E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10

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Board - CBSE
CLASS –X
SUBJECT- MATHEMATICS
CHAPTER 1  :- NUMBER SYSTEM


Lesson Plan For CBSE  Class 10 (Chapter 1) For Mathematics Teacher
TOPIC :-   Chapter 1 Number System (Real Numbers)

DURATION:-   

This lesson is divided into seven modules and it is completed in seven class meetings.

Lesson Plan For CBSE  Class 10 (Chapter 1) For Mathematics Teacher
PRE- REQUISITE KNOWLEDGE:-

Number system of class IX

 Method of finding HCF and LCM of class VI and VII

Ability to factorize the numbers.

TEACHING AIDS:-  

Green Board, Chalk,  Duster, Charts, Smart Board, Projector, laptop  etc.

METHODOLOGY:-  

Demonstration and Lecture method


Lesson Plan For CBSE  Class 10 (Chapter 1) For Mathematics Teacher
OBJECTIVES:-
  • Definition of natural number, whole numbers, Integers, rational numbers, irrational numbers, Real numbers, odd numbers, even numbers, prime numbers, co-prime numbers, composite numbers.
  • Different types of decimals.
  • Rational and irrational decimals.
  • To find HCF by using EDA
  • To find HCF and LCM of numbers by using FTA.
  • Method of proving the given number as  irrational number.
  • Explanation of terminating and non terminating decimals.
https://dinesh51.blogspot.com


Lesson Plan For CBSE  Class 10 (Chapter 1) For Mathematics Teacher
PROCEDURE :- 

Begin the session by providing historical and biological details about Euclid. He was a great mathematician, who lived around 300 BC and was popularly known as Euclid of Alexandria. He was also known as the father of the geometry due to his significant contribution to the subject .He wrote treatise consisting of 13 books called elements.

No. of Periods            
Topic   
Explanation
1  
Introduction of number system, Definitions of all types of numbers with explanations.    


NUMBER SYSTEM - CBSE MATHEMATICS

1. NATURAL NUMBERS:- Counting numbers are called natural numbers.                                                                                            Eg:-  N =  {1,2,3,4,…………}
2. WHOLE NUMBERS – Natural numbers along with zero are called whole numbers.                                                                           Eg:-  W = {0,1,2,3,4,…….}  [N ⊂ W]
3. INTEGERS – All whole number and natural numbers with negative sign are called integers.                                          Eg :-  Z = {….-3, -2, -1, 0, 1, 2, 3…..}  [N ⊂ W ⊂ Z]
4. RATIONAL NUMBERS – The number which can be put in the form of P/q   (Where q ≠ 0) are called rational numbers.                       Eg :-  Q = -5, 0, 7, 3/5, -7/8 etc.  [N ⊂ W ⊂ Z ⊂ Q
NUMBER SYSTEM - CBSE MATHEMATICS

5. FRACTIONS – Positive rational number are called fractions.
  (OR)
Fraction is the ratio of two natural numbers. Eg:-  7/5, 1/2,  5/7 ….etc
6. IRRATIONAL NUMBERS – The number which cannot be put in the form of  p/q are called irrational numbers.
7. REAL NUMBERS – All rational  and irrational numbers are called real numbers.              R =  Q ∪ S
8. PRIME NUMBERS:- The numbers which has only two factors one and itself are called prime numbers.  eg  2, 3, 5, 7, 11, 13
NUMBER SYSTEM - CBSE MATHEMATICS

9. CO-PRIMES :- If H.C.F of two  numbers is 1 then numbers are called   co-prime numbers.                             Eg:- (5, 7), (13, 27), (15,16)…….

10. TWIN PRIMES :- Consecutive prime numbers which are differ by 2 are called twin primes.              Eg :-  (11,13),  (17,21), (29,31)…….etc

11. EVEN NUMBERS:- Natural numbers which are divisible by two are called even numbers. eg  2,4,6,8,10,..........

12. ODD NUMBERS:- Natural numbers which are not divisible by 2 are called odd numbers.
eg:- 1,3,5,7,9,........
NUMBER SYSTEM - CBSE MATHEMATICS

13. COMPOSITE NUMBERS:- The numbers which has more than two factors are called composite numbers.

Note:-  "1" is neither a prime number nor a composite number. It is a unit.
14. IMAGINARY NUMBER or Non-Real Number   :- Negative square root of a natural number is called Imaginary number Or  non-real numbers.  
Eg:−3,5,7....etc

NUMBER SYSTEM - CBSE MATHEMATICS
                               cbsemathematics.com
DECIMALS
Decimals are of three types
a. Terminating Decimal :-
 If prime factors of denominator of a rational number is either the power of 2 or 5 or both (2m x 5n )then the decimal form is known as terminating decimal.        Example: 2.5, 3.6,  7.895

 b. Non-Terminating But Repeating Decimal:- If prime factors of denominator of a rational number contain the factors other than power of 2 or 5 or both then the decimal form is called non terminating but repeating decimal. 
                     Eg :-   3.6767….            14.367367…....

c. Non-Terminating Non-Repeating Decimal :–
Decimalexpansionofthenumberslike3,5,7iscalled

non−terminatingnon−repeatingdecimals.
Eg:-  1.1010010001......,  2.5050050005......,  3.6060060006.......
NUMBER SYSTEM - CBSE MATHEMATICS

12. RATIONAL DECIMALS :-  
Terminating or non- terminating but repeating decimals are  called rational decimals. 

13. IRRATIONAL DECIMALS:-  
Non-terminating, Non-Repeating decimals are called Irrational decimals
https://dinesh51.blogspot.com NUMBER SYSTEM - CBSE MATHEMATICS
                     
EUCLID DIVISION LEMMA :–
 For given positive integers a and b there exist  unique integer q and r such that 
a = bq + r , where 0 is less than or equal to r <b. 
  Lemma – It is the proven statement used for proving another statement.
ALGORITHM – A series of well defined steps which gives a procedure for solving a type of problem.
 FUNDAMENTAL THEOREM OF ARITHMETIC – Every composite number can be expressed as a product of primes, and this factorization is unique irrespective of their order.                                                    
 HCF – Product of common factors with smallest power. 
 LCM – Product of all factors with greatest power.  
 When two numbers are given then      
 HCF x LCM   =  Product of two numbers














2
Different types of decimals, terminating decimals, non-terminating but repeating decimals, non-terminating non-repeating decimals, rational decimals and irrational decimals.

3
Definitions of Lemma, Algorithm, Euclid’s Division Lemma, and application of EDA in some word problems.

4
Method of finding the HCF by using Euclid’s Division Lemma on two numbers and on three numbers.

5 
Definitions of Fundamental Theorem of Arithmetic’s, LCM and HCF. Method of finding the HCF and LCM by using FTA and verification of the relation HCF X LCM = Product of two numbers.

6
Method of contradiction for proving that given number is an irrational number.

7
Method of finding rational and irrational decimals   without actual division and method of converting the given rational number into decimal form.


Lesson Plan For CBSE  Class 10 (Chapter 1) For Mathematics Teacher
EXPECTED OUTCOMES:-

 After studying this lesson, students will be able to explain the EDA, FTA, HCF, LCM. Students should know the method of proving the given number is an irrational number. They will be able to explain that given number is an irrational number, terminating decimal and non terminating but repeating decimals.

STUDENTS DELIVERABLES:-

 Review questions given by the teacher. Presentation on the topic  “prove that given number is irrational number”. Solve NCERT problems with examples, solve assignment given by the teacher.

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