Vedic Activities in the Skills of Arithmetic - Shree Prakashan201… · Vedic Activities in the...

International Multidisciplinary e –Journal - E. Dhivyadeepa, (9205-9220)

www.shreeprakashan.com Vol-III, Issue-I, Jan -2014 Page - 9205

Vedic Activities in the Skills of Arithmetic

E. Dhivyadeepa,

Research Scholar,

Department of Education, Bharathiar University, Coimbatore, Tamil Nadu

Introduction

Although many teaching methodologies in the past were based on the assumption that

young students’ minds are like sponges, today many teachers have done away with traditional

lecture-style Mathematics class in favor of more innovative classroom teaching techniques.

Modern teachers understand the cognitive and psychological development of children and they

can use the knowledge to design more effective Mathematics courses. The best way for a student

to learn Mathematics depends on the best way that student learns. All people learn in different

ways. Addressing all the styles in the classroom by teaching Mathematics concepts with

innovative methods lead to better understanding of the concept. Vedic Mathematics is one among

the innovative methods in teaching of Mathematics at Primary level. Vedic math is entirely done

in mind. Vedic math also starts at a basic level of numbers and gradually progressing to simple

additions, subtractions, multiplications and division. Vedic math goes much more beyond just the

basic calculations. With Vedic math one can also solve complex geometrical theorems and

algebraic problems. Vedic math can be started at later ages as well without any difficulty. Some

Vedic methods used for doing problems in Addition, Subtraction, Multiplication and Division are

explained in detail in this article.

Introductory Activity

Vedic Mathematics is a new concept to the students. Some flash cards contain Vedic

Mathematical concepts were used to motivate the students to learn Vedic Mathematics.

International Multidisciplinary e-Journal ISSN 2277 - 4262

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Addition by Vedic Method

The main problem in solving Addition is transferring the carry number from one column

to another. To avoid this absurdity and to experiment in a unique way, Vedic method can be used.

Vedic method has a higher degree of accuracy and it is much faster than the traditional method.

There are several methods under Vedic Mathematics for Addition. Two methods in Vedic

Mathematics were used to teach Addition.

Method 1: Ekadhikena Purvena (One more than the previous one)

Addition by Ekadhikena purvena method can be summarized in the following steps/rules:

Step 1: Add the ones digit column wise.

Step 2: When the running total becomes greater than 10, put a dot to that number.

Step 3: Move ahead with the excess of ten and write the excess number under the ones digit

column.

Step 4: Lastly count the number of dots and place it down to the number next to the ones

place.

Step 5: Sum the two.

Activity 1: Addition: 3 6 + 4 9

Addition of 36 and 49 was explained by Ekadhikena purvena method in the Black board

by the investigator. A flash card for the clear understanding of the concept of adding is given

below.




Method 2: From left to right

Addition from left to right method can be summarized in the following steps/rules:

Step 1: Separate each column by bars.

Step 2: Add the numbers in one’s digit column.

Step 3: Write the number under the ones digit column.

Step 4: Add the numbers in tens digit column

Step 5: Write the number under the tens digit column. Continue from step 1 to step 3 for each

column.

Step 6: In the resultant row, add the tens digit in each column with ones digit in the previous

column.

Activity 2: Addition: 47 + 89

Addition of 47 and 89 was explained by left to right method in the Black board by the

investigator. A flash card for the clear understanding of the concept is given below.

Subtraction by Vedic Method

Subtraction is considered a difficult mathematical operation. The main problem in solving

Subtraction is borrowing number from one column to another column. Vedic method avoids

borrowing and carrying. It helps to solve problems in Subtraction in few seconds with greater

accuracy and speed.




There are several methods under Vedic Mathematics for Subtraction. Three methods in

Vedic Mathematics were used to teach Subtraction.

Method 1: Ekadhikena Purvena and Parama Mitra Method

This method is the combination of two sutras Ekadhikena Purvena and Parama Mitra. The

first sutra “Ekadhikena Purvena” means “One more than the previous one”. The second sutra

“Parama Mitra” means “Complementary”. Two digits are said to be complementary to each other

if their sum is 10. Subtraction by Ekadhikena purvena and Parama Mitra method can be

summarized in the following steps/rules:

Step 1: If any digit in minuend is greater than the subtrahend, subtract subtrahend from

minuend.


Step 3: If any digit in minuend is less than the subtrahend, subtract minuend from subtrahend.

Step 4: Simply find the complementary of that resultant digit and write it under the tens digit

column.

Step 5: Place a bar to the preceding digit of subtrahend. The bar over any number will make

that number richer by 1.

Step 6: Subtract subtrahend from minuend.

Step 7: Write the number under the hundreds digit column.

Activity 3: Subtract: 3 6 7 - 2 9 5

Subtraction of the number 295 from the number 367 was explained by Ekadhikena

Purvena and Parama Mitra method in the Black board by the investigator. The flash card for the

clear understanding of the concept is given below.




Method 2: From left to right

Addition from left to right method can be summarized in the following steps/rules:

Step 1: Separate each column by bars.

Step 2: Notice the hundreds column from left. Subtract the subtrahend from the minuend.

Step 3: Write the number under the hundreds column.

Step 4: Notice the tens column from left. If the minuend is greater than the subtrahend,

subtract the subtrahend from minuend.

Step 5: Write the number under the tens column.

Step 6: If the minuend is less than the subtrahend, place 1 on the top before the minuend.

There will be a two-digit minuend.

Step 7: And subtract 1 from the previous remainder column.

Step 8: Subtract the subtrahend from the two-digit minuend.

Step 9: Write the number under the ones column.

Activity 4: Subtract: 463-325

Subtracting 325 from 463 was explained by left to right method in the Black board by the

investigator. The flash card to the students for the clear understanding of the concept is given

below.




Method 3: Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10)

Subtracting a number from a base number (10, 100, 1000, etc) is easily solved by using

Nikhilam Navatashcaramam Dashatah sutra. Subtracting by Nikhilam Navatashcaramam

Dashatah method can be summarized in the following steps/rules:

Step 1: Subtract the ones digit of subtrahend by 10.


Step 3: Subtract the tens digit of subtrahend by 9.

Step 4: Write the number under the tens digit column.

Step 5: Subtract the hundreds digit of subtrahend by 9.

Step 6: Write the number under the hundreds digit column.

Activity 5: Subtract: 1000 – 345

Subtraction of the number 345 from the base number 1000 was explained by Nikhilam

Navatashcaramam Dashatah method in the Black board by the investigator. The flash card for the

clear understanding of the concept is given below.

Multiplication by Vedic Method

Multiplication is one of the most commonly used mathematical operations. The basic fact

of Multiplication is to add. In conventional method, unique pattern of Multiplication is being

followed for centuries.




The process of current Multiplication which is taught everywhere in the schools has many

disadvantage. In conventional method of learning Multiplication, the students have to memories

the table up to 10 and it does not allow any experimentation, whereas in Vedic Mathematics, the

students have to memories the table upto 5 alone. The best advantage of Vedic Multiplication

technique over the present-day method is that applying different sutras according to the category

it falls under. There are several methods under Vedic Mathematics for Multiplication. Two

methods in Vedic Mathematics were used to teach Multiplication for the students at standard IV.

Method 1: Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10)

The Nikhilam Navatashcaramam Dashatah sutra is used to multiply the numbers near to

base numbers (10, 100, 100, etc). Multiplication by Nikhilam Navatashcaramam Dashatah

method can be summarized in the following steps/rules:

Step 1: Write the two numbers to be multiplied above and below at the left side.

Step 2: Write the base of the two numbers. The base can be the power of 10 (10, 100, 1000,

etc).

Step 3: Subtract each number from the base and write the remainder with respective plus (+)

or minus (-) sign. Write the resultant numbers above and below at the right side.

Step 4: The product will have two parts. Draw a vertical line for demarcation.

Step 5: The left hand product is obtained by cross operation of two numbers written

diagonally.

Step 6: The right hand product is obtained by multiplying the two numbers at the right side.

Activity 6: Multiply: 7 x 9 (Multiplying number below base)

Multiplication of the numbers 7 and 9 was explained by Nikhilam Navatashcaramam

Dashatah method in the Black board by the investigator. The flash card for the clear

understanding of the concept is given below.




Activity 7: Multiply: 13 x 14 (Multiplying number above base)







Activity 8: Multiply: 8 x 14 (Multiplying numbers, when one number is below the base and

another is above the base)




Method 2: Urdhva Tiryagbyham (Vertically and Crosswise)

The Urdhva Tiryagbyham is a general sutra applicable to all cases of Multiplication.

Multiplication by Urdhva Tiryagbyham method can be summarized in the following steps/rules:

Step 1: Multiply vertically the numbers in the hundreds column.

Step 2: Sum the cross product of two figures.

Step 3: Multiply vertically the numbers in the ones column.

The following flash card was used to the better understanding of Urdhva Tiryagbyham

method.




Activity 9: Multiply: 56 X 81 (2-digit numbers)

Multiplication of the numbers 56 and 81 was explained by Urdhva Tiryagbyham method

in the Black board by the investigator. The flash card for the clear understanding of the concept is

given below.

Activity 10: Multiply 367 x 565 (Alternative way of Multiplication by Urdhva Tiryagbyham

sutra)

The Urdhva Tiryagbyham sutra can be used in different way in multiplying two numbers.

Multiplication of the numbers 367 and 565 was explained by Urdhva Tiryagbyham method in the




Black board by the investigator. The flash card for the clear understanding of the concept is given

below.

Division by Vedic Method

The main difficult part of Division is that a student has to multiply big numbers by the

quotient at every step and subtract that result from each dividend at each step. This is really a

boring process. Vedic Mathematics can be used to solve Division problems quickly and

accurately. The best advantage of Vedic Division technique over the present-day method is that

applying different sutras according to the category it falls under. There are several methods under

Vedic Mathematics for Division. Three methods in Vedic Mathematics were used to teach

Division for the students at standard IV.

Method 1: Anurupyena (Proportionately or halving and doubling) for dividing a number by

2, 4 and 8

The Anurupyena sub-sutra is used for dividing a number by 2, 4 and 8. Division by

Anurupyena method can be summarized in the following steps/rules:

Step 1: If the divisor is 2, split the dividend by vertical bars.

Step 2: If any number between bars is odd, carry 1 to the next column.

Step 3: Find half of each number between bars and write under each number.

Step 4: If the divisor is 4, repeat the step 2 and step 3 twice.




Step 5: If the divisor is 8, repeat the step 2 and step 3 thrice.

Anurupyena (Proportionately or halving and doubling) for dividing a number by 5, 25 and

50

The Anurupyena sub-sutra is used for dividing by 5, 25 and 50. Division by Anurupyena method

can be summarized in the following steps/rules:

Step 1: If the divisor is 5, double the dividend.

Step 2: Divide by 10.

Step 3: If the divisor is 25, double twice the dividend.


Step 5: If the divisor is 50, double the dividend.


Activity 11: Divide: 456 by 2, 4 and 8

Divide the number 456 by the divisors 2, 4 and 8 was explained by Anurupyena method in

the Black board by the investigator. The flash card for the clear understanding of the concept is

given below.




Activity 12: Divide: 600 by 5, 25 and 50

Divide the number 600 by the divisors 5, 25 and 50 was explained by Anurupyena method

in the Black board by the investigator. The flash card for the clear understanding of the concept is

given below.

Method 2: Special Division for dividing a number by 9

The special Division method is used for dividing a number by 9. Division by special

Division method can be summarized in the following steps/rules:

Step 1: Write the first digit of the dividend down as it is.

Step 2: Add the number with the second digit of the dividend diagonally to get the next

quotient digit.

Step 3: If the number is greater than or equal to 9, find how many 9’s are there in that

number and find the remainder.

Step 4: Add the number with the previous quotient digit and carry remainder to the next

digit of dividend.

Step 5: Continue the step till the last digit of the dividend.




Activity 13: Divide: 440 and 675 by 9

Divide the numbers 440 and 675 by the divisor 9 was explained by Anurupyena method in

the Black board by the investigator. The flash for the clear understanding of the concept is given

below.

Method 3: Dhwajanka (On the top of the flag) for straight Division

The Dhwajanka method is helpful in dividing any number comfortably. The main divisor

and the dividend may be of as many digits, depending upon the ability to perform the operation.

Division by Dhwajanka method can be summarized in the following steps/rules:

Step 1: Write the first digit of the divisor down and other digits on the top.

Step 2: Draw a vertical line from right leaving one digit at the end. If the first digit of the

dividend is greater than the first digit of the divisor, continue the step 4.

Step 3: If the first digit of the dividend is less than the first digit of the divisor, take first two

digit of the dividend and continue the step 4.

Step 4: Find how many times the divisor digit goes into dividend digit and write the quotient

down and the remainder near to next dividend digit.

Step 5: Multiply the divisor digit on the top with the quotient digit and subtract it from the

dividend digit.

Step 6: Continue the step 4 and step 5 till the last digit of the dividend.




Activity 14: Divide: 785 by 21

Divide the number 785 by 21 was explained by Dhwajanka method in the Black board by

the investigator. The flash card for the clear understanding of the concept is given below.

Conclusion

The above given vedic math activities are usual for the students at primary level. Practice

given on these activities makes the students perfect in doing Arithmetic calculation. To bring the

vedic mathematics to practice, first the teachers at primary school should be given training on

Vedic methods. Vedic math goes much more beyond just the basic calculations. With Vedic math

one can also solve complex geometrical theorems and algebraic problems. Vedic math can be

started at later ages as well without any difficulty.




References

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Collier, C., & Lerch, H.H. (1969). Teaching of Mathematics in Modern Elementary

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Mariappan, R., Vijaya, A.V., Marirajan, S., Dora, R., Md. Shafiullah Khan, M.J., &

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