Mental Maths Methods

Comparison of Mental Math Methods from Across the Globe.

How to use ChisanbopKorean Finger Mathfor Basic Addition & Counting “Chi” = Finger in Korean“sanpŏp (sanbeop)” = Calculation

History• Created in 1940s by Sung Jin Pai in Korea but probably has ancient roots.• Revised and Brought to the US around 1977 by his son Hang Young Pai• With this method it is possible to display all numbers from 0 to 99 with both hands.

The TechniqueWhile it seems strange at first, and takes some getting used to, the technique is easy, fun, accurate, and can be faster than using a calculator.

The Basics : Numbers 0 – 9 Right Hand 0

The Basics : Numbers 10 – 90 Left Hand

Addition1+3 Add 3 right fingers Start at 1 gives 4.

Addition To do that we tuck3+2 Then add 1 right finger. in our 4 fingers and replace them We still need to add 1 with right thumb to more. show 5.Start at 3

Addition62 + 21 Add 2 Left Hand Fingers and 1 RightStart at 62 Hand finger to give 83

Carryover Addition Concept of Complements come into place here.3+9 When adding 9,Easier to Add 10 and Subtract 1.

Carryover Addition 63 + 28 Concept ofComplements come into place here.When adding 28,Easierto Add 30 and Subtract 2. You can also add in Parts. 63+20+10-2

Scope of Chisanbop• Kids Can pick up Finger Counting And Basic Skills of Addition and Subtraction.• Children love something which is very tactile, something which can be seen hence gets popular with the kids.

Limitations of Chisanbop• Can perform Calculations only involving units and tens places.• Limited Applications in Multiplication & Division• You could think of a typical Japanese Soroban or Abacus as a means of doing Chisanbop with 13 hands instead of 2, allowing calculations into the trillions!

The Chinese Abacus Also known as Soroban in Japan

History• Earliest References dates back to 2nd Century BC.•Chinese Abacus known as “Suan Pan” which meansCounting Tray.•Use of the Abacus spread to Korea, and then to Japanduring the latter part of the 15th century•Russians invented their own Abacus and called it theSchoty during the 17th Century.•Very efficient abacus techniques have been developedto do multiplication, division, addition, subtraction,square root and cube root operations at high speed.

The Soroban Style of abacus •13 Vertical Rods on which beads move up and down. •Dividing upper and lower is a beam also known as the reckoning bar.

• Works from Left to Right. It allows us to solve mathematical problems with great agility and speed, in part, because numbers are added and subtracted in exactly the same way we read and hear them.

Basic Additions

Additions : Complementary Calculations 4 + 8 = 12 = 4 -2 +10 = 12

Basic subtractions

Subtractions : Complementary Calculations11 – 7 = 11- 10 +3 = 4

Multiplication Example: 34 x 7 = 238 Fig 1: Let H Be the Unit Rod. Fig 2: Multiply 4 x 7 = 28, Set on GH3 rods on the left , place Multiplicand 343 rods again on the left place Multiplier 7

MultiplicationExample: 34 x 7 = 238 Fig 3: Next Multiply 7 x 3 = 21 Add to FG You get your answer on FGH = 238.

Scope of the AbacusVery efficient abacus techniques are there to domultiplication, division, addition, subtraction, square rootand cube root operations at high speed.Calculations involving decimals can be achieved on anAbacus.Develops mental calculation, which is the ultimate resourceManifests the concept of decimalplaces and the progression ofunits by tens physically.Helps develop an intuitiveunderstanding of numbers throughtheir concrete representation.

LimitationsCalculation sometimes tends to get complex resulting in highdrop out rates by children in higher levels of the AbacusTraining Module.Concepts of Algebra, Trigonometry, Calculus is not possible todo with the help of an Abacus.

• The Kumon System immensely popular in South East Asia and the US• Based on individual learning and advancement by going through repeated practice sheets.

• Founded by Dr Hideo Sakamoto in Osaka, Japan in 1975.• Only System to teach Arithmetic & Problem Solving by drawing and other unique mental methods.• Simple yet systematic and structured technique to analyze questions in a logical way and solve the questions without any difficulty.• Approved by Ministry of Education, Singapore, in 1997, Sakamoto Maths classes have been conducted in some Asian countries like, Singapore, Thailand, Indonesia, Korea, Philippines and Malaysia.

Trachtenberg’s Speed System ofBasic Mathematics

History• Founded by a Russian Engineer named Jakow Trachtenberg born in June 1888.• He spoke out against Hitler’s fascism in Germany and was thrown into prison and later shipped to a concentration camp.• Around him was death and destruction but he kept his mind active by following the path of numbers without having pens or papers.• He invented a fool proof method to make it easier for a child to add thousands of numbers.• Devised shortcuts from Multiplication to Sq. Roots in 1940s.• In 1950s after his escape founded Mathematical Institute in Zurich.

What is the Trachtenberg System? What can it do for you? • Based on procedures radically different from conventional methods. • No Tables. No Division. • To know the system you should be only able to count. • System based on a series of keys which needs to be memorised. • After which the system becomes easy and friendly!

Speed Multiplication By Trachtenberg’s Method

Multiplication - The Direct Method23 x 14 =23 x 14 = 1223 x 14 = 12223 x 14 = 322

High Speed Column Addition By Trachtenberg’s Method

1256 Add Till 11 only 8563 Add in Shape of L 4658 2387 +Running Total Ticks

Scope• Educators have found out that this system shortens the time for computations by 20%• Has a Unique theory of checking by 9s and 11s gives an assurance of 99% Accuracy.• The ability to do basic arithmetic with the spectacular ease is what this system imparts and it erases the fear and timidity which hinder the student.

Limitations of the Trachtenberg System• Covers upto Basic Square Roots and not beyond.• Does not touch upon Factorization and other Algebraic Concepts which scare students.• Division and Square Roots not accurate results in decimals.• Does not cover Calculus, Trigonometry, etc

VedicMathematics Indian High Speed Mental Math System

Vedic Maths founded by Swami Sri Bharati Krishna Tirthaji Maharaja (1884-1960) Shankaracharyaof Govardhan Matha ,Puri

What is Vedic Mathematics?• Super Fast way of Mental Calculation• Far more systematic, simplified and unified than the conventional system.• Eradicates Math Phobia and creates an interest towards the subject.• Builds and strengthens Mental Math Concepts• System Based on 16 Sutras which are word formulae such as Vertically & Crosswise, All from 9 & Last from 10. etc.

Benefits of High Speed Vedic Math• Vedic Math is 10-15 times faster than Normal Math• Sharpens one’s mind, increases mental agility & intelligence.• Develops left & right side of the Brain• Easy to understand, Apply & Master.• Scientific Approach to Mathematics• Vedic Maths has a foolproof checking tool• Multiple Applications in Research inFields of Information Technology

CubesSanskrit Sutra: “Anurupyena” Anurupyena” Propotionately

(a + b)3 = a3 + a2b + ab2 + b3 2a2b + 2ab2 a3 + 3a2b + 3ab2 + b3 •Multiply by b/a Multiply •Double Double

Working out cubes 3=12

The Base MethodSanskrit Sutra: NikhilamNavatashcaram Dasatah

The Base MethodNumbers below 10 8–2 6–4 7–3 6–4 5/ 6 2/ 6 =3/6 1

The Base MethodNumbers below 100 100 89 – 11 98 – 02 97 – 3 97 – 3 86 / 33 95 / 06 89 – 11 89 – 11 78 / 21 = 79/21 1

The Base MethodNumbers above 10 12 + 2 13 + 3 13 + 3 18 + 8 15 / 6 21 / 4 = 234 2 Vedic Challenge! 103 + 03 104 + 4 107 / 12

The Base MethodNumbers Above the Base 123 + 23 102 + 02 103 + 3 103 + 3 126 / 69 105 / 06 1012 + 12 1003 + 3 1015 /036

Algebra 2x + 3 3x – 2 3x + 5 × x + 7 × 2 26x + 19x + 15 3x + 19x – 14 Also covers Factorization, HCF, Linear Equations, Simultaneous Equations, Quadratic Equations etc (Can show examples on Request)

Scope of Vedic Mathematics• Has Algebraically Proven Methods to speed up Basic Arithmetic, Algebra, Calculus and Trigonometry.• Also solves Astronomical Calculations easily like the Kepler’s Equation.• Has applications in Research and Development in fields of Information Technology to build Chips.• Basically Vedic Maths speeds up Calculations from Primary to High School Level.• Applications in Entrance Examinations like CAT, GMAT etc used extensively to cut on time.• Gaining Popularity so much so that the Americans Copyrighted the Vertically & Crosswise System in August 2009 and we are fighting a legal case to protect it.

Vedic Math Algorithms solve technology related issuesrelating to Chip Designing, RSA Encryption System, Elliptic Encryption System. Papers have been presented onthis by Research Scholars such as Himanshu Thapliyal at conferences organized byNASA, Intel, IEEE, SPIE etc.

Limitations• Many Mathematical Topics in Higher Math like Probability, Statistics, Game Theory, Geometry etc not covered.• It’s a supplement to the curriculum not a curriculum in its self.• Children would at least have to know counting and basic operations in Maths before learning Vedic Maths.• Invisible working: No Steps Involved since it is Mental which means Teachers cant give marks on Step Working.

Summary• Every Method has its scope and limitations.• We should be able to form a basket and mix and match and choose according to our needs at each level.

Q&ASession

thank you

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Mental Maths Methods

by gtekriwal on Dec 09, 2011

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