Think and Reflect

 

Look at the Picture and answer the following?

1. How can you make such pattern in Mathematics Lab?

2. What do you notice?

3. How would you describe, what you see here?

Problem 2 :- 

Here, 3 squares are seen overlapping each other.

What is the greatest number of squares you can make by overlapping three squares of the same size?

Happy Learning 

PI APPROXIMATION DAY (22/07) QUIZ

 Dear All

On the occasion of Pi Approximation Day being celebrated on 22nd July (22/7) every year, Here is one very interesting quiz dedicated to Pi. There are 40 questions related to Pi. Let's know the mysterious number pi. Don't forget to share with your known/students/teachers/

Just give a TRY

 The story of pi is more than 4000 years old but the race to find its value is still continued.

Interesting Facts:-

1.  

                                             (Courtesy:- From the Tweet of @Cliff Pickover)

2. 22nd July is the birthday of -- GAUSTAV HERTZ      ---- WILHELM BESSEL  and great Indian mathematician - SHREERAM SHANKAR ABHYANKAR 

3. 22nd July 2024 is the 204th day of the year.  204 is the sum of consecutive primes in two different ways: ---

a) sum of a twin prime (101 + 103) 

b) sum of six consecutive primes (23 + 29 + 31 + 37 + 41 + 43).

204 is the sum of squares of first eight consecutive natural numbers. 

204 = 1²+2²+3²+4²+5²+6²+7²+8².

                                                      A brief Introduction of Pi

Value of Pi = 22/7 is probably taken because Archimedes (born in 287 BC) calculated the ratio of circumference to diameter coming out to be lying between 223/71 and 22/7.

Aryabhata (born in 476AD) was the first Indian mathematician who calculated the value of pi correct up to 4 decimal places. His value of pi was 3.1416. 

The Mahabharta decodes the value of pi as 3.

योजनानां सहस्राणि विष्कम्भो द्वादशास्य वै ॥ 6-12-40
परिणाहेन षट्त्रिंशद्विपुलत्वेन चानघ ।
षष्टिमाहुः शतान्यस्य बुधाः पौराणिकास्तथा ॥ 6-12-41
चन्द्रमास्तु सहस्राणि राजन्नेकादश स्मृतः ।
विष्कम्भेण कुरुश्रेष्ठ त्रयस्त्रिंशत्तु मण्डलम् ॥ 6-12-42
एकोनषष्टिविष्कम्भं शीतरश्मेर्महात्मनः ॥ 6-12-43
सूर्यस्त्वष्टौ सहस्राणि द्वे चान्ये कुरुनन्दन।
विष्कम्भेण ततो राजन्मण्डलं त्रिंशता समम् ॥ 6-12-44
अष्टपञ्चाशतं राजन्विपुलत्वेन चानघ।
श्रूयते परमोदारः पतगोऽसौ विभावसुः ॥ 6-12-45
एतत्प्रमाणमर्कस्य निर्दिष्टमिह भारत ।

The Moon is handed down by memory to be eleven thousand yojanas in diameter. Its peripheral circle happens to be thirty three thousand yojanas when calculated.

The Sun is eight thousand yojanas and another two thousand yojanas in diameter. From that its peripheral circle comes to be equal to thirty thousand yojanas.

The Bible says -

Also he made a molten sea of ten cubits from brim to brim round in compass and five cubits the height thereof; and a line of thirty cubits and compass it round about.  --- Old Testament

William L Schoff says -

Probably no symbol in mathematics has evolved much mystery, romanticism, misconception and human interest as the number of pi.

      

          Buffon

Buffon calculated the value of pi using needle. Ancient Hebrews who built Solomon's temple used pi = 3 while Shatapatha Brahmin calculated the value of pi equals to 3.085.

In 1901, Italian mathematician Mario Lazzarini Performed the Buffon Needle experiment tossing a needle 3408 times, he obtained the approximation of pi which was a very accurate value. 

Archimedes in 3rd century inscribed and circumscribed regular polygons up to 96 sides and showed the upper limit is 22/7 and lower limit is 223/71.

           Pi  Day = March 14 (3/14)

Aryabhata calculated the value of pi correct  up to 4 decimal places and can be termed as the first mathematician to do so.

Add 4 to 100, multiply it by 8 and then add 62000. The result is approximately the circumference of a circle of diameter 20000.

Madhava, the founder of Kerala School of Mathematics also calculated the value of pi before James Gregory using the infinite series.

व्यासे वारिधिनिहते रूपहृते व्याससागराभिहते।

त्रिशरादिविषमसंख्यामत्तमृणं स्वं पृथक् क्रमात् कुर्यात् ॥

यत्संख्ययात्र हरणे कृते निवृत्ता हृतिस्तु जामितया।

                         तस्या उर्धगताया समसंख्या तद्दालं गुणोऽन्ते स्यात् \\

Ramanujan made several attempt and calculated the value of pi through numerous formula.

You can also calculate the value of pi using his formula.

Yale Bablonian Tablet known as YBC 7302 also approximates pi as 3.125 . . .

Interesting Facts About Pi:- 

At position 763 which is also known as Feynman Point, there are six nines in a row. 

Johann Lambert proved Pi is irrational in 1768.

I hope you have read the information shared here. It is the time to play quiz to explore your knowledge about pi. 

CLICK HERE FOR QUIZ

A certificate is attached with the quiz provided you score 75% marks so try your luck and win certificate.

Rajesh K Thakur

google.com, pub-5194588720185623, DIRECT, f08c47fec0942fa0 google.com, pub-5194588720185623, DIRECT, f08c47fec0942fa0

International Math Relay Competition

 

1st International Math Relay Competition 

In order to Celebrate Pi Approximation Day, which is celebrated every year on 22nd July (22/7), Competition Baba (A unit of Vishwaroop Foundation, Delhi) is organizing 1st International Math Relay Competition.

In order to get the prizes announced by the Managing Committee of Competition Baba, students have to go through two phases of exam. 

In the first phase there will be a Google Form Based Quiz and the selected students will be playing the Group activity in Mathematics, i.e. Mathematical Relay. 

A team of 3 (either from a school/ member chosen by the Competition Baba team) will play the final round on 22nd July.

1st Round:- A google form Based Test. The syllabus of the test for both Junior and Senior are Class 7 and Class 10 only. Though a balanced question based on 6-8 and 9 -12 has been added so that the students get fair chance to perform. 

Duration :- 60 minutes

2nd Round:- It is a group activities and will be performed by a team consisting of 3 students. A set of 9 questions will be given (3 to each) to be solved in 9 - 15 minutes as decided by the management. Suppose the three boys are P, Q and  R 

a) P will solve his first question and give the solution to Q 

b) Q will solve his question and share the solution of both P and Q to R 

c) R will solve his question, that will require the input value of P and Q

Look at the diagram below to understand the game. Here 1 , 2 and 3 are three students sitting back to back. 

Duration :- 10 -15 minutes

TEST LINK FOR JUNIOR CLASS 8

Test Link for Junior (7)

Test Link for Junior (6)

TEST LINK FOR CLASS 9

TEST LINK FOR CLASS 10

Test Link for Senior (12)

TEST LINK FOR SENIOR (11)

CLASSROOM TEST FOR D.EL.ED 2ND YEAR

 Dear Students

This is a test to understand how you prepare yourself after your class and how much time do you devote on your study at home.

This test is based on Unit -1 and Unit - 2. Moreover, 5 questions are based on Mathematical pedagogy.

Number of questions for each section will be different. There are 20 questions of 2 marks each. Every correct answer will give you +2 and every wrong answer will deduct your -1 mark.

Time allowed = 30 minutes

There are 3 numerical questions that may require pen and paper while the other questions are based on your mathematical understanding of the concept taught in the class -room.

CLICK HERE TO OPEN THE TEST

Question Making is an Art -- Dr Rajesh Thakur

 

Thank You

Dr Rajesh Kumar Thakur

Competency Based Learning - K Bhanumoorthy

 

Competency based teaching-learning:

A quote from CLAY P. BEDFORD:

“You can teach a student a lesson for a day; but if you can teach him to learn by curiosity, he will continue the learning process as long as he lives.”

Introduction:

The competency-based teaching is a new approach (an innovative) in teaching- learning process. The word competency means skills, efficient, rather to enhance the abilities, working strategies. First and foremost, the phobia in the subject say mathematics is to be removed, create interest in the subject, the reasons why to study mathematics to be mentioned. Students are three kinds, some are visual, some auditory, some are kinesthetic.

 Teaching methods to be cater to the needs of all kinds of students. Students progress is important, one has to work with vision and mission to see the students acquire skills to solve HOTS (High order thinking skills). The very important aspect how far the learning has taken place and to meet and answer the challenging questions. I would say at least, the minimum level of learning (MLL) should have taken place. In this aspect two people are involved, one teacher and the other the student. 

Of course, the involvement and encouragement of parents are essential. The environment to say HOME, has to be congenial for proper learning. In brief parents have to trust their wards at the same time watch them, guide them then and there, if they are in wrong path. We human beings are blessed with sensory organs. Eyes, ears, nose, tongue, skin. One has to make good use of them. In the class room, eyes and ears are used. 

One has to make best use of them. It’s a matter of pride and pleasure, how one sharpens his/her perception skills. I could make a suggestion. The competency-based teaching could be started right from middle classes (6 to higher secondary), so that there is gradual learning with more confidence and without any stress. It goes without saying teachers to be trained periodically to update their skills. (To adopt changes as and when required)    

Benefits by this approach:

1.      Students acquire skills, be aware of the knowledge acquired, where it is applied in our daily life, linkage with other subjects especially with science.  

2.      To attain proficiency and grip over the subject whatever study.

3.      There is conceptual learning and no rote learning.

4.      There are many methods. Generally, a class is heterogeneous, students are of different calibres. This method/approach is based on students centred.

5.      In the long run help students to write competitive exams, Olympiads, entrance exams ----. Shall definitely help and choose academic career of his/her choice.

Role of teachers:

1.      To train the students where to apply, what has been learnt, the knowledge.

2.      Nowadays collaborative learning is under practice, to be incorporated.

3.      Students are to be encouraged to participate in class room discussion and should not have fear to clarify doubts with teacher.

4.      To link the previous knowledge acquired to the new topic whatever is being taught, there by fear complex is removed/ vanished. There is horizontal as well as vertical integration of each subject. (Students do move from one class to next higher class.)

5.      To solve a question step by step, by involvement of students.

6.      Students are to be told what to study, how to study and why to study. There may be more than a section in a class, if necessary, the teachers have to change the approach depends on students’ calibre, understanding abilities.

7.      Students may be trained and be encouraged to solve, under open-ended approach, so to say solving using different methods using the given data.

8.      To give names of reference books for practice (as there will be some questions apart from the textbook). To refer the syllabus prescribed.

9.      To develop and make an impact, creating curiosity, creativity, thinking aspects (abstract, analytical, divergent, critical, logical----)

10.  To evaluate the progress of students periodically, students are to be guided and encouraged for setting their Goals in academic career.

(Suggestion: Teachers have to keep some time for students’ interaction -to say 10 minutes for interaction out of 45 minutes class duration)

To conclude, every individual is unique, hidden with lots of talents. We are fully aware that teachers are nation builders. I am sure teachers’ fraternity shall dig out and bring the hidden talents to the surface.

Note: There are many subjects to study. I am confined to mathematics teaching - learning aspects.

Learning is a treasure that will follow its owner everywhere---Chinese proverb.

--------------- be continued with questions on various topics of different classes.

 

 

Ramanujan Remembrance Day Quiz

Srinivasa Ramanujan (22 Dec 1887- 26 April 1920) , FRS was an Indian mathematician whose mammoth work in mathematics has created history.

The young generation should make him an ideal, who fought against all odd but never let his first love mathematics go from his mind.

My books on Srinivasa Ramanujan

He struggled to pass his FA twice, left his home, did odd job of tuition and finally got a job of clerk at Madras Port Trust before moving to England in 1914. 

During his stay at England, he was of poor health but that didn't hinder his progress. He together with Hardy wrote 50 research paper and got an FRS degree.

His notebook containing 3400 theorems were proved by Bruce Berndt.

Ramanujan's birthday is celebrated as National Maths Day in India since 2011. 

J B S Haldane once said -- If Ramanujan's work had been recognized in India as early as it was in England, he might not have emigrated and might have been alive today.

Here is a 250 marks quiz that shows you many picture related to Ramanujan and will help you to know Ramanujan in a better way.

                                 Click here to play the Quiz

Don't forget to share with your friends

Yours 

Dr Rajesh Kumar Thakur

Asst Prof

DIET Daryaganj