -- the assumptions

specific to geometry and Axioms—the assumptions

used in common not specific to geometry.

• Explain the seven axioms given in the chapter with

suitable examples.

• Explain the postulates with examples like ‘there is a

unique line that passes through two given points.

• 5th

postulate If <1 + <2 <180, then the lines meet on

that side.

• Explain the different versions with suitable figures

• Do the exercise problems by using appropriate

lemmas and postulates.

•

• Portfolio C/W & H/W

(Qns from exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS





Date :-………………………..


Subject:- Maths

Lesson : a) LINES AND ANGLES

Periods :_ ………………10

Gist Of The lesson


Targeted Learning Outcome

(TLO)

• If a ray stands on a line, then the sum of the two

adjacent angles so formed is 180° and vice-versa.

This property is called as the Linear pair axiom .

• If two lines intersect each other, then the

vertically opposite angles (V.O.A.)are equal.

• If a transversal intersects two parallel lines, then

(i) Each pair of corresponding angles is equal,

(ii) Each pair of alternate interior angles is equal,

(iii) Each pair of interior angles on the same side

of the transversal is supplementary.

• If a transversal intersects two lines such that ,

either

(i) Any one pair of corresponding angles is equal ,

or

(ii) Any one pair of alternate interior angles is

equal , or

(iii) Any one pair of interior angles on the same

side of the transversal is supplementary, then

the lines are parallel.

• Lines which are parallel to a given line are parallel

to each other .

• The sum of the three angles of a triangle is 180°.

• If a side of a triangle is produced , the exterior

angle so formed is equal to the sum of the two

interior opposite angles.

• Understand the basic terms

like angles and different

types of angles, pairs of

angles and their properties

• Understand the linear pair

axiom that Linear pairs are

supplementary and if

two adjacent angles are

supplementary then they

are linear pairs.

• Vertically opposite angles

are always equal

• Understand the properties

of angles formed by a

transversal on two parallel

lines.

• Understand the angle sum

property that the sum of

the three angles of a

triangle is 180°.

• The exterior angle property

is that the exterior angle of

a triangle is the sum of the

opposite interior angles.

REMARKS/

SUGGESTIONS………………………………………………………………………………………………………..

……………………………………………………………………………………………………………………………….






Lesson : a) LINES AND ANGLES



strategies

Assessment

Strategies Planned

• Show various types of angles by drawing them on the black

board.

then ∠AOD = ∠BOC and ∠PQR & ∠RQSare∠AOC = ∠ BOD Adjacent • Show the properties of linear pairs and the property of

vertically opposite angles in different problems.

Corresponding Angles

∠1 =∠ 6 ; ∠2 = ∠5; ∠4 =∠7 ; ∠3 =∠8

Alternate Interior Angles

∠4 =∠5 ; ∠3 =∠6 ………..

CO INTERIOR ANGLES OF THE SAME SIDE

∠ 4 + ∠6 = 180° AND ∠ 3 +∠ 5 = 180°

• Sub. Erichment

Lab Activity:-

Verify the angle

sum property of

a triangle by

cutting and

pasting.

• Portfolio C/W &

H/W (Qns from

exercises)

• Revising

problems from R

D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS

∠1 +∠2+∠3 = 180°

∠3 = 180° - (∠1+∠2)

∠3+∠4 = 180° - (∠1+∠2)

+∠4 = 180°

∠4 = ∠1 ∠2




∠ 2=∠4 and ∠3 = ∠5 and

∠1 + ∠2 +∠3 = 180°, then

∠1 + ∠4 +∠5 = 180°

Then

∠AOB + ∠BOC = 180°

∠AOB &∠∠∠∠BOC are

Linear Pair


Date :-………………………..


Subject:- Maths

Lesson : a) TRIANGLES

Periods :_ ………………12

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• Two figures are congruent, if they are of the same shape and

of the same size.

• Two circles of the same radii are congruent.

• Two squares of the same sides are congruent.

• If two triangles ABC and PQR are congruent under the

correspondence A←→ P, B←→ Q and C←→ R, then

symbolically, it is expressed as ∆ ABC ≅ ∆ PQR.

• If two sides and the included angle of one triangle are equal

to two sides and the included angle of the other triangle,

then the two triangles are congruent (SAS Congruence Rule).

• If two angles and the included side of one triangle are equal

to two angles and the included side of the other triangle,

then the two triangles are congruent (ASA Congruence Rule).

• If two angles and one side of one triangle are equal to two

angles and the corresponding side of the other triangle, then

the two triangles are congruent (AAS Congruence Rule).

• Angles opposite to equal sides of a triangle are equal.

• Sides opposite to equal angles of a triangle are equal.

• Each angle of an equilateral triangle is of 60°.

• If three sides of one triangle are equal to three sides of the

other triangle, then the two triangles are congruent (SSS

Congruence Rule).

• If in two right triangles, hypotenuse and one side of a triangle

are equal to the hypotenuse and one side of other triangle,

then the two triangles are congruent (RHS Congruence Rule).

• In a triangle, angle opposite to the longer side is larger

(greater) and vice versa.

• Sum of any two sides of a triangle is greater than the third

side.

• Recollect the concept

of congruence in

triangles from class

VII.

• To understand how to

verify the congruency

of triangles.

• Understand that if two

sides and the included

angle in a triangle are

respectively equal to

two sides and the

included angle then

the triangles are

congruent.

• To understand and

learn the proof of the

ASA congruence rule.

Also how to apply the

rule in different

problems.

• To understand that if

in a triangle two sides

are equal then the

angles opposite to

them are also equal

• Also if two angles in a

triangle are equal the

sides opposite to them

are also equal.

REMARKS/

SUGGESTIONS……………………………………………………………………………………………………..

……………………………………………………………………………………………………………………………






Lesson : a) TRIANGLES



strategies

Assessment

Strategies Planned

• Define the congruence in figures and then explain the

congruence of triangles.

≅

(i) their corresponding angles are equal

(ii) their corresponding sides are equal

The corresponding parts are also called CPCT

• Show the congruence of different triangles in different

problems in the text book. By using

• ≅

• ≅

• ASA congruence rule

• ≅

SSS congruence rule

• ≅

RHS congruence rule

• Sub. Erichment

Lab Activity:-

• Verify the angle

sum property of a

triangle by cutting

and pasting.

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests MCQs

CLASS TESTS

∠B is the largest angle

so that AC is the

longest side and vice

versa

AB+AC>BC

AB+BC>AC

AC+BC>AB




SAS congruence rule

Two triangles are

congruent if

In ∆ABC , AB = AC ,then

∠B =∠C

If in ∆ABC , ∠B =∠C, then

AB = AC


Date :-………………………..


Subject:- Maths

Lesson : a) Quadrilaterals

Periods :_ ………………12

Gist Of The lesson


Targeted Learning Outcome

(TLO)

• Area of a figure is a number (in some unit ) associated with

the part of the plane enclosed by that figure.

• Two congruent figures have equal areas but the converse

need not be true.

• If a planar region formed by a figure T is made up of two

non – overlapping planar regions formed by figures P and

Q , then ar(T)=ar(P)+ar(Q), where ar(X) denotes the area of

figure X.

• Two figures are said to be on the same base and between

the same parallels, if they have a common base(side)and

the vertices ,(or the vertex) opposite to the common base

of each figure lie on a line parallel to the base.

• Parallelograms on the same base (or equal bases) and

between the same parallels are equal in area.

• Area of a parallelogram is the product of its base and the

corresponding altitude.

• Parallelograms on the same base (or equal bases) and

having equal areas lie between the same parallels.

• If a parallelogram and a triangle are on the same base and

between the same parallels, then area of the triangle is

half the area of the parallelogram.

• Triangles on the same base (or equal bases) and between

the same parallels are equal in area.

• Area of a triangle is half the product of its base and the


• Triangles on the same base (or equal bases) and having

equal areas lie between the same parallels.

• A median of a triangle divides it into two triangles of equal

areas.

• Understand that what are

quadrilaterals, types of

quadrilaterals and types of

parallelograms.

• The sum of the angles of a

quadrilateral is 360°.

• Understand the theorem ‘ a

diagonal divides a

parallelogram into two

congruent triangles’. By

applying the theorem

derive all other properties

of parallelogram.

• Understand the theorem ‘ a

diagonal divides a

parallelogram into two

congruent triangles’. By

applying the theorem

derive all other properties

of parallelogram.

• Understand the property of

a triangle that the line

segment joining the mid-

points of two sides of a

triangle is always parallel to

the third side and its length

is half of the third side.

REMARKS/

SUGGESTIONS……………………………………………………………………………………………………….

……………………………………………………………………………………………………………………………….






Lesson : a) Quadrilaterals



strategies

Assessment Strategies

Planned

• Explain the types of quadrilaterals and parallelograms

by drawing them on the black board.

• Explain the Mid Point Theorem.

A

D E

B C

Apply the theorems in different problems given in the text

book and make the children understand how to apply the

theorems in various situations.

• Sub. Erichment

Lab Activity:-

1-Verify that a

diagonal divides a

parallelogram in to

two congruent

triangles.

2- To verify Mid

point Theorem.

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS




D and E are the Mid-points of the

sides AB and AC respectively then

DE ǁ BC and XY � Z['

The converse is ‘ if D is the midpoint

such that DE ǁ BC then E must be the

mid-point of AC.


Date :-………………………..


Subject:- Maths

Lesson : a) Area of Parallelogram and Triangles

Periods :_ ………………10

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• Area of a figure is a number (in some unit ) associated with

the part of the plane enclosed by that figure.

• Two congruent figures have equal areas but the converse

need not be true.

• If a planar region formed by a figure Tis made up of two non-

overlapping planar regions formed by figures P and Q, then

AR(T)= AR(P)+AR(Q), where AR(X)denotes the area of figure X.

• Two figures are said to be on the same base and between the

same parallels, if they have a common base (side) and the

vertices, (or the vertex) opposite to the common base of each

figure lie parallel to the base.

• Parallelogram on the same base (or equal bases) and between

the same parallels are equal in area.

• Area of a parallelogram is the product of its base and the


• Parallelograms on the same base (or equal bases) and having

equal area lie between the same parallels.

• If a parallelogram and a triangle are on the same base and

between the same parallels, then area of the triangle is half the

area of the parallelogram.

• Triangles on the same base (or equal bases) and between the

same parallels are equal in area.

• Area of a triangle half the product of its base and the


• Triangles on the same base (or equal bases) and having equal

areas lie between the same parallels.


areas.

• Understand which

figures are aid to be

figures on the same

base and between

the same parallels.

• Understand that

two parallelograms

on the same base

and between the

same parallels are

equal in area.

• Able to apply this

theorem to find the

formula for finding

the area of a

parallelogram and

area of a triangle.

• Understand the

property that two

triangles on the

same base and

between the same

parallels are equal

in area and if two

triangles on the

same base and with

equal area lie

between the same

parallels

REMARKS/

SUGGESTIONS………………………………………………………………………………………………………..

……………………………………………………………………………………………………………………………..






Lesson : a) Area of Parallelogram and

Triangles



strategies

Assessment

Strategies Planned

• Figures on the same base only.

• Figures between the same parallel lines

• A diagonal of a parallelogram divides it into two triangles

of equal areas.

• Relationship between the areas of two parallelogram on

the same base and between the same parallel lines

• Two triangles on the same base and between same parallel

lines are equal in areas


area.

If a triangle and a parallelogram are on the same base and

between the same parallels, then prove that the area of the

triangle is equal to half the area of the parallelogram.

• Sub. Erichment

Lab Activity:-

Verify that :

(a) Area of ∥]� on the same

base and

between same

∥sareequal.(b) Area of △s

on the same

base and

between same

∥s are equal.

• Portfolio C/W

& H/W (Qns

from exercises)

• Revising

problems from

R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs





Date :-………………………..


Subject:- Maths

Lesson : a) CIRCLES

Periods :_ ………………12

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• A circle is the collection of all points in a plane, which are

equidistant from a fixed point in the plane.

• The perpendicular from the Centre of a circle to a chord bisects

the chord.

• There is one and only one circle passing through three non-

collinear points.

• If two arcs of a circle are congruent , then their corresponding

chords are equal and conversely if two chords of a circle are

equal, then their corresponding arcs (minor , major) are

congruent.

• Congruent arcs of a circle subtend equal angles at the Centre.

• Angles in the same segment of a circle are equal.

• Angle in a semicircle is a right circle.

• The sum of either pair of opposite angles of a cyclic

quadrilateral is 180°.

• If sum of a pair of opposite angles of a quadrilateral is 180°, the

quadrilateral is cyclic.

• Equal chords of a circle (or of congruent circles )subtend equal

angles at the Centre.

• If the angles subtended by two chords of a circle (or of

congruent circles ) at the Centre (corresponding Centre’s) are

equal, the chords are equal.

• The line drawn through the Centre of a circle to bisect a chord

is perpendicular to the chord.

• Equal chords of a circle (or of congruent circles ) are equidistant

from the Centre ( or corresponding Centre’s).

• Chords equidistant from the Centre ( or corresponding Centre’s)

of a circle (or of congruent circles ) .

• The angle subtended by an arc at the Centre is double the angle

subtended by it at any point on the remaining part of the circle.

• If a line segment joining two points subtends equal angles at

two other points lying on the same side of the line containing

• Understand the basic

terms related with

circles

• Understand the

theorem that the equal

chords make equal

angles at the centre.

• Understand the

perpendicular from the

centre to a chord will

bisect it

• Able to apply the result

in problems

• Understand that there is

a unique circle through

three given points.

• Also understand that

equal chords are

equidistant from the

centre


angle subtended by an

arc at the centre is

double the angle

subtended by the arc at

a point on the other

side of the circle.

• Understand the

necessary and sufficient

conditions of a cyclic

quadrilaterals

REMARKS/

SUGGESTIONS………………………………………………………………………………………………………..

……………………………………………………………………………………………………………………………….






Lesson : a) CIRCLES



strategies


Planned

• Demonstrate the terms, centre, radius, diameter,

chords Arcs, Sectors Segment etc by showing them on

the figure drawn on the board.

• Demonstrate the property that there is a unique circle

passing through three given points.

• Cyclic quadrilateral ⇒⇒⇒⇒All the four vertices lie on the

same circle.

• The Angle x subtended at the centre of a circle by an

arc is twice the size of the angle on the circumference

subtended by the same arc.

• Sub. Erichment

Lab Activity:-

To verify that the

Angle subtended

by an arc at the

Centre of Circle is

double the angle it

subtends at any

point on the

remaining part of

the circle.

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests MCQs

CLASS TESTS

Cross Word Puzzle





Date :-………………………..


Subject:- Maths

Lesson : a) Constructions

Periods :_ ………………10

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• To construct the bisector of a given angle ABC .

• To construct the perpendicular bisector of a given line

segment.

• To construct an angle of 600.

• To draw a triangle whose base , base angle and the sum of

the other two sides.

• To construct a triangle given its base, a base angle and the

difference of the other two sides.

• To construct a triangle, given its perimeter and its two

base angles.

Diagrammatic Skill -- Drawing , understanding , Proper

handling of geometric instruments ( i.e., ruler and

compasses ), Rough Sketching.

• To construct the

bisector of a given

angle.


perpendicular

bisector of a given

line segment

• To construct an

angle of 600.

• To draw a triangle

whose base , base

angle and the

sum of the other

two sides.

• To construct

∆defwith BC, <B

and AB-AC or AC-

AB are given

• To construct a

triangle ABC with

AB+BC+AC and <B

and <C are given

REMARKS/

SUGGESTIONS……………………………………………………………………………………….

……………………………………………………………………………………………………………………………….






Lesson : a) Constructions



strategies


Planned

• To construct the bisector of a given angle ABC .

• To construct a triangle, given its perimeter and its two

base angles. Given the base angles, say ∠∠∠∠ B and ∠∠∠∠ C

and BC + CA + AB, you have to construct the triangle

ABC.

• To construct a triangle given its base, a base angle and

the difference of the other two sides.

Case (i) : Let AB > AC that is AB – AC is given.

Case (ii) : Let AB < AC that is AC – AB is given.

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS


perpendicular

bisector of a given

line segment.





Date :-………………………..


Subject:- Maths

Lesson : a) HERON’S FORMULA

Periods :_ ……………… 8

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• Area of a triangle with the three sides a, b and c is

calculated by using Heron’s formula stated as

A

c b

B a C

• Area of a quadrilateral whose sides and one diagonal

are given , can be calculated by dividing the

quadrilateral into two triangles and using the Heron’s

formula.

• To understand the area

of triangle

= �"

× base × height


formula, area of a

triangle =

h( − �)( − �)( − E)


apply the Heron’s

formula in finding the

area of quadrilaterals.

REMARKS/

SUGGESTIONS……………………………………………………………………………………………………….

……………………………………………………………………………………………………………………………….

A quadrilateral ABCD where

AB=m3 cm, BC= 4 cm, CD=

4cm, DA= 5cm and AC= 5cm.

Area of ABCD = Area of ABC +

area of ADC

Area of a triangle =

h( − �)( − �)( − E),

where � ��E"

which is called the semi

perimeter .






Lesson : a) HERON’S FORMULA



strategies


Planned

• Derive the area of an equilateral triangle = √2F

�"

where � is the side of the equilateral triangle.

a a

a

Find the Area of the following figures.

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS




For an equilateral Triangle � ��"

= 2�"

Now by Heron’s formula

Area of a triangle = h(−�)(− �)(− E), = h( − �)( − �)( − �), = ( − �) h( − �) = i2�" − �j �2�" i2�" − �j = i2��"�" j �2�" i2��"�" j

= i�"j �2�" i�"j

= �" x

�" x √2 = √2

�"F

= √2F �"


Date :-………………………..


Subject:- Maths

Lesson : a) SURFACE AREA AND VOLUMES

Periods :_ ……………… 15

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• •


formula for finding

the surface area of a

cuboid = 2(lb+lh+bh)

and surface area of a

cube = 6a2

• Volume = a3


formula for finding

the total surface area

= 2πr(r+h)

• Volume = k�"l


formula for finding

the area = πr(r+l)

• Volume = �2

k�"l


formula for finding

the area of sphere =

= 4πr^2, and area of

hemisphere = 3πr^2

• Volume of sphere =

4/3 πr^3

• And volume of

hemisphere = 2/3

πr^3

REMARKS/

SUGGESTIONS…………………………………………………………………………………………………….….

……………………………………………………………………………………………………………………………….

Lateral Surface Area(LSA) = 2lh+2b = 2( l + b ) h

= perimeter of base × height

Total Surface Area (TSA) = 2lb+2lh+2bh

= 2(lb+lh+bh)

Volume = base area ×height =l x b x h = lbh

Lateral Surface Area (LSA) = 4 (side)² = 4 ( l ) ²

Total Surface Area (TSA) = 6 (side) = 6 ( l )²

Volume = (side) = ( l )³

Total base area ="4k�",

Curved Surface Area ( CSA ) = "k�l,

Total Surface Area (T S A )

="k�" + "k�l = "k�(� + l) Volume of cylinder = base area ×height

= k�"l

Total Surface Area (T S A ) = Fk�" and

Volume = F2k�2

=�2k�"l

Base area = k�",

C S A = ½ Circumference x slant height.

= �" 2k� g m = k�m

T S A = k�" + k�m = k�(� + m) Volume = �2 nopnmqrsno�s�sEtupsE0mu-vs






Lesson : a) SURFACE AREA AND VOLUMES



strategies

Assessment

Strategies Planned

•

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TEST

Hemisphere




Total Surface Area

(T S A ) = 2k�"

and

Volume = "2

k�2

Exercise 13.2 Q2. Rachel, an

engineering student, was asked to make a

model shaped like a cylinder with two cones

attached at its two ends by using a thin

aluminum sheet. The diameter of the model is

3 cm and its length is 12 cm. if each cone has a

height of 2 cm, find the volume of air contained

in the model that Rachel made. (Assume the

outer and inner dimensions of the model to be

nearly the same.)

Exercise 13.1 Q3. A toy is in the form

of a cone of radius 3.5 cm mounted on a

hemisphere of same radius. The total height

of the toy is 15.5 cm. Find the total surface

area of the toy.

Exercise 13.3

Q7. Water in canal,

6 m wide and 1.5 m

deep, is flowing with

a speed of 10 km/h.

how much area will

it irrigate in 30

minutes, if 8 cm of

standing water is

needed?


Date :-………………………..


Subject:- Maths

Lesson : a) STATISTICS

Periods :_ ………………8

Gist Of The lesson


Targeted Learning

Outcome (TLO) • Facts or figures, which are numerical or other wise , collected with a

definite purpose in mind is called a Data. Data is the plural form of the

Latin word datum.

• Statistics deals with collection, organization, analysis and interpretation

Of data.

• Types of Data ; Primary Data & Secondary Data.

• Primary Data: The data collected by the investigator himself or herself

with a definite objective is called a Primary Data.

• Secondary Data : The data collected by some other person or source and

is used by a different person is called a Secondary Data.

• Data can be presented graphically in the form of bar graphs ,

histograms and frequency polygons.

• The three Measures Of Central Tendencies for Ungrouped Data are ;

Mean , Median and Mode.

• Mode is the most frequently occurring observation.


terms which are

learned in the lower

classes


concept of a data and

how the data is

collected ?

• To understand how a

data can be collected

in the form of raw

data.

• To prepare the

ungrouped frequency

table by using tally

marks

• . To understand the

how to preparation of

a grouped frequency

table.


draw a bar graph and a

histogram.

• To verify which graph

is suitable for the given

data.


draw frequency

polygon from the

histogram and without

drawing histogram.


find the mean median

and mode of a given

data.

REMARKS/

SUGGESTIONS………………………………………………………………………………………………………..

………………………………………………………………………………………………………………………………

MEAN of ungrouped data:

.w = Mean = qrno�mmn�s�p�tun--n.no�mmn�s�p�tun-

.w = (.��."�.2�⋯…….………�.-)

-






Lesson : a) STATISTICS



strategies


Planned

Drawing Of Bar Graph, Histogram And Frequency

Polygon.

• Sub. Erichment

Lab Activity:-

Draw the histograms

for classes of equal

widths and varying

widths.

• Portfolio C/W &

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS

Work sheet

Data Collection





Date :-………………………..


Subject:- Maths

Lesson : a) Probability

Periods :_ ………………

Gist Of The lesson


Targeted Learning

Outcome (TLO)

• In mathematics there is difference between chance

and probability. Chance is measured in percentage and

probability is measured in numbers(fractions).

• Even chance means Equally likely Chance.

• An event for an experiment is the collection of some

outcomes of the experiment.

• EVENT • OUTCOMES

• Tossing the coin • Heads and Tails

• Throwing a dice • 1,2,3,4,5and 6

• A trial is an action which results in one or several

outcomes.

• The empirical (or experimental) probability P(E) of an

event E is given by

• P(E) = z{��|}~��}�� ##| |�

�~��z{��|}~��}��. • The Probability of an event lies between 0 and 1.

(0 and 1 inclusive ).

Probability of an impossible event is 0.

The probability of a sure event (or certain event) is 1.

P( Y& ) + P( Y' ) + ………………..+ P (Yz ) = 1

• Understands the

concept of probability

and the terms used.

• Can do the activity of

throwing a dice or

tossing the coin and

calculate the

probability.

• Be able to calculate

probality of an event.

•

REMARKS/

SUGGESTIONS……………………………………………………………………………………………………….

………………………………………………………………………………………………………………………………






Lesson : a) Probability



strategies


Planned

• A coin is tossed 1000 times with the following frequencies: Head : 455, Tail : 545

Compute the probability for each event. • Two coins are tossed simultaneously 500 times, and we

get • Two heads : 105 times

One head : 275 times No head : 120 times Find the probability of occurrence of each of these events.

• A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table :

• Find the probability of getting each outcome.

• Practice exercise of text book Questions.

• Sub. Erichment

Lab Activity:-

To find

Experimental

probability of each

out come of a die

when it is thrown a

large number of

times.

• Portfolio C/W and

H/W (Qns from

exercises)


from R D Sharma

• MULTIPLE

ASSESSMENT

Oral Tests

MCQs

CLASS TESTS

Work sheets.




Kendriya Vidyalaya, Lesson Plan€¦ · and make the children understand how to use algebraic...

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Transcript of Kendriya Vidyalaya, Lesson Plan€¦ · and make the children understand how to use algebraic...