APRIL TO SEPTEMBER 10/Maths_Class_10.pdfExplains the method of finding zeroes of a given polynomial....

ANNUAL CURICCULUM PLAN 2020-2021

MATHEMATICS

CLASS X

VISION FOR TEACHING MATHEMATICS:

In this changing world, those who understand and have a liking for mathematics will have significantly enhanced opportunities and options for shaping their future.Mathematical competence

opens doors to productive future. The vision of imparting mathematical knowledge is:

to promote students’ confidence in mathematics, curiosity, freedom and belief in learning by doing.

to learn important mathematical ideas with understanding, in challenging environments and to be technologically equipped for the twenty-first century.

to create a liking for learning of mathematics.

to use this knowledge as day to day problem solving technique.

CHAPTER

TRANSACTION STRATEGIES/

INNOVATIVE PEDAGOGY

LEARNING OUTCOME

CORE SKILLS/ART INTEGRATION /

INTERDISCIPLINARY LINKAGE

1. REAL NUMBERS

Euclid’s division lemma, Fundamental Theorem of

Arithmetic

Irrational Numbers

Real numbers, and their decimal

expansion

The teacher encourages different ideas, gives students the freedom to explore about

HCF and LCM of different numbers. She

explains the difference between rational

and irrational numbers. Discussion will be

done about the advantages of learning HCF

and LCM of two numbers in day today life.

The teacher explains the proof of √2 is

irrational through the narration of a story.

Fundamental theorem of arithmetic will be explained through power point presentation

The students will be able to

understand the real

number system and obtain the decimal

representation of rational

and irrational numbers.

use Euclid’s division

lemma to find hcf of

given numbers

CORE SKILL:

Understanding

Application of knowledge

Thinking skill

ART INTEGRATION

Card Activity

Cut out the given number slips and place them on a table. Call

each student one by one and ask them to write the number in

as many columns according to the type of number. Ask them

to find irrational numbers and rational numbers


History and Science

Physical education

Students are asked to give some examples of history to be

used in mathematical concepts.

APRIL TO SEPTEMBER

2. POLYNOMIALS

Zeros of a polynomial.

Relationship between zeros

and coefficients of

quadratic polynomials.

Statement and simple

problems on division

algorithm for polynomials

wi th real coefficients.

The teacher enhances children's ability to

think and reason, to visualize and handle any polynomial, to formulate and solve a

given question

Explains the method of finding zeroes of a

given polynomial.

Encourages children to find zeroes of

linear, quadratic and cubic polynomial by

graphical representation

Students will be able to

encounter a situation to

understand zeroes of a

polynomial with the

previous knowledge

understand the relation

between zeroes and

coefficient

express some life

situations in

mathematical language

using polynomials

appreciate the importance of

polynomials in day to

day life

express the key

terminologies of a

polynomial

CORE SKILLS

Creativity

Problem Solving Application

Understanding

ART INTEGRATION

Drawing graph of quadratic polynomial and finding its zeroes.

Finding the relation between the sign of coefficient of and the

shape of the graph of the quadratic polynomial.


commerce

health and environment

3. PAIR OFLINEAR EQUATIONS IN

TWO VARIABLES

Pair of linear equations in

two variables graphical method of their

solution

consistency/ inconsistency.

Algebraic condit ions for

number of solutions.

Solution of a pair of linear

equations in two variables

algebraically – by

substi tution, by elimination

and by cross multiplication

method.

Simple problems on equations reducible to

linear equations.

The teacher will show any picture on

power point and ask the class to describe

the picture mathematically or construct a

mathematical problem based on this picture.

Relates and demonstrates through real-life

situations that will make the concepts easy

to understand and easy to learn. It is likely

to spark their interest and get them excited

and involved in learning process.

The students will be able

appreciate the beauty of

Mathematics

connect Mathematics to

day to day life

make use of innovative

teaching strategies.

develop assessment for

joyful learning

use technology to

enhance learning

CORE SKILL understand Mathematical concepts

develop Mathematical skills

know mathematical facts

learn the language and vocabulary of Mathematics

develop ability in mental Mathematics

ART INTEGRATION Finding the consistency of linear equations in two variables by

drawing different pairs of equations on graph sheets will be

given as an activity


Science

English

6. TRIANGLES

Definitions, examples,

counter examples of similar

tr iangles. Basic proportionality theorem,

Area theorem, Pythagoras

theorem and its converse,

Application questions

Student’s Work Integrated with Sikkim

Makes time for brainstorming sessions in the classrooms. These sessions are a great way to be creative. When multiple brains focusing on one single idea, one is sure to get numerous ideas. The students will be asked to find the relation between ratio of areas of two similar triangles and its corresponding sides and to verify Pythagoras theorem by cut and paste method


to understand the

theorems

to apply the theorems in

different questions

to draw a diagram by

reading the given

information from a

question

CORE SKILLS

Self-awareness

Understanding

Team spirit

Creative thinking

ART INTEGRATION

To verify Pythagoras theorem by performing an activity. The

area of the square constructed on the hypotenuse of a right-

angled triangle is equal to the sum of the areas of squares

constructed on the other two sides of a right-angled triangle.

Pythagoras theorem Activity

In this activity children will be encouraged to use the art and

culture of the state of Sikkim.


Art and craft

Design making engineering

8. INTRODUCTION TO

TRIGONOMETRY

Trigonometric ratios of an

acute angle of a r ight -

angled tr iangle.

Proof of their existence

(well defined); motivate the

ratios, whichever are

defined at 0° and 90°.

Values of the

tr igonometric ratios of 30°,

45° and 60°. Rela tionships between the

ratios.

Proof and applications of

the identity.

Now a basic query, how did this word sine

originate, there are several stories told in

different ways, but what is found to be

most authentic was an early Hindu work on

astronomy, the Surya Siddhanta gives a

table of half-chords based on Ptolemy’s

table.

The sine as a function of an angle was first

described in the Aryabhatiya of Aryabhata

(ca. 510), considered the earliest Hindu treatise on pure mathematics. In this work

Aryabhata II (also known as Aryabhata the

elder; born 475 or 476, died ca. 550) uses

the word ardha-jya for the half-chord which

is shortened to jya or jiva.

The etymological journey of the modern

word “sine” is interesting and starts from

here.

When the Arabs translated the Aryabhatiya

into their own language, they retained the

word jiva without translating its meaning.


to understand various

trigonometric ratios

to apply trigonometric values in calculation

to understand the

identities

CORE SKILLS

Developing curiosity

Sharing knowledge to others

Knowledge of concept

ART INTEGRATION

Learning trigonometric identities and ratios through a flow of

music developed

pre content activities can be conducted in the class to reinforce the knowledge of trigonometric ratios, value of T-

ratios at prescribed angles.

Prepare some flash cards on which various right triangles are

drawn. Some of the sides and angles are missing. Ask the

students to find them


astronomy

geography

trigonometry is applicable in various fields like satellite

navigation, developing computer music, chemistry number

In Arabic and Hebrew, words consist

mostly of consonants, the pronunciation of

the missing vowels being understood

through common usage. Thus jiva could

also be pronounced as jiba or jaib, and jaib

in Arabic means bosom, fold, or bay. When the Arabic version was translated

into Latin, jaib was translated into sinus,

which means bosom, bay, or curve. Soon

the word sinus or sine in its English version

became common in mathematical texts

throughout Europe. The abbreviated

notation sin was first used by Edmund

Gunter (1581–1626), an English minister

who later became professor of astronomy at

Gresham College in London. In 1624 he

invented a mechanical device, the “Gunter

scale” for computing with logarithms - a forerunner of the familiar slide rule - and

the notation sin (as well as tan) first

appeared in a drawing describing his

invention.

Explains the trigonometric ratios with lot of

examples. Makes it clear to the students

that the values of trigonometric ratios of an

angle do not vary with the lengths of the

sides of the triangle, if the angle remains

the same.

theory, medical imaging, electronics, electrical engineering,

9. APPLICATIONS OF

TRIGONOMETRY

Concept of angle

of elevat ion and angle of

depression

Use of tr igonometric ratios

in word problems using

standard angles 30°, 45°,

60°

Explains simple and believable

problems on heights and distances.

The problems should not involve

more than two right tr iangles.

Shapes mathematical language by

The students will be able:

to be motivated in

solving simple problems

related to real life

situation using trigonometry

to draw a proper diagram

by reading the question

to understand the

concept of angle of

CORE SKILLS

Developing curiosity

acquire the skills in using

them in problem solving

appreciate the application in day to day life

ART INTEGRATION

To make a model to show angle of elevation of any given

object

To make a model to show angle of depression of any given object


It is used in oceanography in calculating the height of tides in

oceans. The sine and cosine functions are fundamental to the

theory of periodic functions, those that describe the sound and

modelling appropriate terms and

communicating their meaning in ways that

students understand. Value based questions

are framed to understand the concepts in a

better way

elevation and depression light waves

14. STATISTICS

Mean, median and mode of grouped data (bimodal

situation to be avoided).

Relation between mean,

median and mode of a data .

The teacher makes the students to find the median of a given data by cumulative

frequency curve and verifies it by

calculation. She makes the learners

think individually and then share with the

class about different situations in which

measures of central tendency is used. The

children will be explained to calculate

mean, median, and mode of a given

grouped data


to calculate the mean,

median and mode of a

grouped frequency

distribution

to understand the

relation between mean

,median and mode and

interpreting a given data.

CORE SKILLS

Communication

self-expression

creative and critical thinking

information

skill of drawing accurate figures

skill of interpretation

skill of solving with appropriate method.

Art integration

Showing children how to tally no. of patients admitted in a

hospital due to corona, age wise.

Find the median weight of the patient in the data.


Political science

economics

4.QUADRATIC EQUATION Standard form of a quadratic

equation ax2+bx+c=0, (a ≠ 0).

Solution of the quadratic

equations (only r eal roots) by

factorization and by using quadratic

formula.

Rela tionship between discriminant

and nature of roots

Moves from simple step problem solving modes to increasingly complex and multi- step problem solving. Situational

problems based on quadratic equations rela ted to day

to day activities are incorporated


to solve

quadratic

equation in

different

methods

to find the

nature of the

roots

to understand

the word

problems in quadratic

equation

CORE SKILLS Logical Thinking

enthusiasm

self-confidence

arithmetic skills

ART INTEGRATION

Finding the solution of a quadratic

equation by completing the squire

figure3

INTERDISCIPLINARY

LINKAGE

Physics Statistics

Calculus

Computer programming

5. ARITHMETIC PROGRESSION

Definition of Arithmetic Progression

Derivation of the n t h term and sum of the first n terms of A.P.

application in solving daily li fe

problems by using the formula

Inculcates positive, persevering problem-solving approaches and

solves problems with the students building a rapport. Thus, building their self-esteem and confidence. She demonstrates a

method to find the sum of first n natural numbers by cut and

paste. Children will be asked to make a design through the

concept of arithmetic progression


to understand

different

sequences

to visualize

arithmetic

progression

to calculate the

nth term and

sum of n terms

of any given

A.P

CORE SKILLS

Application

Understanding Caring and sharing

ART INTEGRATION

To find the formula for the sum of

first ―n natural numbers. (Figure 2) To find the formula for the sum of

first ―n odd natural numbers.

Mathematical designs and patterns

using AP and integrating with art and

cuture of sikkim

INTERDISCIPLINARY

LINKAGE

Sequence and series

Arts and science

Computer programming

OCTOBER TO MARCH

7. COORDINATE GEOMETRY

Concepts of coordinate geometry

Distance formula. Section formula

( internal division).

The theory of finding the distance between two points, the

section formula and area of a triangle by using co-ordinate

geometry will be taught to the students with general co-ordinates

in the cartesian plane. Use of Cartesian plane will be explained

in derivation of each formula


to understand

different

questions in coordinate

geometry

to calculate

distances

between two

points

to calculate area

of a triangle

when the

coordinates of

the vertices are

given

CORE SKILLS

acquire subject learning

competencies

develop problem solving skills

boost their confidence in the

subject

widen their interest in the areas of mathematics

sustain self-directed and self-

motivated activities in mathematical

learning.

ART INTEGRATION

To mark coordinate axes on your city

map and find distances between

important landmarks-bus stand,

railway station, airport, hospital,

school, your house etc.

INTERDISCIPLINARY

LINKAGE

coordinate geometry helps us to

study geometry using algebra, and

understand algebra with the help of

geometry. Because of this,

Coordinate geometry is widely

applied in various fields such as

physics, engineering, navigation,

seismology and art.

10. CIRCLES

Tangents to a circle motivated by

chords drawn from points coming

closer and closer to the point. (Prove) The tangent at any point of a

cir cle is perpendicular to the radius

through the point of contact.

(Prove) The lengths of tangents

drawn from an external point to circle

are equal

Application questions

Students will be encouraged to draw tangents to a circle at a

point on the circle. They will be talked about the infinitely many

tangents that can be drawn to a circle since a circle is made up of infinite points. They will be well explained about the fact that

only two tangents can be drawn from an external point of a

circle. Problems based on tangent to a circle will be detailed to

the students by proper figures using smartboard.


to know the meaning of

tangent to a

circle

to know the

properties of

tangent from an

external point of

a circle

to understand

the application

questions

to improve the skill of drawing,

reasoning and select appropriate

method for solving

ART INTEGRATION

Tangents are equally inclined to the

line segment joining the centre with

the external point. 1. Cut out the two

triangles, ∆OPA and ∆OPB, so

formed [figure 3]. 2. Colour the two

triangles with different colours. 3.

Put one triangle on the other.

Observation: You will observe that

two triangles are congruent to each

other (i.e., one triangle exactly superimposes the other) with the

following (angle) correspondence.

INTERDISCIPLINARY

LINKAGE

Dance

Geography (Planetary system)

11. CONSTRUCTIONS

Division of a line segment in a given

ratio ( internally).

Tangent to a circle from a point

outside it.

Construction of a tr iangle similar to a

given tr iangle.

Teacher helps the students who have traditionally struggled with

mathematics construction. This will help them to build

confidence in their skills

. When students answer a problem incorrectly, does not allow

them to quit. Encourages students to figure out where they went

wrong and keeps working at the problem until they get the

correct answer, providing support and guidance wherever

needed.

To construct pair of tangents to a circle from an external point

and to construct similar triangle to a given triangle will be given

to the students as assignments


to construct

tangent to circle

from an external point

to construct

similar triangles

to another

triangle with the

given scale

factor

to divide a line

segment

internally in a

given ratio to justify a

geometrical

construction

through various

method

CORE SKILLS

It reinforces accurate measuring

constructing skills

Analytical thinking

concentration

Neatness and accuracy in drawing To read and understand the verbal

sum given to construct and draw

rough figures

ART INTEGRATION

Encourages students to construct

similar triangles and tangents on their

own

INTERDISCIPLINARY

LINKAGE

Arts Engineering

Building construction

12. AREA RELATED TO

CIRCLE

Area of a circle;

Area of sectors and segments of a

cir cle.

Problems based on areas and

perimeter/circumference of the

above-said plane figures.

calculating the area of a segment of a

cir cle

Gives assignments which have learning goals and gives students

ample opportunity to practice new skills.

Uses Vedic maths in calculation wherever possible

Finding area of different figures by constructing a figure with

combination of 2D figures will be explained in the class through

power point presentation


to understand

the concept of

sector area and

segment area

to know the

calculation of

area of different

sectors and

segments to visualize the

areas of shaded

portion

CORE SKILLS

Honesty

Application Understanding

knowledge

ART INTEGRATION

Design Parks

Mathematicians, whether they’re

engineers or architects or otherwise,

know the importance of

technology. We can find interactive

games where students can design a

park in the centre of town and find

the area of sector, segment etc

figure4

INTERDISCIPLINARY

LINKAGE

Science

Social studies

painting

13. SURFACE AREAS AND VOLUMES

Recapitulation of volume and surface area of

different solids Problems on finding surface areas and

volumes of combinations of any two

of the following: cubes, cuboids,

spheres hemispheres and r ight

cir cular cylinders/cones.

Frustum of a cone.

Problems involving converting one

type of metallic solid into another

and other mixed problems

Asks questions frequently to make sure students follow the concepts. Tries to engage the whole class, and does not allow a

few students to dominate the class. Keeps students motivated

with varied, lively approaches.

Converting 2D figure in to 3D figure (a sector of a circle to a

cone) and finding a formula for the curved surface area of the

cone will be explained.


to understand the previous

knowledge of

surface area and

volumes

to calculate the

problems

involving

converting of a

solid to another

solid

to know more about frustum of

a cone

CORE SKILLS

analysing and interpreting skill

problem solving skill computational skill

ART INTEGRATION

Converting 2D figure in to 3D figure

(a sector of a circle to a cone) and

finding a formula for the curved

surface area of the cone will be

explained.

The same will be given as an activity

figure5

To prepare 3-D decorative object from a 2-d circular disc.

INTERDISCIPLINARY

LINKAGE

Architecture

history

construction of infrastructure

15. PROBABILITY

Classical or theoret ical definition of

probability.

Simple problems on single events

The fundamental concept of probability will be explained with

diversities of examples from day to day life. Children are

explained about the sure events and the impossible events with

respect to the measure of likelihood of the occurrence of an

event. Random experiment, trial, sample space, event and

elementary event are well explained with lot of examples.

To appreciate that finding probability through experiment is

different from finding probability by calculation. Students

become sensitive towards the fact that if they increase the

number of observations, probability found through experiment approaches the calculated probability


to understand

equally likely

event

the probabilities

of all possible

outcomes add

up to 1

about sure event and impossible

event

the probability

of an event lies

between 0 and 1

CORE SKILLS

Critical analysis

enhance children’s ability to think

and reason

, to visualize and handle abstractions

to formulate and solve problems

ART INTEGRATION

The student work individually or at

most in groups by performing the basic experiments like tossing of

coins, throwing a die etc.

INTERDISCIPLINARY

LINKAGE

Weather forecasting in geography

Exit polls in election (political

science)

Sports

Figure2

THE SUM OF FIRST n TERMS OF AN A. P

Aim : To verify that the sum of first n natural numbers is n (n + 1) / 2, i.e. Σ n = n (n + 1) / 2, by graphical method.

Material Required : Coloured paper, squared paper, sketch pen ,ruler

Procedure: Let us consider the sum of natural numbers say from 1 to 10, i.e. 1 + 2 + 3 + … + 9 + 10. Here n = 10 and n + 1 = 11. 1. Take a squared paper of size 10 × 11 squares and paste it

on a chart paper. 2. On the left side vertical line, mark the squares by 1, 2, 3, … 10 and on the horizontal line, mark the squares by 1, 2, 3 …. 11. 3.

With the help of sketch pen, shade rectangles of length equal to 1 cm, 2 cm, …, 10cm and of 1 cm width each.

Figure3

figure4

Figure5

Sikkim

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APRIL TO SEPTEMBER 10/Maths_Class_10.pdfExplains the method of finding zeroes of a given polynomial....

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