Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

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


E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10

lesson plan for maths class X chapter 5 Arithmetic Progression(AP), lesson plans for mathematics teachers,  Method to write lesson plan for maths class 10, lesson plan for maths class X, lesson plan for mathematics grade X, lesson plan for maths teacher in B.Ed.

Board - CBSE

CLASS –X

SUBJECT- MATHEMATICS

CHAPTER 5  :- Arithmetic Progression


TOPIC:-
Chapter 5 :  Arithmetic Progression (AP)

DURATION:-  
This chapter is divided into seven modules and it is completed in fifteen 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:- 
Demonstration and Lecture method.

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.
PROCEDURE :-
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.

S.No.

TOPICS

[FOR COMPLETE EXPLANATION OF THE TOPIC]

1

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 + …..

2

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.

3

General or nth 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.

an or tn = 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.           

4

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

an  or  tn = 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.

5

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.

 


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.

6

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.

Where: l is the last term of the sequence.

Teacher will assign some problems based on the implementation of this formula.

7

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

8

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.


EXPECTED 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.
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

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.


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