Lesson Plan Math Class XI Ch-6 | Permutations & Combinations

LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+1

Lesson plan for maths class XI  Permutations and combinations, cbse lesson plans for mathematics teachers,  lesson plan for maths class XI, lesson plan for maths teacher in B.Ed.

Rmb dav centnary public school Nawanshahr
NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+1	CHAPTER	06	SUBJECT	MATHEMATICS
TOPIC	PERMUTATIONS & COMBINATIONS			DURATION : 20 CLASS MEETINGS

TOPIC:- 

Chapter 6 : Permutations and Combinations

DURATION:-  

This chapter is divided into 9 modules and is completed in 10 class meetings.

PRE- REQUISITE KNOWLEDGE:-

General Knowledge of mathematical concepts

TEACHING AIDS:- 

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

METHODOLOGY:-   Lecture method  and Demonstration.

LEARNING OBJECTIVES:-

• Fundamental Principal of Counting.

• Factorial Notations.

• Permutations and derivation of formula 

• Combinations and derivation of formula 

• Simple applications based on Permutations and Combinations.

EXPECTED OUTCOMES:-

After studying the chapter Permutations and Combinations, students will be able to: 

• Understand the meaning of factorial notation and use it in calculations. 

• Differentiate between permutation and combination. 

• Apply the fundamental principle of counting in various situations. 

• Calculate the number of arrangements using permutations: 

• when all objects are different, 

• when some objects are repeated, and in circular arrangements. 

• Solve problems based on: arrangement of letters, arrangement of numbers, seating arrangements, and selection of objects. 

• Identify situations where order matters (permutation) and where order does not matter (combination). 

RESOURCES

• NCERT Text Book,

• NCERT Exemplar Book of mathematics,

RESOURCE MATERIAL : 

Worksheets , E-content, Basics and formulas from  (cbsemathematics.com)

KEY WORDS

Permutation Keywords

Arrangement, Selection with arrangement, Factorial Notation, Linear arrangement, Circular arrangement, Repetition allowed, Without repetition, Distinct objects, Repeated objects, Position / Places, Rank, Formation of numbers / words.

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Combination Keywords,

Selection, Order does not matter, Choosing objects, Grouping, Committee formation, Team selection, Subsets, Without arrangement, Selection without repetition, Choosing representatives, Distribution into groups

PROCEDURE :-

Start the session by giving little introduction about the arrangements of the objects and its types.  Now introduce the topic Permutation and combination step by step as follows.

TOPICS

[For complete explanation Click Here]

Fundamental Principal of Counting :  

If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is  m x n.
This principal can be generalized for any finite number of terms.

If an event can occur in m different ways, following which another event can occur in n different ways, following which another event can occur in p different ways, and so on.  Then the total number of occurrence of the events in the given order is  m x n x p…………..

Factorial Notation :  

The product of n natural numbers is denoted by  n! and read as  n factorial

i.e. n! = 1 . 2 . 3 . 4 ……… (n - 2)(n - 1) n  or

n! = n(n - 1)(n - 2) …… 3 . 2 . 1

Permutations: 

A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.

Permutations when all the objects are distinct.

The number of permutations of n different objects taken r at a time is  
Now explain the derivation of formula:
 
Number of permutations of n different objects taken r at a time, where repetition is allowed is  n^r.

Number of permutations of n objects, where p are of the same kind and rest are all different is given by        

Permutations when all the objects are not distinct:

The number of permutations of n objects, where P₁ objects are of one kind, P₂ objects are of second kind ……….. P_k are of k^th kind and rest if any are different is given by: 
 
The number of combinations of n different objects taken r at a time is given by : 

• Permutation → Position important

• Combination → Choice important

STUDENTS DELIVERABLES:-

• Review questions given by the teacher. 

• Students should prepare the presentation individually or in groups on the basic concepts and formulas based on the topic permutation and combinations.  

• Solve NCERT problems with examples.

EXTENDED LEARNING:-

Students can extend their learning in   through the Resource Centre Mathematics . Students can also find many interesting topics on mathematics at the site:   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.

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

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