Lesson Plan, Class XI Ch-14 | Mathematical Reasoning

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+1

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Board – CBSE	CLASS –XI	SUBJECT- MATHEMATICS
CHAPTER 14 : Mathematical Reasoning

TOPIC:- Chapter 14 : Mathematical Reasoning

DURATION:-  

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

PRE- REQUISITE KNOWLEDGE:-

Knowledge of simple mathematical concepts.

TEACHING AIDS:- 

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

METHODOLOGY:-   Lecture method  and Demonstration

OBJECTIVES:-

• Mathematical acceptable statement, difference between a sentence and statement. Negation of a statement, compound statement and their components.

• Special words/phrases, connectives ‘and’ , ‘or’ compound statement with and, compound statement with or, Inclusive ‘or’ exclusive ‘or’

• Quantifiers are the phrases like  like : “There exist” , “for all” , “for every” .

• Consolidating the understanding of  “If and only if (necessary and sufficient condition” “implies” , “and/or” , “Implied by” , “and” , “or”, “there exist” , and their use through  variety of examples related to real life and mathematics.

• Validation of the statement involving the connecting words.

• Explanation of contradiction, converse and contrapositive.

PROCEDURE :-

Start the session by asking the question related to the simple sentences of English and  discuss with the students whether it is true or false and the explain its importance with each result.  Now  introduce the topic Mathematical Reasoning  step by step as follows.

S. No.	Topic [For Complete Explanation Click Here]
1	Introduction and then explain the difference between a sentence and statement : Statement : A sentence is called a mathematical acceptable statement if it is true or false but not both. Explain this topic by giving counter examples. Exclamatory(!) sentences, order-able sentences, interrogative (?) sentences are never be the statement. Sentences involving time : today, tomorrow, and yesterday are never be the statement. Sentences which involves the terms  like : he, she, it, you, here, there etc. all are not be the sentences.
2	Explain the formation of negation of the statement from the given statement by using the words “It is not the case” or “ It is false that” or simply using not with the helping verb .
3	Explain the formation of compound statement by using the connecting words “and/or”. Also explain its component statements.
4	Explain the statement with “and” : A compound statement with “and” is true if all its component statements are true. A compound statement with ‘and’ is false if any of its compound statement is false. Note : Do not think that a statement with ‘and’ is always a compound statement. Example : A mixture of alcohol and water can be separated by chemical method. In this statement and is not act as connective and it is only a one statement.
5	Explain the statement with ‘or’ A compound statement with ‘or’ is true when one component statement is true or both the component statements are true. A compound statement with ‘or’ is false when both the component statements are false.
6	Inclusive ‘or’ : Example : A student who has taken Biology or Chemistry can apply for M.Sc. microbiology. In this statement ‘or’ is inclusive. Exclusive ‘or’ : Example : An ice-cream or pepsi is available with a thali in a restaurant. Here ‘or’ is exclusive.
7	Quantifiers : Quantifiers are the phrase like : “There exist” , “for all” , “for every” . Explain the use of these words in different examples.
8	Implications : Explain the use of implications like : ‘If-then’ ,      ‘only if ’ , ‘if and only if’ ,  in the different statements.
9	Contra-positive : It is the method of righting the reverse of a given statement with  negation. Converse : It is the method of writing the reverse of the statement. Method of contradiction : It is the method of proving the given statement by taking counter example.

EXPECTED OUTCOMES:-

After studying this lesson student should know 

• The difference between the sentence and statement 
• The connecting words ‘and/or’ quantifiers, Implications, contrapositive, converse and the method of contradiction. 
• Students should know the validity of the statement with ‘and/or’ inclusive ‘or’ and inclusive ‘or’.

STUDENTS DELIVERABLES:-

• Review questions given by the teacher. 
• 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.

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