### Common Errors in Secondary Mathematics

Common Errors Committed  by the  Students  in Secondary Mathematics   Errors  that students often make in doing secondary mathematics  during their practice and during the examinations  and their remedial measures are well explained here stp by step.  Some Common Errors in Mathematics

### 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

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

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.

Euclid's Division Lemma:

For given two positive integers a and b there exist unique integers q and r such that a = bq + r ,    where  0 ≤ r < b

HCF by using Euclid Division Lemma

Explain the Method of finding the HCF by using Euclid’s Division Lemma with two numbers and with three numbers. Also apply this statement in some word problems.

Fundamental Theorem of Arithmetic's

Teacher will introduce F.T.A. as follows

• Definitions of Fundamental Theorem of Arithmetic’s,
• Definition of L.C.M and H.C.F.
• Method of finding the HCF and L.C.M. by using F.T.A. and verification of the relation

H.C.F. X L.C.M. = Product of two numbers.

• Method of finding HCF and LCM of more then two terms by using F.T.A.

Fundamental Theorem of Arithmetic:

Every composite number can be expressed as the product of primes and this factorization is unique irrespective of their order.

L.C.M:- Product of all factors with greatest power.

H.C.F:- Product of common factors with smallest power.

Teacher will explain the Method of contradiction to prove that given number is an irrational number.

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

Condition of denominator of a Rational Decimal: Denominator can be expressed in the form 2m x 5n

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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1. Very nicely written

2. This comment has been removed by a blog administrator.

3. 4. Very useful for me thank u so much . From Sukma chhattisgarh.

5. 6. Excellent lesson plan.

7. 8. Well defined and precisely covered all topics

9. very nice

10. Very Good..