### Fourth Intra School Mathematics Olympiad - RESULT

Dear All

The Fourth Intra School Mathematics Olympiad was held in CRPF Public School, Rohini on 8 November 2013.
Hopefully, it was a great learning experience for all. It surely provided an extended platform for all the participating students and it is wished that it is utilized to its fullest.
Here are many young Ramanujan’s and Shakuntala Devi’s in our school who had performed very well in the exam.
Check out the result here:
Congratulations to all the rank and merit holders for their brilliant performance in the  Olympiad.
You may again like to see the question papers and their solutions.

### Fourth Intra School Mathematics Olympiad

Dear All,

Mathematics, often called as language of nature has become an integral part of everyone’s life. In today's highly competitive world, one has to bear a lot of mental stress and also have to get involved in so many things in order to acquire knowledge. This is where co-scholastic activities play a very significant role. They provide the much needed exposure for a student.
CRPF Public School has fulfilled its motto of striving towards excellence by organizing and successfully completing its Fourth Intra School Mathematics Olympiad on 8rd November 2013. Around 250 students enthusiastically participated in the Olympiad held in school premises.
Such Olympiads and events provide a great and extended platform for the students to nurture and showcase their ability and talent. It was a towering learning experience for the students of the school from class V to XII. To encourage students, merit certificates will be given to those scoring at least 60% along with the normal prizes for the top scorers.
I hope that all the participating students must have done well in the exam. To access your performance, check out the solution keys of the question papers below:-

Question papers:-
Solutions keys:-

The result would be declared on 30th  November 2013 and would be available here on the blog.
Wishing you all the best!!!

### CONJECTURES IN MATHEMATICS

Dear All,

Generalization is a very important tool for obtaining new results in mathematics. We first experiments with numbers and geometrical shapes and observe some patterns emerging and then we make some conjectures on the basis of these observations. These conjectures do not get the status of theorems unless these can be deducted either from certain axioms or can be deduced from other results which have been earlier proved in mathematics.
Let us consider some examples of valid as well as invalid generalizations.
CONJECTURES BASED ON PRIME NUMBERS:

SOME MORE CONJECTURES:

Conjectures are obtained by generalizations but only those generalizations are valid which can be proved rigorously. We must continue to generalize, but we must generalize with care.
So, what did you conjecture today!
Note: I could not type mathematical symbols on the blog. So, I have attached images in this post. Click here to download pdf file for printing.

### Mathematics Movement Phase II - held at SDPS Pitam Pura

Dear All,

S.D. Public School, Pitam Pura in collaboration with NCSTC, Department of Science and Technology is organized “Mathematics Movement - (Phase II)” from 3rd to 5th October 2013. There were many interactive sessions for the teachers and the students. The main focus of the event was to enhance the student’s skills in various areas of Mathematics.
I had my sessions on all three days with class IX and X students.

@ Mathematics Movement held at SDPS Day 1:
An interdisciplinary activity relating mathematics with environment was taken. This activity was planned by Mr. Ajay Marwah (HOD – Math’s) from SDPS.
The calculations were based on rough estimation.
While preparing myself for this activity, I came across another area where mathematics is used. It's about various paper sizes like A4, A3 etc. Some interesting results are here. I will be doing a project soon on this topic with my students.

@ Mathematics Movement held at SDPS Day 2:
An activity based on counting without counting was taken. Students took actively part and interest in it and enjoyed beauty of mathematics.

@ Mathematics Movement held at SDPS Day 3:
On day 3, I took session on the theme “Thought Provoking Mathematical Problems”.
If anyone is interested to check solutions, he/she can email to me at amitbajajcrpf@gmail.com

I am thankful to Mrs. Anita Sharma, Principal SDPS Pitam Pura for having trust in me and giving an opportunity to interact with the kids. I am also thankful to my Principal Sir Sh. H. R. Sharma for allowing me to attend this mega event. My sincere thanks to Mrs. Rashmi Kathuria, a Math's teacher from Kulachi Hansraj School, Ashok Vihar who is a true passionate math's teacher I have ever met.

It was a great teaching and learning experience.

### Problem Posing in Mathematics

Dear All,

A famous quote about Isidor Isaac Rabi (born American physicist and Nobel laureate recognized in 1944 for his discovery of nuclear magnetic resonance )
“My mother made me a scientist without ever intending to. Every other Jewish mother in Brooklyn would ask her child after school: So? Did you learn anything today? But not my mother. She would say, "Did you ask a good question today?" That difference--asking good questions--made me become a scientist.”
We all are aware that Problem Solving is the focus of learning and teaching of Mathematics. However the problems have to be exciting, non-routine and challenging. In order to get thrill and excitement in Mathematics, students and teachers have to be trained not only in problem solving, but also in Problem Posing in Mathematics. Posing problems in Mathematics is not as difficult as it may appear, if students can learn some techniques for posing problems.
As suggested by late Prof. J. N. Kapur, some techniques for posing problems are as follows:
(i)                Generalising of known results
(ii)             Extending known results
(iii)           Adding or removing some of the conditions of the theorem and seeing whether the same result or a modified result continues to hold under the modified conditions.
(iv)           Combining different known results to get a new result.
(v)              Finding whether the converse of a result is true.
(vi)           Finding new proofs of known results or solving problems by alternative methods.
Here are some examples:
Problems posed by attempts to generalise or extend known results:
(1)  Known Result: The roots of quadratic equations.
Problems Posed:
(i)                Can we get similar expressions for the roots of third degree, fourth degree or higher degree equations?
(ii)             Can we say how many roots will an nth degree equation have?
(iii)           Can we find all the roots numerically or graphically?

(2)   Known Result: We can in general construct a triangle if three elements of the triangle, including length of one side, are known.
Problems Posed:
(i)                Can we construct a quadrilateral if the lengths of the four sides are given or if any four elements out of the lengths of four sides, lengths of two diagonals, the magnitudes of four angles are given?
(i)               Do  we require more than 4 elements for constructing a unique quadrilateral?
(ii)             Similarly for a pentagon, how many elements should be given?

(3)  Known Result: The sum of squares and cubes of the first n natural numbers.
Problems Posed:
(i)                Can we find the sum of rth powers of the first n natural numbers where r = 4, 5, 6, …

(4)  Known Result: Given two positive numbers a and b, we can find their HCF (h) and LCM (l).
Problems Posed:
(i)                Given h and l, can we find a and b?
(ii)             Given h and a, we can find l and b?
(iii)           Given any two of a, b, h, l, can we find the other two?

(5)  Known Result: The area of the square on the hypotenuse of a right-angled triangle is equal to sum of the areas on the two sides of the right-angled triangle.
Problems Posed:
(i)                Will the same result hold if we construct semicircles or similar triangles or equilateral triangles or regular hexagons on the three sides?
(ii)             For what other shapes will the same result hold?

Posing new problems via Inverse Problems:
(1)  Known Result: For a given value of x the value of sin x, cos x, tan x are known.
Problems Posed:
(i)                Given the value of sin x or cos x or tan x, find the value of x. (This solution is not unique and this led to the development of theory of inverse trigonometric functions.

(2)   Known Result: Given a function f(x), find its derivative.
Problems Posed:
(i)                Given the derivative, find the function of which it is the derivative. (Obviously there will be infinitely many answers are possible).

These are only sample problems provided. One may now begin to think of similar and other such problems to arouse curiosity in Mathematics. We may not know all the answers to the problems posed by us or others. But it is certain in search of answers there will surely be a great deal of learning.
It is said that “Focus on the journey, not the destination. Joy is found not in finishing an activity but in doing it”.
Do give your reflections, ideas, suggestions in comment section.

### Mathematics Movement (Phase II) at S. D. Public School, Pitam Pura

Dear All,
S. D. Public School, Pitam Pura in collaboration with NCSTC, Department of Science and Technology is organizing Mathematics Movement (Phase II) from 3rd to 5th October 2013. There will be many sessions for the teachers and the students. The main focus of the event will be enhancing student’s skills in various areas of Mathematics.
The following students from our school will be attending these three day programme.
1.      Sarthak Jain              V Class
2.      Nihit Bhatia               V Class
3.      Shivansh Dogra        VI Class
4.      Nikhil Dahiya           VI Class
5.      Vaibhav Gupta         VII Class
6.      Snigdha Jain            VIII Class
7.      Lakshay Grover        IX Class
8.      Rishabh Trehan        X Class
Two teachers Mrs. Shipla Gupta and Mrs. Sandhya Talwar will also attend this programme.
I hope that there will be a great mathematical learning for all of them.

Amit Sir

### Open-Day session at CIC, Delhi University

Dear All,

I am pleased to share that Cluster Innovation Centre; University of Delhi organized an Open-Day session on 18 September 2013 to interact with School Principals, Mathematics Teachers/ Academic Heads to focus on the issues and concerns in School Mathematics Education and how to bring into university academia and research community together to address these issues in more tangible and concrete ways.

I joined the forum as a panelist. The panel discussion addressed the critical issues in school mathematics education.
The session was presided by the Honourable Vice Chancellor of University of Delhi,  Prof. Dinesh Singh.

All the Photographs of the session can be viewed here.

Here is the presentation used by me on the topic- What Successful Math‘s Teachers must do!

### Class XII First Term Exam(2013-14) Mathematics - SOLUTIONS

Dear class XII Students,
Hope you all must have done your maths paper well. Here is the Question Paper.
Please check out the Solutions here
(Right click the above link and choose the option "Save link/target as")
ALL THE BEST