Your rating(Clear)Rate this item

- The Trachtenberg Speed System of Basic Mathematics
- ›
- Customer Reviews

Your rating(Clear)Rate this item

55 people found this helpful

ByPhillip Martinon 22 February 2006

The contents of this book should be printed on gold leaf!

A person found time to record this work whilst facing death.

A work that removes the shroud of mystery that covers a branch of mathematics that holds painful memories for many people.

Mental Maths.

Mathematicians manipulate numbers with ease; general members of the public or school kids don't.

This book shows worked examples of how to do various calculations easier and quicker than 'conventional' means.

Example.

23 x 11

2 is the 'first digit'

3 is the 'last digit'

2 + 3 is the 'middle digit'

So 23 x 11 = 253

Many more examples and information are presented, so that with practice the 'sums' can be done in your head.

It's maths without the tears.

A person found time to record this work whilst facing death.

A work that removes the shroud of mystery that covers a branch of mathematics that holds painful memories for many people.

Mental Maths.

Mathematicians manipulate numbers with ease; general members of the public or school kids don't.

This book shows worked examples of how to do various calculations easier and quicker than 'conventional' means.

Example.

23 x 11

2 is the 'first digit'

3 is the 'last digit'

2 + 3 is the 'middle digit'

So 23 x 11 = 253

Many more examples and information are presented, so that with practice the 'sums' can be done in your head.

It's maths without the tears.

ByC. L. Roeon 19 March 2014

OK - the simple examples are fun and easy to apply and offer as a party piece. But to do large numbers requires a huge amount of learning time. True it is about adding and small numbers to hold as carry overs - but is a complete misnomer to call it a 'speed system.' It is like saying once you learn a foreign language you will be able to speak it fluently - possible; but just like the Trachenberg system takes a huge amount of learning.

I bought the book because I was inspired to have learned the creator worked out the system whilst in prision. But I will stick to the maths I learned at school along wwith the shortcuts I acquired as I grew up.

I bought the book because I was inspired to have learned the creator worked out the system whilst in prision. But I will stick to the maths I learned at school along wwith the shortcuts I acquired as I grew up.

ByPhillip Martinon 22 February 2006

The contents of this book should be printed on gold leaf!

A person found time to record this work whilst facing death.

A work that removes the shroud of mystery that covers a branch of mathematics that holds painful memories for many people.

Mental Maths.

Mathematicians manipulate numbers with ease; general members of the public or school kids don't.

This book shows worked examples of how to do various calculations easier and quicker than 'conventional' means.

Example.

23 x 11

2 is the 'first digit'

3 is the 'last digit'

2 + 3 is the 'middle digit'

So 23 x 11 = 253

Many more examples and information are presented, so that with practice the 'sums' can be done in your head.

It's maths without the tears.

A person found time to record this work whilst facing death.

A work that removes the shroud of mystery that covers a branch of mathematics that holds painful memories for many people.

Mental Maths.

Mathematicians manipulate numbers with ease; general members of the public or school kids don't.

This book shows worked examples of how to do various calculations easier and quicker than 'conventional' means.

Example.

23 x 11

2 is the 'first digit'

3 is the 'last digit'

2 + 3 is the 'middle digit'

So 23 x 11 = 253

Many more examples and information are presented, so that with practice the 'sums' can be done in your head.

It's maths without the tears.

ByLeahGon 22 November 2005

I have an older edition of this book, and have ordered this edition for a friend. This is an incredible book, you can learn very simple techniques in minutes, that will amaze your friends and family with the speed and ease at which you can do math. You can write the answer down without any calculations as the work is done very simply in your head. This is a book I delve into from time to time, in an effort to really acquaint myself with the techniques. The only prior math’s knowledge you need is the ability to count to 10! Would revolutionise maths if we taught this in schools!

0Comment*|*
41 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByA customeron 8 January 2001

I originally read this book when I was 13 and I have remembered it ever since. When I started vocational teaching of disadvantaged adults I remembered it and bought a copy for my students. I was impressed with what my students achieved and the faculty was astounded.

11 comment*|*
29 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByMr. Dennis Addeyon 8 February 2000

I read this book 28 years ago in 1972. It was a wonderful insight into the world of arithmetic and maths. I still continue my Jakow inspired interest in things numerical. What a brilliant and resilient man.

0Comment*|*
19 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByP. Fogartyon 2 May 2010

When I first saw this book - I thought 'Oh no - another book on Maths!' - however it is a real gem of great ideas!

I sat and read through it, and thought 'Wow - there are so many simple tricks I did not know about!' - and as SATs is coming up, teaching my class how to check their answers is really important.

Another reviewer pointed out that you had to learn a lot of rules - this is true - but for my Year 3 class, they loved having to follow each of these rules and the fact that each rule progressively moved onto the next rule! They all tell me what a wonderful book I have!

Next year, I plan to start in the school a club which is designed to teach Primary School children all about the Trachtenberg Speed system, as if they learn it early enough, I am sure it will prove to be be of great value to them throughout their lives.

I cannot recommend this book enough to anyone who has a child struggling with maths.

I sat and read through it, and thought 'Wow - there are so many simple tricks I did not know about!' - and as SATs is coming up, teaching my class how to check their answers is really important.

Another reviewer pointed out that you had to learn a lot of rules - this is true - but for my Year 3 class, they loved having to follow each of these rules and the fact that each rule progressively moved onto the next rule! They all tell me what a wonderful book I have!

Next year, I plan to start in the school a club which is designed to teach Primary School children all about the Trachtenberg Speed system, as if they learn it early enough, I am sure it will prove to be be of great value to them throughout their lives.

I cannot recommend this book enough to anyone who has a child struggling with maths.

0Comment*|*
12 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByA customeron 1 September 2000

A good book for those who want better mental arithmetic skills. Whilst a large number of the basic techniques applied were discovered by mathematicians well before Trachtenburg was born (Euler and Cauchy come to mind), this is almost certainly the first time that the thinking was brought to bear on simple arithmetic in such a systematic fashion.

0Comment*|*
19 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByA customeron 1 October 2001

This book shows you a wonderful step by step method for improving mental calculations that you use everyday without realising. By learning the methods described your confidence in using mathematics will sky rocket. I cannot recommend this book highly enough.

0Comment*|*
19 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByA customeron 21 January 2000

I took a 30min lunch break and started this book. 30mins later I could multiply by 11 and 12 faster than most people can punch the numbers into a calculator. This is just the start of an amazing jouney..... if I had read this when I was a child who knows where I could be today !!

Thank you Jakow Trachtenberg, your genius lives on.

Thank you Jakow Trachtenberg, your genius lives on.

0Comment*|*
12 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByLeon Kowalskion 5 November 2009

I have found `Trachtenberg Speed system of basic Mathematics' an illuminating approach to basic maths. I am 39 yrs old. I have not needed a great deal of maths throughout my life and extensively used calculators or spreadsheets for when I did. After working through this book, I can do exactly what it claims a reader will be able to achieve; mental basic arithmetic involving multiplication, addition, division, squaring and square roots, along with being introduced to algebra once again. This last point is the main reason I have returned to maths at this point in my life.

The book is presented in a logical format, not always obvious until you have progressed to division.

The first part deals with multiplication, using numbers between 1 and 12. It [the book] claims that it is not required for the reader to know their tables. However, it states that knowledge of them is very useful.

To explain, the system demonstrates a method of multiplying single numbers by single numbers - the times tables. With this knowledge, all other calculations within the book can be completed. However, with a solid understanding of times tables, many calculations, such as squaring 2 digit numbers and multiplication of up to 4 digits by numbers between 1 and 12, can be completed in less than 10 seconds, in your head, once the system is fully understood.

The multiplication sequence to learn is broken down into groups;

a. 11 & 12

b. 5,6 & 7

c. 8 & 9 (I suggest learning 9x before 8x)

d. 4 & 3

The reason for this is that each group uses extensions of a given method, such as:

a. Multiplication by 11:

11 x 45 = first digit + right hand digit= 5 + 0 = 5

Next digit + right hand digit = 4 + 5 = 9

Next digit + right hand digit = 0 + 4 = 4

Answer: 495

b. Multiplication by 12:

12 x 45 = first digit x 2 + right hand digit = 5 x 2=10 + 0 = 10 which is 0 carry 1

Next digit x 2 + right hand digit + carry = 4x2=8 + 5+carry(1)= 14 which is 4 carry 1

Next digit x 2 + right hand digit + carry = 0x2=0 + 4+ carry(1)= 5 which is 5

Answer: 540

A fictitious zero is used to facilitate the method at either end of the number to be multiplied so that the number would resemble 045.0 for calculation purposes.

I hope my examples illustrate the point that both 11x & 12x use a system that takes the first digit and adds it to the digit immediately to its right to find each digit of the answer in turn. However, the method for multoiplying by 12 also doubles the digit before it adds the neighbour (right hand digit), which is an extension to the method of multiplying by 11. It is not my intent to reproduce any part of the book, nor demonstrate rigorously any method taught. My example is to illustrate that the methods are broken into groups, as each group method is a successive extension of the last within that group.

One point I should like to mention at this point is that the methods for multiplying any given number by 4 and by 3 are the most complex of all the methods given. As such, it is quicker to mentally multiply each digit from right to left, writing down the product as you go. The methods for 3 & 4 are given for completeness but are slower than the conventional method of multiplication. Likewise, the method for multiplying by 1 & 2 are also given for completeness.

After basic multiplication, the multiplication of larger numbers is taught. This is a single, simple method for multiplication of any number by any number. It is at the end of this chapter that I found my first surprise - how to quickly and accurately check the sum of any calculation without having to re-calculate the sum. The logic is very easy to pick up and became instantly and constantly used by me once I had learnt it.

Chapter 3 - "Two Finger" method was the most confusing chapter of the book as I could not understand why I should learn another way of multiplication, which is longer, when I had just learnt how to mentally multiply utilising rules learnt in the previous chapter. However, this chapter is essential to understand how to carry out division, covered in Chapter 5.

After the, initial, struggle of Ch 3, Ch-4 Addition is covered, and comes as a nice break. I thought this would be rather dull but was again surprised at the simplicity, logic and ability of the system. Furthermore, the way of checking the answers of long addition without re-calculation is demonstrated. I would say that Chapter 4 is the most immediately useable chapter of the book for daily living.

Division is covered in Chapter 5 and where the skills of Chapter 3 come to the fore, along with an extension to them. This is almost as intense as Chapter 3 but once the system was fully understood, I was left, as with every chapter covered, wondering what the fuss was about. I was able to carry out all basic arithmetic either in my head or by writing just the sum down, followed by the answers, as they evolved and in a record time, even with answer checking, which I now do as a matter of course.

Chapter 6 deals with the very simple methods of squaring 2 and 3 digit numbers. After this, the method of finding the square root is dealt with and warns that the method is unlike any method so far learnt. This method is the most intense to learn as there are numerous steps to remember. However, once I set out the work in front of me, I began to understand the sequence and finally learnt it.

Lastly, algebra is discussed. This chapter is an addition and not required unless the reader wishes to articulate the logic of the systems or intends to go further into mathematics. For me, it was a nice gentle way of brushing the cobwebs from my brain as I intend to embark upon a technical degree (Astronomy), which is heavily maths based.

It is not my intent to comment on the extraordinary life of the author. Nor discuss whether this is a better system than the currently conventional one taught in state schools. I will say, however, that having been given a foundation in mathematics from the state methods taught within school and with my mature approach to re-visiting mathematics, I found this system fascinating, fun and exciting. The buzz of learning and maximising mathematical work with the least amount of effort (excluding the effort of learning the methods) and being able to carry out much greater mental arithmetic than I have ever been previously able to do, was a very enjoyable experience.

Helping my daughter sees me using speed maths for her homework, along with answer checking. She does not know how I do it but also does not see me reaching for calculators. I would hope that, through observation and time together, and once she has reached a suitable level of understanding with conventional methods, she will be curious to know how I did what I did so much quicker than her. This may lead her to `discover' the speed method for herself. I am not a teacher and could never expect her to learn another system whilst dealing with the conventional one. I prefer, and believe in, leading by example and action, although I will probably show her how to verify her answers in the near future.

Finally, I should like to say that I was greatly assisted in practising the methods with a purchased downloadable program based directly on this book but not associated with it. This program greatly speeded up my understanding of the systems and provided me with 1000's of random sums to calculate. With both, the book and program, I was able to learn and cement the system into my understanding within 10 days, spending about an hour an evening on it. I am currently revising on GCSE maths in preparation for an Astronomy degree next year. I have also purchased the book `Vedic Mathematics', which is similarly system based but, in my opinion, is for applied mathematical procedures using algebraic equations. It is a much heavier book and very hard going due to its terminology and premise.

The book is presented in a logical format, not always obvious until you have progressed to division.

The first part deals with multiplication, using numbers between 1 and 12. It [the book] claims that it is not required for the reader to know their tables. However, it states that knowledge of them is very useful.

To explain, the system demonstrates a method of multiplying single numbers by single numbers - the times tables. With this knowledge, all other calculations within the book can be completed. However, with a solid understanding of times tables, many calculations, such as squaring 2 digit numbers and multiplication of up to 4 digits by numbers between 1 and 12, can be completed in less than 10 seconds, in your head, once the system is fully understood.

The multiplication sequence to learn is broken down into groups;

a. 11 & 12

b. 5,6 & 7

c. 8 & 9 (I suggest learning 9x before 8x)

d. 4 & 3

The reason for this is that each group uses extensions of a given method, such as:

a. Multiplication by 11:

11 x 45 = first digit + right hand digit= 5 + 0 = 5

Next digit + right hand digit = 4 + 5 = 9

Next digit + right hand digit = 0 + 4 = 4

Answer: 495

b. Multiplication by 12:

12 x 45 = first digit x 2 + right hand digit = 5 x 2=10 + 0 = 10 which is 0 carry 1

Next digit x 2 + right hand digit + carry = 4x2=8 + 5+carry(1)= 14 which is 4 carry 1

Next digit x 2 + right hand digit + carry = 0x2=0 + 4+ carry(1)= 5 which is 5

Answer: 540

A fictitious zero is used to facilitate the method at either end of the number to be multiplied so that the number would resemble 045.0 for calculation purposes.

I hope my examples illustrate the point that both 11x & 12x use a system that takes the first digit and adds it to the digit immediately to its right to find each digit of the answer in turn. However, the method for multoiplying by 12 also doubles the digit before it adds the neighbour (right hand digit), which is an extension to the method of multiplying by 11. It is not my intent to reproduce any part of the book, nor demonstrate rigorously any method taught. My example is to illustrate that the methods are broken into groups, as each group method is a successive extension of the last within that group.

One point I should like to mention at this point is that the methods for multiplying any given number by 4 and by 3 are the most complex of all the methods given. As such, it is quicker to mentally multiply each digit from right to left, writing down the product as you go. The methods for 3 & 4 are given for completeness but are slower than the conventional method of multiplication. Likewise, the method for multiplying by 1 & 2 are also given for completeness.

After basic multiplication, the multiplication of larger numbers is taught. This is a single, simple method for multiplication of any number by any number. It is at the end of this chapter that I found my first surprise - how to quickly and accurately check the sum of any calculation without having to re-calculate the sum. The logic is very easy to pick up and became instantly and constantly used by me once I had learnt it.

Chapter 3 - "Two Finger" method was the most confusing chapter of the book as I could not understand why I should learn another way of multiplication, which is longer, when I had just learnt how to mentally multiply utilising rules learnt in the previous chapter. However, this chapter is essential to understand how to carry out division, covered in Chapter 5.

After the, initial, struggle of Ch 3, Ch-4 Addition is covered, and comes as a nice break. I thought this would be rather dull but was again surprised at the simplicity, logic and ability of the system. Furthermore, the way of checking the answers of long addition without re-calculation is demonstrated. I would say that Chapter 4 is the most immediately useable chapter of the book for daily living.

Division is covered in Chapter 5 and where the skills of Chapter 3 come to the fore, along with an extension to them. This is almost as intense as Chapter 3 but once the system was fully understood, I was left, as with every chapter covered, wondering what the fuss was about. I was able to carry out all basic arithmetic either in my head or by writing just the sum down, followed by the answers, as they evolved and in a record time, even with answer checking, which I now do as a matter of course.

Chapter 6 deals with the very simple methods of squaring 2 and 3 digit numbers. After this, the method of finding the square root is dealt with and warns that the method is unlike any method so far learnt. This method is the most intense to learn as there are numerous steps to remember. However, once I set out the work in front of me, I began to understand the sequence and finally learnt it.

Lastly, algebra is discussed. This chapter is an addition and not required unless the reader wishes to articulate the logic of the systems or intends to go further into mathematics. For me, it was a nice gentle way of brushing the cobwebs from my brain as I intend to embark upon a technical degree (Astronomy), which is heavily maths based.

It is not my intent to comment on the extraordinary life of the author. Nor discuss whether this is a better system than the currently conventional one taught in state schools. I will say, however, that having been given a foundation in mathematics from the state methods taught within school and with my mature approach to re-visiting mathematics, I found this system fascinating, fun and exciting. The buzz of learning and maximising mathematical work with the least amount of effort (excluding the effort of learning the methods) and being able to carry out much greater mental arithmetic than I have ever been previously able to do, was a very enjoyable experience.

Helping my daughter sees me using speed maths for her homework, along with answer checking. She does not know how I do it but also does not see me reaching for calculators. I would hope that, through observation and time together, and once she has reached a suitable level of understanding with conventional methods, she will be curious to know how I did what I did so much quicker than her. This may lead her to `discover' the speed method for herself. I am not a teacher and could never expect her to learn another system whilst dealing with the conventional one. I prefer, and believe in, leading by example and action, although I will probably show her how to verify her answers in the near future.

Finally, I should like to say that I was greatly assisted in practising the methods with a purchased downloadable program based directly on this book but not associated with it. This program greatly speeded up my understanding of the systems and provided me with 1000's of random sums to calculate. With both, the book and program, I was able to learn and cement the system into my understanding within 10 days, spending about an hour an evening on it. I am currently revising on GCSE maths in preparation for an Astronomy degree next year. I have also purchased the book `Vedic Mathematics', which is similarly system based but, in my opinion, is for applied mathematical procedures using algebraic equations. It is a much heavier book and very hard going due to its terminology and premise.

44 comments*|*
19 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByMr. J Tootillon 13 March 2010

I wish every primary school age child would be taught maths this way!!People don't like maths because it seems too difficult, this book makes it seem enjoyable and very manageable. The examples are well chosen with each fully-worked example actually helping you understand how to try it on your own. I would recommend this to anyone who has ever wanted (or needed) to do simple maths with long numbers quickly without a calculator.

0Comment*|*
5 people found this helpful.
Was this review helpful to you?YesNoReport abuse#### There was a problem loading the comments at the moment. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

byEdward H. Julius

£11.99

Let us know here.

Unlimited One-Day Delivery and more

Prime members also enjoy exclusive access to movies and TV shows, a million songs and much more.

There's a problem loading this menu at the moment.

Back to top

Get to Know Us | Make Money with Us | Amazon Payment Methods | Let Us Help You |

- Conditions of Use & Sale
- Privacy Notice
- Cookies & Internet Advertising
- © 1996-2016, Amazon.com, Inc. or its affiliates

|55 people found this helpful. Was this review helpful to you?YesNoReport abuse