If I am understanding your question correctly, there are tricks to make it easier. For example, when multiplying by 9, one digit goes up and the other goes down. No need for mnemonic images -- just remember the pattern: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...

There are mental calculation tricks that would avoid a lot of the memorization. For example, if you multiply any 2-digit number by 11, just add the digits and put the result in the middle:

For 11 * 10, add 1 + 0 and put the answer in the middle: 110.

11 * 11 = 1(2)1
11 * 12 = 1(3)2
11 * 25 = 2(7)5

If the two digits add up to more than 10, just carry the 10:
11 * 58 = 638 because 5 + 8 = 13.
11 * 97 = 1067 because 9 + 7 = 16.

That's probably easier to learn than memorizing all the answers between 11 * 10 and 11 * 20. There are many tricks for other numbers too...

Yes I already do have the images of 00-99 in my mind.

I know about mental math, and my next step will be working hard with the book "secrets of mental math" which after reviewing the current literature, seems to be the best option(anyone with different few - let me know).

Sadly I have a gap from school and I don't remember the basic time tables by heart(embarrassing I know). A lot of the more complex mental math require knowing this by heart.

Therefore, any mnemonic which will help with memorizing the time tables up to 9x9 will be great. I'm sure someone has came up with mnemonic version of it. I hope to avoid memorizing it by root which will take some time...

Therefore, any mnemonic which will help with memorizing the time tables up to 9x9 will be great. I'm sure someone has came up with mnemonic version of it. I hope to avoid memorizing it by root which will take some time...

Brainstorming some ideas:

If you have a smartphone, look for a mental calculation app. One of the apps I have runs you through multiplying single digits near the beginning, which you have to pass to get to the next level. 15 minutes of that per day for a week would probably do the trick.

Some of them I learned by chanting them when I was a kid. Until recently, when I started trying to make the answer come instantly, when I would multiply 6 * 8, I would say "six times eight is forty eight", because it rhymes.

I know that I must have chanted a lot of them, because it easier to go in one order. If I say "eight times six" instead of "six times eight" I have to stop and think for an extra second, because my brain doesn't have as quick of a path from that to the answer.

You could try learning them by going through the rows -- don't read them from a table, but do the addition:

I haven't been in your position in relation to times tables but using wrote to memorise the first 9 times tables wouldn't take long I would imagine, especially if you performed this task before sleep, on the toilet, in the shower etc.

2 2s are 4
2 3s are 6
2 4s are 8
2 5s are 10

That's how I learnt them anyway. A few weeks, probably even a few days and you could become quite well known with them. Even find combinations that you like. 8 x 8 = 64 was always my favourite etc. Good luck mate

I still think that use mnemonics for timetable memorization is fast. Making crazy story is enough. This is coming from my experience as i am teaching some primary pupils in this regards :)

Yes I already do have the images of 00-99 in my mind.
...
Therefore, any mnemonic which will help with memorizing the time tables up to 9x9 will be great. I'm sure someone has came up with mnemonic version of it. I hope to avoid memorizing it by root which will take some time...

Create an Anki deck with all the tables you want to learn in image form.

So for: 9 x 8 = 72
Create an Anki card: Pie x UFO = Coin

I'd suggest also NOT skipping learning the other combination (UFO x Pie = Coin)

Then just use Anki's spaced repetition magic to get it stuck in your head.
(And make use of Anki's Cloze feature.)

This is surely a much better way than the sitting on the floor and chanting the tables that we had to do in school.

Another hint, if you already have your 0-99 in a spreadsheet creating all the equations you need there and importing them into Anki should be fairly easy.

Old post, but in case this is still relevant to anyone. There is an iOS app that teaches multiplication tables (0-12) for kids using the major memory system, so you end up learning both. It uses cartoons to teach them. Funtimes Tables! Fun Times Table

The major memory system is covered first, then cartoons that put it together.

I have a kid that is learning basic math now. I know that multiplication tables are coming. Wondering how you would teach a kid math in a way that is not by rote. I with I had learned another way. Major system? Memory palace? What would you recommend?

I know you mnemonists are fast but I find that learning to either calculate or old fashioned rote learning is a fair bit quicker than encoding/decoding a memory system... However I suspect the end result may be the same if one practices consistently.

Well, we just started learning the major system today via the app someone mentioned earlier. So, totally clean slate, except for today. I was surprised at how interested she was, but not sure if it was the subject matter or just that she got to use my phone...

Ah okay. hmmm I think it would be good to figure out if she was interested in the system or phone because a lot of young kids may have trouble creating a bigger system like the major system. The way I taught the children was with simplicity

Park- I'd love to hear more about how you taught the children, even if I don't end up using it. I'm fascinated in education at the moment, and thinking back to ways mine could have been improved or still be improved!

Hello,
I'am maths professor in France and I've a basic (and perhaps controversy) question : why learn "by rote", or with memory technique, the timetables ?. It's more efficient to understand the relations between the numbers. Understanding the relation between numbers make the further learning more easier and develop the comprehension
For my daughter who begin to learn the timetables in school, I prefer playing with the number than rote learning (or memory techniques). It's work very well, she had no problem.

It's a bit difficult to write clearly my ideas : English isn't my native language....

@Geoff Was such a deck created? From where can I download it?
I want to be able to recall times tables upto 50 (or multiplication facts upto 50x50) instantly in my head without having the need to work them out mentally or on paper because doing that distracts me from the problem at hand and also takes time which I am short of as I am preparing for competitive exams after my graduation. For example: I know 8x4=32, I donâ€™t have to work it out in my head. In the same way I want to be able to recall 27x13, 43x29 etc. Any ideas?

Mental calculation is aided dramatically by the addition of facts. Knowing two digit multiplication by rote will make 6 digit calculation much faster. Knowing the first 100 squares also makes multiplication much faster. Knowing the first hundred primes similarly saves you from trying mentally factor a number that can not be factored.

Similarly, numerical relationships and functions.

Mental arithmetic from addition to logarithms and trigonometry is aided by our ability to treat intermediate abstractions as concrete.

One does not generally prove a theorem from first principles but instead relies on other theorem as proven. Real math is dependent on these links. Mental arithmetic is similar.

If all you wish to learn is to multiply 2 digit number in 5 seconds then calculation is a good tool.

If you wish to extend to 6 or 8 digit multiplication in 5 seconds then you require more efficient methods.

If you would like to calculate trig, logs, or roots to 5 or 6 digits of precision mentally there are similar additional facts required.

Developing this level of numeracy should relieve a great deal of mental stress when concentrating on algebra, Geometry, calculus, statistics. While not directly applicable to analysis the practice of linking abstractions mentally has a reasonable relationship with logic.

Mnemonics can aid this process tremendously but ultimately rote memorization is faster than mnemonics or calculation.

The only mental method of addition I have seen that is faster is Anzan. I have yet to see a presentation of multiplication with Anzan and would love to know if mental visual manipulation can outperform classic mental calculation on average or if they could be combined.

Mnemonics do not preclude/replace calculation, rote memorization, or familiarizity with functions or relationships. Rather they enhance it by providing a dictionary of abstractions that would otherwise not be available to mental calculation.

Why anyone would want to attempt to train their brain to do this is an entirely different question. We do not seem to be able to get smarter but there appears to be enough (maybe) plasticity left in an adult brain to improve efficiency through practice that can allow us to perform more quickly and with more precision.

... In terms of plasticity the learning curve seems to flattens out dramatically after about 12-16 weeks. After that it becomes an endurance sport.

Tools like Anki and drilling are intended to help us make those skills permanent. Mnemonics can be used both on the front end or back end of the process.

Integrating a skill into life is the last step....
When someone walks up and asks you to perform it is surprising how quickly your brain sits off and performance anxiety occurs. Again you have to do it. Talking about it or preparing for it are simply not the same.

Do you already have mnemonic images for 0-9 and 00-99?

If not, you could use the number shape system for 0-9 and the Major System for 00-99.

(See also: other mnemonic systems)

If I am understanding your question correctly, there are tricks to make it easier. For example, when multiplying by 9, one digit goes up and the other goes down. No need for mnemonic images -- just remember the pattern: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90...

There are mental calculation tricks that would avoid a lot of the memorization. For example, if you multiply any 2-digit number by 11, just add the digits and put the result in the middle:

For 11 * 10, add 1 + 0 and put the answer in the middle: 110.

11 * 11 = 1(2)1

11 * 12 = 1(3)2

11 * 25 = 2(7)5

If the two digits add up to more than 10, just carry the 10:

11 * 58 = 638 because 5 + 8 = 13.

11 * 97 = 1067 because 9 + 7 = 16.

That's probably easier to learn than memorizing all the answers between 11 * 10 and 11 * 20. There are many tricks for other numbers too...

More info here:

https://en.wikipedia.org/wiki/Mental_calculation

http://mt.artofmemory.com/wiki/Trachtenberg_System

Yes I already do have the images of 00-99 in my mind.

I know about mental math, and my next step will be working hard with the book "secrets of mental math" which after reviewing the current literature, seems to be the best option(anyone with different few - let me know).

Sadly I have a gap from school and I don't remember the basic time tables by heart(embarrassing I know). A lot of the more complex mental math require knowing this by heart.

Therefore, any mnemonic which will help with memorizing the time tables up to 9x9 will be great. I'm sure someone has came up with mnemonic version of it. I hope to avoid memorizing it by root which will take some time...

Thanks.

Brainstorming some ideas:

If you have a smartphone, look for a mental calculation app. One of the apps I have runs you through multiplying single digits near the beginning, which you have to pass to get to the next level. 15 minutes of that per day for a week would probably do the trick.

Some of them I learned by chanting them when I was a kid. Until recently, when I started trying to make the answer come instantly, when I would multiply 6 * 8, I would say "six times eight is forty eight", because it rhymes.

I know that I must have chanted a lot of them, because it easier to go in one order. If I say "eight times six" instead of "six times eight" I have to stop and think for an extra second, because my brain doesn't have as quick of a path from that to the answer.

You could try learning them by going through the rows -- don't read them from a table, but do the addition:

Example: for sevens:

7, 14, 21, 28, 35, 42, 49, 56, 63

Then maybe chant them with a rhythm:

"two times seven is fourteen"

"three times seven is twenty one"

"four times seven is twenty eight"

etc.

Mnemonic images might even be slower than repetition in this case.

I don't know any tricks for single digits other than 9s.

I haven't been in your position in relation to times tables but using wrote to memorise the first 9 times tables wouldn't take long I would imagine, especially if you performed this task before sleep, on the toilet, in the shower etc.

2 2s are 4

2 3s are 6

2 4s are 8

2 5s are 10

That's how I learnt them anyway. A few weeks, probably even a few days and you could become quite well known with them. Even find combinations that you like. 8 x 8 = 64 was always my favourite etc. Good luck mate

Good idea...

I run through Anki flashcards before I go to sleep, because studying right before sleep helps with memorization.

There

issomething nice about that one. :)I still think that use mnemonics for timetable memorization is fast. Making crazy story is enough. This is coming from my experience as i am teaching some primary pupils in this regards :)

Create an Anki deck with all the tables you want to learn in image form.

So for: 9 x 8 = 72

Create an Anki card: Pie x UFO = Coin

I'd suggest also NOT skipping learning the other combination (UFO x Pie = Coin)

Then just use Anki's spaced repetition magic to get it stuck in your head.

(And make use of Anki's Cloze feature.)

This is surely a much better way than the sitting on the floor and chanting the tables that we had to do in school.

Geoff.

Another hint, if you already have your 0-99 in a spreadsheet creating all the equations you need there and importing them into Anki should be fairly easy.

Old post, but in case this is still relevant to anyone. There is an iOS app that teaches multiplication tables (0-12) for kids using the major memory system, so you end up learning both. It uses cartoons to teach them. Funtimes Tables! Fun Times Table

The major memory system is covered first, then cartoons that put it together.

I have a kid that is learning basic math now. I know that multiplication tables are coming. Wondering how you would teach a kid math in a way that is not by rote. I with I had learned another way. Major system? Memory palace? What would you recommend?

yotsn,

I have actually taught children this specifically and had good results. Does your kid know anything about memory techniques or is it a clean slate?

I know you mnemonists are fast but I find that learning to either calculate or old fashioned rote learning is a fair bit quicker than encoding/decoding a memory system... However I suspect the end result may be the same if one practices consistently.

Well, we just started learning the major system today via the app someone mentioned earlier. So, totally clean slate, except for today. I was surprised at how interested she was, but not sure if it was the subject matter or just that she got to use my phone...

Ah okay. hmmm I think it would be good to figure out if she was interested in the system or phone because a lot of young kids may have trouble creating a bigger system like the major system. The way I taught the children was with simplicity

Park- I'd love to hear more about how you taught the children, even if I don't end up using it. I'm fascinated in education at the moment, and thinking back to ways mine could have been improved or still be improved!

Hello,

I'am maths professor in France and I've a basic (and perhaps controversy) question : why learn "by rote", or with memory technique, the timetables ?. It's more efficient to understand the relations between the numbers. Understanding the relation between numbers make the further learning more easier and develop the comprehension

For my daughter who begin to learn the timetables in school, I prefer playing with the number than rote learning (or memory techniques). It's work very well, she had no problem.

It's a bit difficult to write clearly my ideas : English isn't my native language....

@Geoff Was such a deck created? From where can I download it?

I want to be able to recall times tables upto 50 (or multiplication facts upto 50x50) instantly in my head without having the need to work them out mentally or on paper because doing that distracts me from the problem at hand and also takes time which I am short of as I am preparing for competitive exams after my graduation. For example: I know 8x4=32, I donâ€™t have to work it out in my head. In the same way I want to be able to recall 27x13, 43x29 etc. Any ideas?

Mental calculation is aided dramatically by the addition of facts. Knowing two digit multiplication by rote will make 6 digit calculation much faster. Knowing the first 100 squares also makes multiplication much faster. Knowing the first hundred primes similarly saves you from trying mentally factor a number that can not be factored.

Similarly, numerical relationships and functions.

Mental arithmetic from addition to logarithms and trigonometry is aided by our ability to treat intermediate abstractions as concrete.

One does not generally prove a theorem from first principles but instead relies on other theorem as proven. Real math is dependent on these links. Mental arithmetic is similar.

If all you wish to learn is to multiply 2 digit number in 5 seconds then calculation is a good tool.

If you wish to extend to 6 or 8 digit multiplication in 5 seconds then you require more efficient methods.

If you would like to calculate trig, logs, or roots to 5 or 6 digits of precision mentally there are similar additional facts required.

Developing this level of numeracy should relieve a great deal of mental stress when concentrating on algebra, Geometry, calculus, statistics. While not directly applicable to analysis the practice of linking abstractions mentally has a reasonable relationship with logic.

Mnemonics can aid this process tremendously but ultimately rote memorization is faster than mnemonics or calculation.

The only mental method of addition I have seen that is faster is Anzan. I have yet to see a presentation of multiplication with Anzan and would love to know if mental visual manipulation can outperform classic mental calculation on average or if they could be combined.

Mnemonics do not preclude/replace calculation, rote memorization, or familiarizity with functions or relationships. Rather they enhance it by providing a dictionary of abstractions that would otherwise not be available to mental calculation.

Why anyone would want to attempt to train their brain to do this is an entirely different question. We do not seem to be able to get smarter but there appears to be enough (maybe) plasticity left in an adult brain to improve efficiency through practice that can allow us to perform more quickly and with more precision.

... In terms of plasticity the learning curve seems to flattens out dramatically after about 12-16 weeks. After that it becomes an endurance sport.

Tools like Anki and drilling are intended to help us make those skills permanent. Mnemonics can be used both on the front end or back end of the process.

Integrating a skill into life is the last step....

When someone walks up and asks you to perform it is surprising how quickly your brain sits off and performance anxiety occurs. Again you have to do it. Talking about it or preparing for it are simply not the same.

Do you know mnemonics for memorizing times tables?