The Trachtenberg Speed System of Basic Mathematics

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The Trachtenberg Speed System of Basic Mathematics is a revolutionary system for calculating and teaching basic math. Children, who had repeatedly failed in arithmetic until their parents sent them to learn this method, were able to perform amazing calculations within seconds. In one demonstration, a ten year old child, when asked to multiply 5132437201 times 452736502785, simply wrote on the blackboard the answer, 2323641669144374104785, in seventy seconds. He never set up the basic and familiar line by line chart, multiplying and adding each row of numbers. Instead, he just wrote down the answer without any of the intermediate steps. To demonstrate his method, Trachtenberg chose children who were doing poorly in their school work. These were children used to failure, shy and withdrawn; or at the other extreme, rebellious and unmanageable. The children's responses to the new, easy way of doing arithmetic was immediate. They found it delightfully like a game. The feeling of accomplishment soon made them lose their disagreeable traits. Equally important were the by-products the pupils attained while learning this new system. As these youngsters became proficient in handling numbers, they began to spurt ahead in all their studies. Their IQs went up as well! Not only did the child learn to compute, but his IQ also went up. Since all problems were worked out in his head, he developed an excellent memory and his ability to concentrate was increased. The Trachtenberg system, once learned, can take the drudgery out of the arithmetic that is part of everyone's daily stint. Experts believe that the Trachtenberg system could have far-reaching effects on education and science.

Author(s): Jakow Trachtenberg, Rudolph McShane, Ann Cutler, Sam Sloan
Publisher: Ishi Press
Year: 2011

Language: English
Commentary: OCR, Front and Back Covers, Bookmarks, Pagination
Pages: 272

Contents
Foreword
1: Tables Or No Tables?
Basic Multiplication
Multiplication by eleven
Multiplication by twelve
Multiplication by six
Multiplication by seven
Multiplication by five
Multiplication by eight and nine
Multiplication by four
Multiplication by other digits
Summary
2: Rapid Multiplication By The Direct Method
Short multiplicands: Two digits by two digits
Long multiplicands
Three-digit multipliers
Multipliers of any length
Summary
Checking the answer
3: Speed Multiplication - "Two-finger" Method
Multiplication by a single digit
Multiplication by two-digit numbers
Long number by two-digit multiplier
Three-digit multipliers
Summary
4: Addition And The Right Answer
Finding the total
Checking the answer
General method of checking
5: Division - Speed And Accuracy
The simple method of division
The fast method of division
The division process
The method in detail
Three-digit divisors
Divisors of any length
Checking the division
6: Squares And Square Roots
Introduction
Squaring
Three-digit numbers
Square roots
Seven-digit and eight-digit numbers
Longer numbers
Checking
7: Algebraic Description Of The Method
Numbers in general
The rule for eleven
Algebraic manipulation
The Trachtenberg system in algebra
Non-table multiplications in general
Squaring numbers
Multiplication by the units-and-tens method
Numbers of any length
8: Postscript