Lesson Plan Math Class 10 (Ch-1) | Real Numbers

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10

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TEACHER  :   DINESH KUMAR	SCHOOL :  RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR
SUBJECT   :   MATHEMATICS	CLASS                  :   X  STANDARD BOARD                 :  CBSE
LESSON TOPIC / TITLE   :  CHAPTER 1: REAL NUMBERS	ESTIMATED DURATION:  This lesson is divided into seven modules and it is completed in seven class meetings.

PRE- REQUISITE KNOWLEDGE:-

Number system of class IX

 Method of finding H.C.F. and L.C.M. of class VI and VII

Ability to factorize the numbers (Divisibility Test)

TEACHING AIDS:- 

Green Board, Chalk,  Duster, Charts, Models, Worksheet, Assignments etc

TECNOLOGY REQUIRED

Smart Board, Projector, Laptop, Internet

METHODOLOGY:-  

Demonstration, Learning by doing and Lecture method

LEARNING 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.

LEARNING OUTCOMES

 After studying this lesson, students will be able to explain the 

i) Euclid's Division Algorithm (EDA) and HCF by EDA,

ii) Fundamental Theorem of Arithmetic (FTA),

iii)  HCF, LCM by FTA,

iv)  Students should know the method of proving the given number is an irrational number. 

v) Students will be able to explain that given number is an irrational number, terminating decimal and non terminating but repeating decimals.

RESOURCES

NCERT Text book of Mathematics

NCERT Exemplar Text Book

RESOURCE CENTRE at cbsemathematics.com

DAV Resource Material for class 10

KEY WORDS :
HCF, LCM, GCD, Rational, Irrational, Euclid, Lemma, Algorithm, Terminating, Non-terminating etc.

(CONTENT & PRESENTATION)

• Euclid's Division Lemma and Algorithm (Deleted from CBSE)
• Fundamental theorem of Arithmetics
• Highest common factor (H.C.F.)
• Least common multiple (L.C.M.)
• Method of proving an irrational number
• Decimal Explanation of rational and irrational numbers.(Deleted from CBSE)

LEARNING ACTIVITIES:

INTRODUCTORY ACTIVITY

EXPERIENTIAL ACTIVITY

ART INTEGRATED ACTIVITY

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. 

PRESENTATION OF THE TOPIC 

[CLICK HERE FOR COMPLETE  EXPLANATION]

Introduction

First of all teacher give complete knowledge of number system to the students. Teacher will explain all the definitions of natural number, whole number, integers, rational numbers, irrational numbers and real numbers. 

Teacher will also explain the following: even number, odd number, prime number, composite number, co-prime number and twin prime numbers. For this teacher may complete family of number system through charts or diagrams.

Along with the number system teacher will also explain the Decimal System.

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

Now teacher will introduce the Definitions of Lemma, Algorithm, Euclid’s Division Lemma, and application of Euclid Division Algorithm in some word problems.

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]

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. 

For Example :   all are 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

"2" is the smallest prime number.

"2" is the only even prime number.

There are 10 prime number in a counting from 1 to 30

There are 25 prime numbers in a counting from 1 to 100

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)…….

Note: HCF of any two consecutive Natural Numbers is always 1. So any two consecutive natural numbers are always a pair of coprime.

10. TWIN PRIMES :- Consecutive prime numbers which are differ by 2 are called twin primes.     Eg :-  (11, 13),  (17, 19), (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, ........

13. COMPOSITE NUMBERS:- The numbers which has more than two factors are called composite numbers. Eg:- 4, 6, 9, 10, ....

"4" is the smallest composite number.

"9" is the smallest odd composite number

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.  

For Example  are irrational numbers.

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

This rule is not valid for more than two numbers.

MIND MAP 

STUDENTS DELIVERABLES:-

• Review questions given by the teacher. 
• Students can prepare a Presentation on the topic  “prove that given number is irrational number”. 
• Solve N.C.E.R.T. problems with examples, 
• Solve assignment of 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

Students can also extend their leaning by watching this topic on video.

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 , MCQ 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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