Author Topic: The importance today, of "Times-Tables" ???  (Read 25167 times)

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Offline Brumby

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Re: The importance today, of "Times-Tables" ???
« Reply #75 on: April 08, 2018, 04:04:40 pm »
Yeah ... It is.
 

Offline IanB

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Re: The importance today, of "Times-Tables" ???
« Reply #76 on: April 08, 2018, 04:45:08 pm »
Yeah ... It is.

No, it isn't  ::)

I couldn't possibly do everything helius wrote down in my head.

"Six sixes are 36, keep the 6, carry the three. Six times 30 is 180, add the carried 30 makes 210, add the original 6 makes 216. Remember that. Now 4 x 6 is 24, keep the 4, carry the 2. Four threes are 12, add the carried 2 for 14, add the 4, ... oh crap, now where was I? Let's start over...  :("

You're nuts if you think someone can keep track of all that in their head as they go along.

« Last Edit: April 08, 2018, 04:46:44 pm by IanB »
 

Offline helius

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Re: The importance today, of "Times-Tables" ???
« Reply #77 on: April 08, 2018, 05:00:03 pm »
It was harder to make the columns line up in bbcode then to do the mental arithmetic  :-//

When you want to remember a series of digits (like 216) while you work with other digits, it helps to convert them into rhyming words or trenchant images. So you might remember "junior prom" instead of the digits and then convert it back later after you had 1440.
 

Offline T3sl4co1l

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Re: The importance today, of "Times-Tables" ???
« Reply #78 on: April 08, 2018, 05:12:09 pm »
You're nuts if you think someone can keep track of all that in their head as they go along.



Seriously, short and long term memorization tricks are just something you practice at.  Maybe you can't ever do it, maybe not. But if you aren't practicing it at all, you definitely aren't going to do it. :)

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Offline IanB

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Re: The importance today, of "Times-Tables" ???
« Reply #79 on: April 08, 2018, 05:16:57 pm »
Just so it's clear, I wrote 40 x 36 and 6 x 36 because both of these were possible to do directly from memory without doing them bit by bit.

For example, 40 x 36 is easily recognizable as a variation of 2 x 72 or 12 x 12, both of which are known to be 144. Similarly, 6 x 36 is a variation of 3 x 72, which is then instantly 216.

Therefore I only had to keep track of 1440 and 216 in my head and add them together.
 

Offline mtdoc

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Re: The importance today, of "Times-Tables" ???
« Reply #80 on: April 08, 2018, 06:13:35 pm »
You're nuts if you think someone can keep track of all that in their head as they go along.

It is possible with practice. When I was a kid I used to do that with long multiplication as a challenge. My dad (who was an engineer with a degree in math) used to show me off to his friends doing this.  Which is why, perhaps, he really thought I should be an engineer.  Sometime later I began to dislike math and went another direction (biology).

Now my feeble middle aged mind has problems with much simpler math problems....  :o

My kids - who did learn their multiplication tables, refuse to try and do anything "in their head" beyond what they've memorized already. When I ask them to try they say  "Why? just use a calculator" -  despite that fact that they do know very well how to do it with paper and pencil.  ::)
 

Online coppice

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Re: The importance today, of "Times-Tables" ???
« Reply #81 on: April 08, 2018, 08:25:37 pm »
Yeah ... It is.

No, it isn't  ::)

I couldn't possibly do everything helius wrote down in my head.

"Six sixes are 36, keep the 6, carry the three. Six times 30 is 180, add the carried 30 makes 210, add the original 6 makes 216. Remember that. Now 4 x 6 is 24, keep the 4, carry the 2. Four threes are 12, add the carried 2 for 14, add the 4, ... oh crap, now where was I? Let's start over...  :("

You're nuts if you think someone can keep track of all that in their head as they go along.
Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.
 

Offline IanB

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Re: The importance today, of "Times-Tables" ???
« Reply #82 on: April 08, 2018, 09:33:56 pm »
Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it  :)
 

Offline rstofer

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Re: The importance today, of "Times-Tables" ???
« Reply #83 on: April 08, 2018, 10:42:41 pm »
I see your point, but '6 x 6' is not obviously the first step, especially if doing mental arithmetic. In fact, trying to do long form multiplication in your head this way is likely to lead to too many partial sums to keep track of, and it gets very difficult.

A more productive first step is 40 x 36 = 1440, and then 6 x 36 = 216, and then add them to give 1656.
Code: [Select]
   36
x  46
------
   3
  186
  2
+124
------
  216
+1440
------
 1656

Isn't what you did exactly "long form multiplication"?

How about this:  36 * 50 = 1800 (half of 36 times 100) and 36 * 4 = 144.  1800 - 144 = 1656.  That PARTICULAR problem is easy to do in your head.

 

Offline T3sl4co1l

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Re: The importance today, of "Times-Tables" ???
« Reply #84 on: April 08, 2018, 11:03:53 pm »
Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it  :)

Easy.  Mere mortals have no need of such precision, so let's approximate it as:
2.5 x 10^6 (~7% high)
* 8 x 10^6 (~4% low)
= 20 x 10^12 + 3% or 2.06 x 10^12.

Need more decimals?  Get a better slide rule. ;D

Real result: 19.804... x 10^12, slightly lower, surprisingly.

And yeah, math savants can do real time combinatorics on that many figures, I think?

Tim
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Offline Cerebus

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Re: The importance today, of "Times-Tables" ???
« Reply #85 on: April 08, 2018, 11:49:48 pm »
OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

"So, Ian, how did you get this nickname, Queenie?"
"Well, I was posting on this forum..."
Anybody got a syringe I can use to squeeze the magic smoke back into this?
 

Offline Brumby

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Re: The importance today, of "Times-Tables" ???
« Reply #86 on: April 09, 2018, 02:24:03 am »
Yeah ... It is.

No, it isn't  ::)
Yeah, it is.

Quote
I couldn't possibly do everything helius wrote down in my head.

"Six sixes are 36, keep the 6, carry the three. Six times 30 is 180, add the carried 30 makes 210, add the original 6 makes 216. Remember that. Now 4 x 6 is 24, keep the 4, carry the 2. Four threes are 12, add the carried 2 for 14, add the 4, ... oh crap, now where was I? Let's start over...  :("

You're nuts if you think someone can keep track of all that in their head as they go along.
The way I was taught is exactly how you expressed it...

A more productive first step is 40 x 36 = 1440, and then 6 x 36 = 216, and then add them to give 1656.

  36 x
  46
----
 216
1440
====
1656

« Last Edit: April 09, 2018, 02:28:50 am by Brumby »
 

Offline IanB

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Re: The importance today, of "Times-Tables" ???
« Reply #87 on: April 09, 2018, 02:57:44 am »

  36 x
  46
----
 216
1440
====
1656



Yes, and isn't that rather simpler than this: ?

  36 x
  46
----
  36
 180
 240
1200
====
1656


 

Offline james_s

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Re: The importance today, of "Times-Tables" ???
« Reply #88 on: April 09, 2018, 03:04:47 am »
Simpler as in less writing, but not nearly as easy to do, at least for me.
 

Offline Johnboy

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Re: The importance today, of "Times-Tables" ???
« Reply #89 on: April 09, 2018, 05:11:50 am »
There was a book published in the US that advocated the abacus/soroban method of multiplying from "left to right", establishing the magnitude before the small stuff. This approach makes sense for several reasons to me-- but the main one is that we don't really need precision, just accuracy. Things constructed using slide rules ended up being somewhat overengineered for safety, sure-- but no one cares about the umpteenth significant digit. There's a story I read somewhere about a certain professor calculating the last few digit(s) in his head and pretending to read them off the rule.

Again, I'm only bringing this up because learning "times tables" by rote is useful, sure, particularly the squares and cubes-- but parallel calculators really were a great teaching tool for this. Punching numbers in just doesn't impart the same feel to me.
 

Offline bd139

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Re: The importance today, of "Times-Tables" ???
« Reply #90 on: April 09, 2018, 11:40:31 am »
Here's how I do 36x46 in my head with tables. Use place value system:

Sum := AB * CD

R := B*D
R := R + (A*D*10)
R := R + (B*C*10)
R := R + (A*C*100)

Example:

6*6 -> 36
36 + (3*6*10) -> 216
216 + (4*6*10) -> 456
456 + (3*4*100) -> 1656

Note lack of temporary variables other than the accumulator R.

You can do this with decimals by counting the place values in later. Just move the decimal over by the number of digits to the right of all of the decimals together.
« Last Edit: April 09, 2018, 11:43:02 am by bd139 »
 

Offline GlennSpriggTopic starter

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Re: The importance today, of "Times-Tables" ???
« Reply #91 on: April 10, 2018, 01:09:57 pm »
WOW.... All very interesting reading, for many reasons, as were put forward !!!! (Thank you all).
(I'm the original 'Poster' of this statement/question).
I know there are many other ways of performing 'maths', either in your head or on paper   :)
However, when I mentioned that the "first step is 6 x 6", that is irrelevant in regard to what I meant  :D
I simply meant that kids these days should know that "6 x 6 = 36", as that can't be broken down!.......

To our Overseas friends, I'm in Australia, and our primary schools go to year 6, and then start 'High'
school at 11 years old. (Some are 12). As stated, some kids 'know' the times tables, as it is/was
drummed into them by diligent teachers and/or parents, (which is good!), but the fact remains that
it is not (now) enforced (here) as a curriculum requirement... though I CERTAINLY think it should be!  :)

Out of interest though...  I learnt LOTS of shortcuts in Maths!!!...  like......
To multiply by 11, add the digits and put them in the middle.....
35 x 11....  3+5 =8...   result = 385   (Do in your head in 2 secs!)
63 x 11....  6+3 =9...   result = 693
If the 'addition' adds up to more than '9' then carry the '1'..... like.....
68 x 11....  6+8 =14...  carry the '1' to the '6'...  result = 748  (Do in your head in 2 secs!)
Do you know that ALL multiples of '9', have the digits add up to '9' ??.....
9x9 = 81   (8+1 = 9)
9x7 = 45   (4+5 = 9)
9x123 = 1107   (1+1+0+7 = 9)
9x3764 = 33876   (3+3+8+7+6 = 27.   2+7 = 9)  :D

There are so many more it is not funny !!!!
Just teach our kids/grandkids the basics !!   :D :D
Diagonal of 1x1 square = Root-2. Ok.
Diagonal of 1x1x1 cube = Root-3 !!!  Beautiful !!
 

Online coppice

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Re: The importance today, of "Times-Tables" ???
« Reply #92 on: April 10, 2018, 01:16:04 pm »
Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it  :)
Its interesting how technology often makes people think that humans are not capable of tasks that used to be accomplished routinely by humans. Those are most often physical things, but increasingly the way machines have removed the pressing need to train various mental tasks is making people think only very special humans could ever do them before the machines. You didn't need to be a savant to multiply two numbers in your head. It just took enough practice doing it on paper, until you could take away the paper.
 

Offline BradC

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Re: The importance today, of "Times-Tables" ???
« Reply #93 on: April 10, 2018, 01:27:04 pm »
Its interesting how technology often makes people think that humans are not capable of tasks that used to be accomplished routinely by humans. Those are most often physical things, but increasingly the way machines have removed the pressing need to train various mental tasks is making people think only very special humans could ever do them before the machines. You didn't need to be a savant to multiply two numbers in your head. It just took enough practice doing it on paper, until you could take away the paper.

Admittedly not with paper, but my highschool Chem teacher (who was in his 60's at the time) could, and regularly did multiply or divide 7 digit numbers on the blackboard faster than we could get them into a Casio fx82 and get an answer out.

He was cool. His "continuity" demonstrator to illustrate the conductivity of certain liquids was a bit of wood with a bayonet socket screwed to each side and wired in series with a bit of 24/0.20 figure 8 and a standard 2 pin plug. In the top socket he put a standard 240V light bulb. In the bottom socket he put a standard 240V light bulb sans glass and filament leaving a pair of probes that he would dip in the liquid. We were amused when he lay it on the desk one day and forgot about it, only to lean on the probes later in the lesson. RCD's were invented, but not installed.
 

Offline Johnboy

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Re: The importance today, of "Times-Tables" ???
« Reply #94 on: April 10, 2018, 02:01:52 pm »
Back before pocket calculators lots of people used slide rules or log tables. However, some of us learned to multiply 7 figure numbers in our heads. The deep mystical secret of this capability - practice.

OK, whatever you say. If you can multiply 2367735 by 8364229 in your head, then I'm the Queen of Sheba.

Sure, I believe some savants can do this trick, but I'm not sure it is the best use of brain cells for mere mortals to learn how to do it  :)
Its interesting how technology often makes people think that humans are not capable of tasks that used to be accomplished routinely by humans. Those are most often physical things, but increasingly the way machines have removed the pressing need to train various mental tasks is making people think only very special humans could ever do them before the machines. You didn't need to be a savant to multiply two numbers in your head. It just took enough practice doing it on paper, until you could take away the paper.

And sometimes using paper is unnecessary in the first place. Here are examples of several methods by which those skills can be acquired (although it's admittedly a little cringeworthy in places).


 

Offline GlennSpriggTopic starter

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Re: The importance today, of "Times-Tables" ???
« Reply #95 on: April 20, 2018, 12:38:21 pm »
Wow, what an interesting Saga that all was... (again  :) )
(I'm the original 'poster' again...)
My hat's off to the gentleman from the U.S. (and others...), that stated that their kids
ARE taught the times-tables, and that it is a 'requirement'...  That's GOOD !!  :)
But it still sadly doesn't 'here'. (In Australia. No Aussie jokes please  :D)......
I can/have asked my 1st year high-school grand-kids, and their friends, the likes of....
"What is 6x6", or "what is 8x4".... let alone.... "what is 9x7"... (F%$# that's hard!),
and NONE of them can tell me !!!  They ALL have iPhone/Android 'Tablets' these days
in class, (so no need for ancient 'Calculators' ), [lets show them a slide-rule haha].

What is it about a lot of you responders, that make you think that any/all of your own
'methods', and the 'Effort' it takes to remember it/them, is ANY better than SIMPLY
remembering BASIC times-tables, from/with which anyone can calculate anything ??
I RESPECT all your 'abilities'..... but what are you fighting against ??? Seriously ??
May we all, (teachers, parents, grandparents) simply teach our kids the 'basics'  :)

'Brumby' seems to prefer 'Yep..', 'Nope..', {quote} then 'yep..' without 'adding' to
anything at all except his unadulterated 'Piousness'.... He seems to now 'seek' out
my many/varied Posts now, (even though I have moved on...), from a time that he
chose to (attempt to) 'Belittle' me repeatedly.... when I 'dared' to ask for a resolution
on this 'Forums' MAIN? forum topic.  This 'Demi-God' (in his Godness & Greatness)
decided at 2am one morning, (with nothing else to do obviously), to RANT at me, and
tell me I am just a "TROLL"... (Haah?! it was MY post he was continuously abusing??).
After swallowing my pride/rights, I apologized to him, and explained all that I could.....
'HE' then ridiculed me about what I offered, and repeated how 'I'm' just a "TROLL" ????
Well I have many scientific interests, that go WAY beyond listening to this "No-Life",
and as such I keep posting/discussing in areas "I Hope" is beyond 'his' REALM.....
I'm a peaceful Pensioner, who likes to invoke dialog with REAL people, not Demi-Gods...
« Last Edit: April 20, 2018, 12:40:00 pm by GlennSprigg »
Diagonal of 1x1 square = Root-2. Ok.
Diagonal of 1x1x1 cube = Root-3 !!!  Beautiful !!
 

Offline Cerebus

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Re: The importance today, of "Times-Tables" ???
« Reply #96 on: April 20, 2018, 01:26:44 pm »
Well if you want a peaceful life, why make a post that dredges up some spat you've had elsewhere with Brumby in an unrelated topic? That does seem to be trolling for a response. 

Oh and please, less smilies, less brackets, less ... ellipses, less random punctuation in general and RANDOM changing into ALL CAPS in the middle of run on sentences. It makes it incredibly hard to read what you've written.
Anybody got a syringe I can use to squeeze the magic smoke back into this?
 

Offline Halcyon

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Re: The importance today, of "Times-Tables" ???
« Reply #97 on: April 20, 2018, 01:35:37 pm »
I'm a bit late to the conversion however my thoughts are as follows...

The traditional "times tables", i.e. multiplication of two numbers between 1 and 12 is largely irrelevant these days. Unless your profession, hobby or interests involve reciting a table of figures which don't change, but that's just data recall.

The function and knowledge of how maths works is far more important than remembering results. Remember BODMAS/BEDMAS? Brackets, Exponents, Divide, Multiply, Add and Subtract... in that order.

I'm the first to admit that I can't do mathematics in my head, even simple equations. Yet, for the most part, I know how maths works and with a calculator I can come to a correct result.
 

Offline rstofer

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Re: The importance today, of "Times-Tables" ???
« Reply #98 on: April 20, 2018, 03:19:11 pm »
I'm a bit late to the conversion however my thoughts are as follows...

The traditional "times tables", i.e. multiplication of two numbers between 1 and 12 is largely irrelevant these days. Unless your profession, hobby or interests involve reciting a table of figures which don't change, but that's just data recall.


Or your continuing education.  I don't see how anybody can graduate from EE school without being able to do simple multiplication and division.  There simply isn't time to use a calculator for things like factoring polynomials.  You just look at the coefficients and the factors jump out of the paper.  If they don't, you're in for a long night.

I will agree that the average burger-flipper probably doesn't need arithmetic or times tables.  A lack of basic calculating skills is why they're flipping burgers in the first place.

Quote

The function and knowledge of how maths works is far more important than remembering results. Remember BODMAS/BEDMAS? Brackets, Exponents, Divide, Multiply, Add and Subtract... in that order.


And strictly left to right within a precedence level. 6 ÷ 2(1+2) = 9, not 1.

http://www.slate.com/articles/health_and_science/science/2013/03/facebook_math_problem_why_pemdas_doesn_t_always_give_a_clear_answer.html

Quote
I'm the first to admit that I can't do mathematics in my head, even simple equations. Yet, for the most part, I know how maths works and with a calculator I can come to a correct result.

I'm of the opinion that more class time should be spent on setting up problems (word problems) and less time grinding through page-long solutions.  Spend the time to learn Matlab or wxMaxima and let the computer do the number crunching.  symbolab.com and desmos.com get a lot of traffic from my house.
 

Offline IanB

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Re: The importance today, of "Times-Tables" ???
« Reply #99 on: April 20, 2018, 06:45:39 pm »
The function and knowledge of how maths works is far more important than remembering results. Remember BODMAS/BEDMAS? Brackets, Exponents, Divide, Multiply, Add and Subtract... in that order.


And strictly left to right within a precedence level. 6 ÷ 2(1+2) = 9, not 1.


Really though, this kind of high school level rule following doesn't have much place in the professional world. Once you leave school and get into advanced studies it becomes more important to communicate effectively and unambiguously. For example the above expression has a spacing and grouping that would suggest this:
$$6 \over 2(1+2)$$
Rather than this:
$${6 \over 2} (1+2)$$
In any professional publication one or other of the above forms would be expected and preferred.

If it was really wanted on a single line one would probably write something like this: \$(6 / 2)(1+2)\$
« Last Edit: April 20, 2018, 06:49:07 pm by IanB »
 
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