Sunday, February 10, 2008

Napier Multiplication strips.

The well known Scottish Mathematician, John Napier prepared a device around 1617, which was used to multiply. He called these strips as "Bones". In this article we are going to explain you how to prepare and use it in your class room teaching.

Material Required :

1. A big sheet of thin cardboard

2. White papers

Steps of Construction:

1. Paste the white board on the sheet of cardboard.

2. Cut nearly 50 strips of size 20 cm x 2 cm from the cardboard.

3. Mark the line to divide the strips into 10 squares of side 2 cm.

4. Mark the diagonals of the each of the squares on every strips as shown in the below figure.

5. Writedown the tables of the numbers from 0 to 9 as shown in the figure.

6. Prepare at least 5 strips for each table.


Suppose you want to multiply 7859786 x 4


1. Arrange the table strips in the order of the digits of the multiplicant (7859786) as shown in the figure.

2. Select the 4th row (since multiplier is 4).

(In the ascending order of the place value.)

3. Add the numbers diagonally from right to left, incase, you get sum as two digit number in any diagonal then carry its 10 digit to the next diagonal.


It can be used as teaching aids for class room teaching as well as Maths Laboratory.

Saturday, February 2, 2008


Mathematics is a Great Subject because of it the development of the world arrived as it is today. The Great Mathematicians contributed the greatest wealth for the society and we all are benefiting the luxirous life today. It is the time to remember them right now. Here I have given some of the Great Mathematicians who contributed Mathematics treasures for us with their creativity by their thesis, research and written plenty of great books. This list is not end only beginning.
1. EUCLID: (About 365 BC):
A famous Greek Mathematician first developed geometry in an order. It is called Euclidean Geometry. He wrote a famous book “The Element” which consists of 13 parts.

2. PLATO: (429-348 BC):
A Greek mathematician who lived in Athens. He explained the relation between mathematics and Philosophy.

3. PYTHAGORAS: (580-500 BC):
A Greek mathematician. He explained the relation between the sides of a right angled triangle. According to PYTHAGORAS THEOREM “The Square on the hypotenuse of a right angled triangle is equal to sum of the squares on the other two sides”. He developed the mathematical ideas in a logical way.

4. THALES: (640-546 BC):
A Greek mathematician. He was the first man who initiated and formulated the theoretical study of geometry to make astronomy a more exact science.

5. DIOPHANTUS (3rd Century A.D):
A Greek mathematician is known as the Father of Algebra. He was the first to use symbols to represents an algebraic problem.

6. FRANCOIS VIETE (1540-1603):
A French mathematician He found modern Algebra. He used the Vowels a,e,i,o,u and the consonants b,c,d,f,g to represent unknown numbers.

7. JOHN NAPIER (1550-1617):
A Scottish mathematician. He invented logarithms.

8. RENE DESCARTES (1596-1650):
A French mathematician. He showed that with a pair of intersecting straight lines, an algebraic equation can be represented as a geometrical shape. In his honor, this system of intersecting straight lines is called the system of “Cartesian Co-Ordinates”, with the vertical line known as the Y-axis, the horizontal line known as the X-axis. He is the founder of Analytical Geometry. Descartes linked Algebra with Geometry. This link which we call Analytical Geometry today totally changed the face of Mathematics.

9. PIERRE DE FERMAT (1601-1665):
A French mathematician. He is considered along with Pascal as the founder of probability theory. As the co-inventor of Analytical Geometry he is considered along with Descartes, as one of the first modern Mathematicians. He introduced a theorem in elementary number theory.

10. BLAISE PASCAL (1623-1662):
A French mathematician. He and Fermat founded probability theory. He invented and constructed first calculating machine which is used in gear wheel. His discoverer that the sum of interior angles of a triangle is always 180degree. Pascal’s triangle is famous for Binomial Coefficients.

11. LEIBNITZ (1646-1716):
A German mathematician. He formulated the basic ideas of Differential calculus He introduced the Binary system in 1679. He found the value of “pie”.

12. CHRISTIAN GOLDBACH (1690-1764):
He was from Russia. He conjectured (Unproved) that “every even number (except 2) is equal to the sum of two Prime numbers.”

13. HISEOG KAGRABGE (1736-1813):
A French mathematician. He contributed especially to the calculus of variations, analytical mechanics and astronomy. He introduced a method to solve the equations called Lagrange’s multipliers.

14. CARL FEDRIC GAUSS (1777-1855):
A German mathematician. He introduced the converse theorem of fundamental theorem of Algebra. Usually considered along with Archimedes and Newton to be one of the three greatest mathematicians of all times. He is known as Prince of Mathematicians and according to him Mathematics is considered to be the Queen of all sciences.

15. NIELS HENRIK ABEL (1802-1829):
He is a Norwegian mathematician. He made fundamental contributions to the theories of infinite series, transcendental functions, groups and elliptic functions. In his honor, the group which satisfies the commutative law is called Abelian group.

16. GEORGE BOOLEE (1815-1864):
A British mathematician. He worked as a high teacher. He worked in algebra, calculus of variations and probability theory. He introduced Boolean algebra of elementary logical properties of statements.

17. LOBACHEVSKI (1793-1856):
A Russian mathematician. He published first system on non Euclidean Geometry. He invented a theorem on “twin prime numbers”.

18. GEORGE CANTOR (1845-1918):
A German mathematician. He was the first to develop the “Set Theory” and stress its importance in Mathematics.

19. KEPLER JOHANN (1571-1630):
German mathematician and Astronomer. His laws, known as “Kepler’s laws of planetary motion” were determined empirically, based on over twenty years of ingenious and laborious calculations. He explained the conditions in the construction of telescope and the uses of lenses etc.,

20. ERATOSTHENES (276-194B.C):
He was a Greek astronomer, Geographer and mathematician. 2000 years ago he found a method of measure the perimeter of the earth. He found a method called “Sieve of Eratosthenes” to find prime numbers.

21. LEONHARD EULER (1707-1783):
He was Swiss mathematician. To find prime numbers he found a formula “if n <>

22. JOHN VENN (1D834-1923):
He was an English mathematician. He first used simple closed figures to represent Sets. These figures were also used by Leonhard Euler. So these closed figures are called Venn Euler diagrams, simply Venn diagrams.

23. ARTHUR CAYLAY (1821-1895):
He was an English mathematician. He introduced Matrices, Conations (non associative, non commutative).

24. J.J.SYLVESTER (1814-1897):
He was an English mathematician. He gave the name matrix to a rectangular arrangement of numbers (in rows and columns).

Friday, February 1, 2008

Super Power Memory


Memory is a faculty pertaining to the brain. There is nothing like good memory and bad memory. There is only trained memory and untrained memory.

Brain is the STORE HOUSE of memory. Memory is one of the vital building blocks of intelligence. Without memory there would be no learning, no recall, no communication. Every second of the day, our memory is busy processing images from the world around us and storing them in the appropriate portion of our brain’s data banks.

Memory is a process of 3 R’s

R1 - Record
R2 - Retain
R3 - Recall

Left brain Right brain

Conscious mind
Unconscious mind
Logic Rhythm
Reasoning Memory
Calculations Symbols
Reading vision
Writing imagination
Language Dreams
Analysis Synthesis
Ego Emotions
Linear Lateral
Thinking Thinking


NOTE: Our brain (1.4Kg weight in adult) contains over 10 thousand million nerve cells.

MEMORY TRAINING: Just like our body, our memory capacity stays fit only if we exercise it regularly. The proper development of our mental abilities requires the full use of our intellect. The brain uses about 20% of the body’s oxygen requirements, soit clearly needs to be in top form. A healthy lifestyle and a balanced diet will go a long way towards keeping the mind young and supple.


In certain subjects like arithmetic, the memory sometimes becomes lazy and lethargic through lack of practice. And a calculator is so very useful because of the dependency on it more and more frequently. The four basic operations of arithmetic are always retained in our memory, but we need to appeal to this memory more insistently.

With a good practice of four basic operations by using our new techniques help to overcome the mental fatigue.

1,536 + 541 = ?
18,659 + 3,876 = ?
59,246 + 66,666 + 8,756 = ?
589 – 821 = ?
5,896 – 4,172 = ?
147 X 654 = ?
5,891 x 258 = ?
47,985 x 4,658 = ?
583 / 52 = ?
4,627 / 111 = ?
31,772 / 325 = ?

The brain understands only and only language of pictures. The corpus collosum acts as a link between left brain and right brain. The data from left brain enters right brain obly through corpus collosum and vice versa.
The brain accepts unusual, illogical and ridiculous things easily other than logical things Your true memory will help you only if you aid with techniques.


The memory techniques help us to develop memory which in turn is useful in our classroom studies.

It is strongly believed that NOTHING IS IMPOSSIBLE in this world and the POWER OF THE BRAIN IS THE ULTIMATE! One cannot imagine how powerful it is! We have to try to utilize maximum brain power capacities by practicing dirrent ways.

Thursday, January 31, 2008

Make the Maths that Kids would Love


Mathematics is called the “Queen of all science”. Despite of the vast potential, students start getting “Math Phobia” at an early stage of education. What is the reason? Is it the biased opinion perpetuated by the parents? Is there something wrong with the curriculum? Are our mathematics teachers to blame? Unfortunately our education planners though aware of this, are showing little to remedy the situation. In any case, mathematics teachers have a great role to play. An innovative method is always appreciated by the students and leaves long lasting impression on the young mind. The technological developments have opened a host of possibilities to enhance teaching.

This is a modest beginning to bring mathematics teachers, mathematics experts and mathematics educators to a common platform for the exchange of ideas and innovations, with a hope that this will provided the teachers with new ideas and tools to impart knowledge in a more interesting and effective manner.

We would like to take this opportunity to express our sincere gratitude to all those who have made this event possible:

We have planned “math expo” which consists of an exhibition of posters, models, and books on mathematics. The other component of the Expo is the book exhibition. We also thank the publishers and booksellers participating in the book exhibition.

Enabling mathematics learning through a technology integrated mathematics laboratory

This presentation focuses on enabling the teaching and learning of mathematics through a mathematics laboratory. In the mathematics laboratory the learning by discovery approach is practised where the teacher acts as a facilitator guiding the student in the discovery of results and important mathematical ideal .
Here carefully designed projects and activities are conducted to help students appreciate the beauty and relevance of mathematics. The laboratory approach focuses on implementing innovative teaching methods, which emphasize on concept formation rather than acquiring by-hand skills.

The mathematics laboratory is a part of the curriculum offered by the school to students from classes 6 to 12. In the lab, students are made to explore and visualize concepts using various technologies such as computer algebra systems, graphics calculators etc. the author describes the various activities of the center, which also serves as a resource and training center for teachers of schools across the country. The presentation highlights some of the pioneering effort made by the mathematics technology center in integrating technology with traditional mathematics teaching.

Recent research in student attitudes towards mathematics in school curricula have been very disturbing….students shy away from science and mathematics. The reasons attributed to this trend are many viz.,
(i) lack of motivated teachers,
(ii) problems and applications divorced from real life and
(iii) assignments that do no excite the normal child.
Further, many of the problems in the school textbooks talk of loans and hypothecation rather than deposits and increased savings.

ICT could possibly complement the teacher in terms of providing the rural child an opportunity to explore the world and understand basic mathematics through interactive scenarios based on common day-to-day transactions. Keeping this in focus, a virtual market has been created. This has shops selling fruits and vegetables, clothes, books & stationary etc. A learner can access a particular section of the market and transact in one or more ways viz.,

(i) buying a particular quantity of a commodity, given its price
(ii) buying a list of commodities, given a certain amount of money
(iii) buying a larger spread of commodities, given a certain amount of money

The above transaction will teach the child
(i) the basic mathematical operations like addition & subtraction,
(ii) managing resources and
(iii) optimal use of given resources.
In each case, the student will be able to use trial and error methods and thereby realize the critical role of accurate and correct input data in each of the transactions. The application
Will have appropriate corrective messages and helps to guide the slow learner as well.

Wednesday, January 30, 2008

Play and Fun with Maths Models.

Learning Mathematics is a complex and tiredsome activity for the students. Where as Maths subject is an essential one to prosper in their career. Now a days mathematics also entered into the laboratory concept and arrived creative models. CBSE board also makes that the Mathematics laboratory and the projects are the compulsory for the academic. Setting up the Maths Laboratory and making Maths Projects are not as easy as Physics or Chemistry.

I have done excellent work in this field to make students learn mathematics with "Fun & Play" through my “Sharp Institute” I am conducting various Mathematics workshops and programmes by which I am training and guiding teachers and students in setting up Mathematics Laboratory and Projects.
Here are some of the basic directions for setting up the Mathematics Laboratory.
  1. What is a Mathematics Laboratory : Mathematics Laboratory is a place where students can learn and explore mathematical concepts and verify mathematical facts and theorems through a variety of activities using different materials. These activities may be carried out by the teacher or the students to explore, to learn, to stimulate interest and develop favorable attitude towards mathematics.
  2. Need and purpose of Mathematics Laboratory: Some of the ways in which a Mathematics Laboratory can contribute to the learning of the subject are:
    • It provides an opportunity to students to understand and internalize the basic mathematical
    concepts through concrete objects and situations.
    • It enables the students to verify or discover several geometrical properties and facts
    using models or by paper cutting and folding techniques.
    • It helps the students to build interest and confidence in learning the subject.
    • The laboratory provides opportunity to exhibit the relatedness of mathematical concepts
    with everyday life.
    • It provides greater scope for individual participation in the process of learning and
    becoming autonomous learners.
    • It provides scope for greater involvement of both the mind and the hand which facilates
    • The laboratory allows and encourages the students to think, discuss with each other
    and the teacher and assimilate the concepts in a more effective manner.
    • It enables the teacher to demonstrate, explain and reinforce abstract mathematical ideas
    by using concrete objects, models, charts, graphs, pictures, posters, etc.
  3. Design and general layout: A suggested design and general layout of laboratory which can accommodate about 32 students at a time is given here. The design is only a suggestion. The schools may change the design and general layout to suit their own requirements.
  4. Physical infrastructure and materials: It is envisaged that every school will have a Mathematics Laboratory with a general design and layout as indicated with suitable change, if desired, to meet its own requirements. The minimum materials required to be kept in the laboratory may include furniture, all essential equipment, raw materials and other necessary things to carry out the activities included in the document effectively. The quantity of different materials may vary from one school to another depending upon the size of the group.
  5. Human Resources : It is desirable that a person with minimum qualification of graduation (with mathematics as one of the subjects) and professional qualification of Bachelor in Education be made incharge of the Mathematics Laboratory. He/she is expected to have special skills and interest to carry out practical work in the subject. The concerned mathematics teacher will accompany the class to the laboratory and the two will jointly conduct the desired activities. A laboratory attendant or laboratory assistant with suitable qualification and desired knowledge in the subject can be an added advantage.
  6. Time Allocation for activities : It is desirable that about 15% - 20% of the total available time for mathematics be devoted to activities. Proper allocation of periods for laboratory activities may be made in the time table. The total available time may be divided judiciously between theory classes and practical