Lesson Plan Maths Class X (Ch-5) | Arithmetic Progression

LESSON PLAN, math. CLASS-10
Ch-04, Quadratic Equations

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Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	X	CHAPTERS	05	SUBJECT	MATHEMATICS
TOPIC	ARITHMATIC PROGRESSION			DURATION : 15 CLASS MEETINGS

PRE- REQUISITE KNOWLEDGE:-

Knowledge of number system, Simple methods of calculating the numbers.

TEACHING AIDS:-

Green Board, Chalk, Duster, Charts, smart board, laptop, projector etc.

METHODOLOGY:-

Lecture method, Demonstration method , Learning by doing, and Scaffolding method of teaching.

LEARNING OBJECTIVES:

Knowledge of sequence and series.

Motivation for studying Arithmetic Progression (AP).

Derivation of nth term of an AP.

Derivation of the formula to find the nth term from the end of the sequence.

Derivation of sum to n terms of an AP.

Application of the formulas of AP to solve the daily life problems.

LEARNING OUTCOMES:
After studying this lesson students should know
Sequence, Series and Arithmetic Progression.
All formulas and all important concepts related to the Arithmetic progression.
Students should be able to find the nth term of the AP from the starting and from the end of the sequences.
Students should also be able to find the sum to n terms of the AP from the starting and from the end of the sequences.

RESOURCES
NCERT Text book of Mathematics
NCERT Exemplar Text Book
RESOURCE CENTRE at cbsemathematics.com
DAV Resource Material for class 10

KEY WORDS :
Sequence, series, progression, nth term of an AP, Sum to n terms of an AP, Arithmetic Progression (AP), Terms of an AP, First Term (a) , Common Difference (d) , Consecutive Terms, General Term, nth Term, Last Term (l) , Number of Terms (n), nth Term from the End

CONTENT & PRESENTATION
Difference between sequence and series
General Arithmatic Progression and its components.
General term of an AP.
Sum to n terms in an AP when first term and common difference are given.
Sum to n terrms of an AP when first term and last terms are given.
Formula of finding nth term from the end of the sequence.
Formula of finding sum to n terms from the end of the sequence.

LEARNING ACTIVITIES:
INTRODUCTORY ACTIVITY :
EXPERIENTIAL ACTIVITY
ART INTEGRATED ACTIVITY

PROCEDURE

COMPLETE EXPLANATION

Start the session by checking their previous knowledge, by asking the questions of number system like natural number, whole number, odd numbers, even numbers and multiples of seven, five etc. After this explain the topic to the students.

Introduction :
Start the session by explaining the terms sequence and series.
Sequence
If different terms are separated by commas then it is called sequence
Example : 2, 5, 7, 9, 11, 12, …..
Series :
If different terms are separated by “+” or “-“ then it is called series.
Example : 2 + 5 + 7 + 9 + 11 + 12 + ….
Arithmetic Progression:
Now teacher will introduce the concept of Arithmetic Progression(AP), to the students. Teacher may write few sequences on the board and explain the difference between the A.P. and the other sequences.
General or n^th Term of an AP
Now teacher will write general A.P. on the board and explain its term and common difference.
a, a + d, a + 2d, a + 3d, …….. a + (n - 1)d
With the help of these terms find the formula for general term of an A.P.
a_n or t_n = a + (n - 1)d
Where :
a is the first term,
n is the number of terms
d is the common difference.
Teacher will also help the students in the implementation of this formula in different problems.
General Term from the end of the AP sequence
Now teacher will explain the method of finding the general terms of an AP from the end of the sequence. The formula derived is given below
a_n or t_n = l - (n-1)d
Where:
l is the last term of the sequence
n is the number of terms
d is the common difference
Students should be given sufficient number of problems for practice and implementation of the formula.
Sum to n terms of an AP
Now teacher will introduce the formula for finding sum to n terms of an AP and explain its components and the derivation.
$\mathbf{S_{n}=\frac{n}{2}\left [ 2a+(n-1)d \right ]}$
$\mathbf{S_{n}=\frac{n}{2}\left [ a+l \right ]}$
Where :

a is the first term
n is the number of terms
d is the common difference
l is the last term

Teacher will assign sufficient number of problems to the students for practice.
Sum to n terms from the end of an AP
Now teacher will introduce the formula for finding sum to n terms from the end of an AP and explain its components and the derivation.
$\mathbf{S_{n}=\frac{n}{2}\left [ 2l-(n-1)d \right ]}$
Where: l is the last term of the sequence.
Teacher will assign some problems based on the implementation of this formula.
Taking 3, 4, 5 terms in AP
Teacher will also provide the knowledge to the students, of taking three, four and five terms in an AP.
Three terms in an AP can be taken as
a - d, a, a + d
Four terms in an AP can be taken as
a - 3d, a - d, a + d, a + 3d
Five terms in an AP can be taken as
a - 2d, a - d, a, a + d, a + 2d
Applications:
Now teacher will assign some word problems based on our daily life situations and help the students in the implementations of the above formulas in these problems.

MIND MAP ACTIVITIES

STUDENTS DELIVERABLES:-

Review questions given by the teacher.

Students should prepare the presentation on the derivation of the formula for finding the nth term of the sequence and the formula for finding the sum to n terms from the starting and end of the sequence.

Solve N.C.E.R.T. problems with examples.

Solve assignment on Multiple Choice Questions (MCQ) given by the teacher.

EXTENDED LEARNING:-

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at cbsemathematics.com

SKILLS ENHANCED
Observation skill, analytical skill, critical & creative thinking, team work, constructive approach, interpersonal skill, engagement in learning process etc.
ASSESSMENT TECHNIQUES:

Assignment sheet will be given as home work at the end of the topic.
Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.
Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.
Puzzle
Quiz
Misconception check
Peer check
Students discussion
Competency Based Assessment link: M C Q

FEEDBACK:
All those students who performed well will be appreciated positively, and all those who can not perform up to the mark will again be given some important tips, guidance and positive motivation to go through the topic again and then re-evaluated again.
If possible then provision of remedial classes can be made for batter results.

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