Download Vedic Mathematics: E-DOCKET

Vedic Mathematics: E-DOCKET
Background
Vedic mathematics is an ancient form of understanding mathematics which enables the
students to understand the subject in a more holistic way, thus creating higher interest in the
subject.
Mathematics was simplified during the Vedic times by creating 16 ‘Sutras’ or word formula’s
which explained most of the concepts of mathematics. These sutras beautifully correlate and
unify different concepts, thus making us understand mathematics in a more holistic way.
th
These sutras were rediscovered in the early 20 century by Sri Bharati Krishna Tirthaji.
Research continues on using these sutras to create and develop applications on Geometry,
calculus, computing etc.
Thus, Vedic maths allows a student to master the concepts of mathematics in a simplified way.
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Important aspects of Vedic Mathematics
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Vedic Math is far more systematic, simplified, intuitive and unified than the
conventional system. It
lays emphasis on fast and simplified techniques to solve
complicated problems.
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Problems can be solved with high accuracy and speed
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Both the left and right side of the brain are used while solving problems in Vedic
 Maths. There is
improvement in mental ability, focus, sharpness, creativity and intelligence.
Teaches students alternative approaches to problem solving and provides
with a set of checking
procedures for independent crosschecking at the time of examinations.
It complements the Mathematics curriculum conventionally taught in schools
 by acting as a
powerful checking tool and goes to save precious time in examinations.
It reduces the burden
 of remembering large number tables because it requires you to learn
tables upto 9 only.
Vedic Math opens
 student’s mind and expands the possibilities when dealing with different
math problems.
In the Vedic system, the very first
step is to recognize the pattern of the problem and pick up the
most efficient Vedic technique.
Reduces dependence on calculators and therefore sharpens your quantitative bent of mind
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Vedic Maths is complementary to regular
Maths in schools, hence on learning Vedic Maths,
one can excel in mathematics at school
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It keeps the mind alert and lively because of the element of choice and flexibility.
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It can introduce creativity in intelligent and smart students, while helping the slowlearners grasp the basic concepts of mathematics. More and more use
of Vedic math
can generate interest in a subject that is generally dreaded by children.
Extremely beneficial specially to students who are sitting for entrance examinations
such as SAT, CAT, IIT (engineering entrance exam), ACT etc. Research has shown that
learning vedic techniques can help save about 10-12 minutes in entrance examinations.
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HOW IS VEDIC MATHEMATICS DIFFERENT THAN ABACUS
Difference between Vedic mathematics and abacus:
o Vedic Math is quite different from Abacus. Vedic mathematics simplifies mathematical
operations where one uses shorter & simpler techniques to solve large calculations.
Thus the focus can be on finding the right approach to the solution rather than the
calculation itself.
o Abacus on the other hand uses a system where one uses an abacus frame with beads
where calculations are done using visualization of beads in clusters. It is quite a different
method when compared with conventional math. Vedic mathematics uses numbers the
way they are used in the conventional math.
Magic of Vedic Mathematics
What is 8 x 9?
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In conventional math, one would simply rote it, but in Vedic math, a student can improvise
the answer just using bit of addition and subtraction. 
Write the difference between the number and the base (the base is 10 here) below each
number. You get 2 and 1. Write them below 8 and 9. 
8x9
2 1
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If the child can do this, he/she can get the answer readily and easily. To get the unit place,
multiply the differences written below 8 and 9 (2 and 1). 2 x 1 is 2. Write it as the unit place
of the answer. 
Now, to get the 10’s place digit, subtract any of the difference from the original number
crosswise (subtract either 1 from 8 or 2 from 9). This is the 10’s place digit of the answer. 
8 – 1 is 7.
So 8 x 9 = 72.
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VEDIC MATHEMATICS VS CONVENTIONAL METHOD
Few examples
a) Addition of big numbers : 1768 + 2829 + 957 + 9657 + 589
CONVENTIONAL
3
3
4
1
7
6
2
0
9
+
1 5
8
9
6
5
8
2
5
5
8
0
VEDIC
Lets see how the first column adds up
through vedic method
8
1
9
2
7
0*
7
9
0
9*
1
0*
5
7
8
9*
6*
5*
8
6
2*
5*
5*
8*
0
8
9
7
7
9
0
8+9 = 7,
where the 1 from
17 carries left ward
as a star next to 2
7+7 = 4
where the 1 from
14 carries left ward
as a star next to 5
4+7 = 1
where the 1 from
11 carries left ward
as a star next to 5
1+9 = 0
where the 1 from
10 carries left ward
as a star next to 8
n* = n+1
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Conventional method:
-
Has carry over
Requires addition of multiple digit numbers (in the above sum, in the ones place the
addition goes like 17+7=24+7=31+9=40, 4 carries over)
Need to remember big numbers while adding
Vedic method:
-
No carry over concept, n*=n+1
Requires addition of single digits always
Does not require remembering big numbers while adding
b) Multiplying Two Digit Numbers
CONVENTIONAL
VEDIC
1
1
2
4
6
1
1
6
*
+
1
1
4
2
8
0
8
*
1
4
2
8
Multiplication parts through the vedic approach
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c) Multiplying big numbers
CONVENTIONAL
VEDIC
1
*
1
1
+
3
4
6
7
4
1
2
1
2
1
3
8
2
2
2
2
5
6
0
0
6
4
7
8
0
0
8
3
*
5
6
1
4
3
4
1
3
7
12
10
0*3
2
2
5
14
20
2
6
4
7
28
Multiplicand
Multiplier
Parts of multiplication
8
Multiplication parts through Vedic approach
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In the above multiplication, the conventional method has atleast 5 steps more than the vedic
method.
Through vedic, more big numbers can be calculated faster than the conventional method
d) Cube root of perfect cube numbers with maximum six digits
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Group the given numbers into two parts such as the right part (RP) will consist of units,
tens and hundreds place digit and left part (LP) will have remaining digits.
Select a number whose cube is nearest less than or equal to LP.
Observe the unit place digit of RP and choose corresponding possible units place digits
of cube root
Find cube root of 1728
1
1
7
2
2
8
Answer
STEPS:
-
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Grouping: LP = 1 , RP – 728
3
1 = 1 is equal to 1
Units place digit of RP = 8 hence d = 2
Cube root of 1728 is 12
e) Finding Square Root of a number ending with 5
Conventional
Vedic
Number
2
(a5 )
Left part
a× (a+1)
f) Algebraic Computation
Multiplication parts through Vedic approach
g) Finding squares of Numbers Nearing 100
Conventional method
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Vedic
Right part
2
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THE COURSE STRUCTURE
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The course has been broken down into 9 levels. Please refer to the appendix for details
of the topics to be taught in each level. 
Grades
4&5
6
7&8
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Level Upto
3
6
9
No. of hours / Level
8 hrs
8 hrs
8 hrs
The following is the class wise break for the different levels
o Classes 4 & 5 : Can be taught till level 3 
o Class 6 : Can be taught till level 6 
o Classes 7 & 8: Can be taught all the 9 levels 
Every student needs to start from level 1 itself. 
The main book that we are going to be following is ‘Enjoy Vedic Mathematics’ by 
Shriram M Chauthaiwale & Dr Ramesh Kolluru. This is an Art of living book. 
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The book would be supplemented by worksheets in every session. Each level will end
with a test. 
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We would also be having group activities in every level. The group activities would
involve solving interesting problems, puzzles, games etc using different concepts of
vedic maths. 
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TEACHER PROFILE
Abhiyendra Kumar - IIT Delhi : M.Tech-Maths and Computing
Professor Abhiyendra Kumar holds a M.tech in integrated mathematics and computing from IIT
Delhi. He has been involved in Mathematical research at internships in Technical University
Vienna, Charles University , Prague and Technical University Eindhoven , Netherlands. His paper
on E learning, a tool for rural education in India was selected for presentation at the ‘Education
without borders’ conference , Abu Dhabi in 2005 as a student. He has worked as a Technical
Consultant with sun Microsystems , Delhi, a financial analyst at a startup in Mumbai, BI
consultant with Infosys , Chandigarh and Credit RIsk Analyst with mashreq bank over his 6 years
tenure in the corporate world.
He has been actively involved in teaching with NGOs in Chandigarh like Nanhe Kadam and
founded a Slum class at infosys CSR.
His passion for teaching persuaded him to be a full time teacher in maths and has interest in
developing key quantitative tools to make mathematics more interesting. His latest interest is
in the area of vedic mathematics and is active in propagating it in the UAE.
Alakananda Ghose – B.Sc (Statistics Hons.) MBA (Marketing)
Founder – Quest4educatioN
Alakananda is a major in statistics along with economics and mathematics. She pursued
management studies after that, her core being marketing and IT systems.
While studying MBA, she was selected to hold extra classes in statistics for her peers in the
campus. She started her career in marketing research in India and has experience in multiple
sectors in the corporate world. She started in Ipsos India and worked on cutting edge consumer
research tools to consult her clients in their business and consumer related projects. Her clients
included the largest multinational companies like Lafarge, Unilevers, ITC (a BAT company) and
the largest Indian corporate house, the TATA group of companies. She has also worked in UAE
and KSA in conglomerates like Al Futtaim and Synovate in marketing consulting across various
categories in key management positions for 8 years. Her interests lie in travelling, music,
reading and theatre.
Alakananda has been a winner in various inter-school maths olympiads and her latest interest
lies in vedic mathematics and wishes to promote and popularise the subject in the UAE. She is
currently involved in various assignments in this area with various schools across the UAE.
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APPENDIX - : Details of the different levels
Level 1 : Addition and Subtraction (Grades 4 - 8)
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Addition by shuddha method 
Subtraction by shuddha method 
Simultaneous addition and subtraction 
Single digit multiplier, 
Group activity 
Level 2: Multiplication (Grades 4 - 8)
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Two digit multiplier 
Three digit multiplier 
Four digit multiplier 
Decimal number multiplication 
Group activity 
Level 3: Multiplication special cases(Grades 4 - 8)
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Special Multiplication 
o When sum of units digits is 10 and other higher place digits are identical
o
Sum of numbers formed by tens and unit place digit is 100 and digits placed at hundreds
place are identical
o Sum of numbers formed by hundreds, tens and unit place digit is 1000 and digits placed
at thousands place are identical
o Multiplier is 9, 99 , 999 or 9999
o Multiplication by 11, 101 , 1001
o Group activity
Level 4: Mixed operation, multiplication and addition (Grades 6 - 8)
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Sum of products with single digit multiplier - e.g. (27 x 5) + (63 x 9) 
Sum of products with two digit multiplier - e.g. (306 x 24 ) + (517 x41) 
Sum of products with three and four digit multiplier - e.g. (2143 x 6450 ) + (781 x 854) 
Sum of products of decimal numbers 
Product of sum and differences e.g. 324 ( 2313 +725) -95 (532 +1082) 
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Level 5: Multiplication Special cases (Grades 6 - 8)
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Base multiplication –numbers near 10,100 ,1000 o
12 x 13 
o Near multiples of 10 e.g. 52 x 57 o
99 x 97 , 107 x 112 
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o 498 x 497 o
5994 x 5988 
Multiplication of numbers near to each other 
o 229 x 232
o 7353 x 7349
Squares 
o 2 , 3 ,4 digits
o Proportionality and duplex method
Group activity 
Level 6 : Square of numbers(Grades 6 - 8)
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Square of numbers ending with 5 
Squares of numbers near 50 , 500, 5000 
Sum of squares – e.g. 3241 ^2 + 4035 ^2 
Multiplication with squares of numbers 54^2 ( 312 + 98 -243 ) 
Proportionality method for cube of numbers 
Group activity 
Level 7: Cube of numbers (Grades 7 & 8 )
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Sum or difference of cubes – 65 ^3 + 27 ^3 
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Cube of numbers near 10,100 ,1000 – 991 ^3 o
95^3 + 104^3 
Product with cube of 2 digit numbers - e.g. 234 x 53 ^3 
Division with single digit divisor – e.g. 62965 / 5 , 67 / 4 = 16.75 
Division by 2 digit divisor , 547 /31, 4644 /54 
Division by 3 digit divisors - e.g. 1178490 / 489 
Group activity 
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Level 8: Division (Grades 7 & 8 )
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Division by four digit divisor – e.g. 6739 / 2246, 2501224 / 5288 
Division of sums 
o ( 27453 +19829 ) / 998
Division of products 
o ( 634 x 281 ) / 2361
o ( 6002 x 4125 ) / 8851
Division of sum of products 
o [ ( 125 x 204 ) + ( 752 x 84 ) ] / 514
Division of product of sums 
o [ 272 ( 1323 + 5027 ) ] / 278
Division of Squares and cubes 
2
2
2
o ( 46 + 34 - 23 ) / 432
3
o ( 53 ) / 2463
Group activity 
Level 9 : Square and Cube roots(Grades 7 & 8 )
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Square root of at most four digits perfect square numbers 
Square root of any number - 20439441 , 126.92 
Square root of sum or product 
o Square root of ( 2198 – 829 )
o Square root of 1152 x 288
Square root of sum of squares 
o Square root of 2175 ^2 + 2392 ^2
o Square root of 6722 ^2 – 3360 ^2
Cube root of numbers with at most six digits perfect cube numbers 
o Cube root of 592704
Group activity 
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