> "Show your work" to me means just show your answers. "Show your working
> (out)" means explain how you got from the question to that answer and
> prove that you didn't copy it from Perkins.
That doesn't prove you didn't copy it. You could have copied his working as well.
> On Tue, 13 Nov 2012 13:15:45 +0000, the Omrud <usenet.om...@gmail.com>
> wrote:
> >I had no choice but to learn my tables by rote - we chanted them in
> >class when I was about five or six. Thank goodness for that, I say.
> Absolutely. And children usually like learning things by heart,
> anyway: their play and socialisation require it.
I don't recall that most of the children I was at school with enjoyed learning their times tables. (I knew mine before I went to school, but then I was a precocious little brat.)
Here's something I've never understood. We don't teach addition tables by rote, and yet children usually seem to pick them up all right. How's that?
Funnily enough, the one blind spot I had at school was in my addition tables - for some reason I kept thinking that 7 plus 4 was 13. I knew 4+7 = 11 all right, but that one kept coming out wrong. Odd.
> In Peter's 13x27 example, I would be saying to myself "seven threes are > twenty-one" for the first step.
Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7), which is the same as 20 squared minus 7 squared, which is 400 minus 49, which is 351.
One reason why I was always good at mental arithmetic was that I could usually see several different ways of performing a calculation and would usually pick the most convenient one.
> > Yes. I'd agree. 'Show your working' means that you have to write down
> > the steps that you took, mentally, to show that you know what the
> > agreed method is. So, even if you've a very helpful unconscious that
> > does your maths for you, you'll not get the marks for the right answer
> > if your 'working' is described as 'intuitive'.
> > I had some difficulty with this at school. I'd spent my early youth
> > resisting learning my tables - I still don't know them today. So, when
> > asked what 6 x 8 or 9 x 7 was, I'd have to work it out. This was, to
> > me, sensible, as I couldn't see much value in a system of memorising
> > things when it was inevitably going to break down when I got to 13 x
> > 27, while my method would continue to work - and my method didn't
> > involve the agony of learning stuff by rote. [not that I had a problem
> > with learning poetry or plays by rote, but they were interesting,
> > unlike the seven times table].
> I had no choice but to learn my tables by rote - we chanted them in
> class when I was about five or six. Thank goodness for that, I say.
They tried that with me for a while, but I was resistant.
Mike L <n...@yahoo.co.uk> writes:
> On Tue, 13 Nov 2012 14:34:29 -0800 (PST), Jerry Friedman
> <jerry_fried...@yahoo.com> wrote:
>>On Nov 13, 12:40 pm, Dr Nick <nospa...@temporary-address.org.uk>
>>wrote:
>>[show your work(ing)]
>>> Yup. We appear to have found a previously unidentified pondian
>>> difference. Have we yet established which version the other
>>> English Speaking Nations cleave to?
>>Is the rule simply that you show your work on a math problem,
>> In Peter's 13x27 example, I would be saying to myself "seven threes
> are twenty-one" for the first step.
> Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7),
> which is the same as 20 squared minus 7 squared, which is 400 minus
> 49, which is 351.
Oh that's good. I'd do 12x24 = 2x12x12 = 288. Plus another 24, plus
13x(27-24) = 39. Total = 351
> One reason why I was always good at mental arithmetic was that I could
> usually see several different ways of performing a calculation and
> would usually pick the most convenient one.
For multiplications like this, dividing into separate rectangles is the
way I've taught myself to do it.
>> "Show your work" to me means just show your answers. "Show your
>> working (out)" means explain how you got from the question to that
>> answer and prove that you didn't copy it from Perkins.
> That doesn't prove you didn't copy it. You could have copied his
> working as well.
Yes but it's much, much more obvious. Trust me, I've marked
undergraduate lab work.
> >> "Show your work" to me means just show your answers. "Show your
> >> working (out)" means explain how you got from the question to that
> >> answer and prove that you didn't copy it from Perkins.
> > That doesn't prove you didn't copy it. You could have copied his
> > working as well.
> Yes but it's much, much more obvious. Trust me, I've marked
> undergraduate lab work.
There's an art to copying. You don't copy it verbatim. You rework things slightly and phrase it differently. Sometimes it can even be a good idea to introduce deliberate mistakes if you're under any suspicion. I've done it a few times and never been found out. (I used to let people copy my work as well, so I didn't feel bad about it.)
> > On Tue, 13 Nov 2012 13:15:45 +0000, the Omrud <usenet.om...@gmail.com>
> > wrote:
> > >I had no choice but to learn my tables by rote - we chanted them in
> > >class when I was about five or six. Thank goodness for that, I say.
> > Absolutely. And children usually like learning things by heart,
> > anyway: their play and socialisation require it.
> I don't recall that most of the children I was at school with enjoyed
> learning their times tables. (I knew mine before I went to school, but then
> I was a precocious little brat.)
> Here's something I've never understood. We don't teach addition tables by
> rote, and yet children usually seem to pick them up all right. How's that?
> Funnily enough, the one blind spot I had at school was in my addition
> tables - for some reason I kept thinking that 7 plus 4 was 13. I knew 4+7 =
> 11 all right, but that one kept coming out wrong. Odd.
Probably because there's a nineishness to a seven, visually.
> > In Peter's 13x27 example, I would be saying to myself "seven threes are
> > twenty-one" for the first step.
> Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7), which is
> the same as 20 squared minus 7 squared, which is 400 minus 49, which is 351.
> One reason why I was always good at mental arithmetic was that I could
> usually see several different ways of performing a calculation and would
> usually pick the most convenient one.
"Dr Nick" wrote in message news:87a9uk1vcb.fsf@temporary-address.org.uk...
> "Guy Barry" <guy.ba...@blueyonder.co.uk> writes:
> > Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7),
> > which is the same as 20 squared minus 7 squared, which is 400 minus
> > 49, which is 351.
> Oh that's good.
Do many people use the "difference of squares" method for multiplication? I can't remember where I learned it - I was taught that (a+b)(a-b) is a^2-b^2 quite early on, but I don't remember being taught it explicitly as a method of calculation. I remember I once had to set a question for the rest of the class and asked them to multiply something like 993 x 1007 without the aid of a calculator. I don't think many of them got it.
If you memorize the squares of numbers from 1 to 25 (which isn't hard), there are simple rules that allow you to derive the squares of numbers up to 100. Once you've learned those, you can use "difference of squares" to multiply any two numbers below 100, as long as they're both odd or both even. If one's odd and the other's even you can reduce one of the numbers by 1 and then add the other on. So for (e.g.) 27 x 38 I'd calculate 27 x 37, which is 32 squared minus 5 squared or (1024-25) = 999. Add 27 to give 1026.
> I'd do 12x24 = 2x12x12 = 288. Plus another 24, plus
> 13x(27-24) = 39. Total = 351
So you think in the duodecimal system?
> For multiplications like this, dividing into separate rectangles is the
> way I've taught myself to do it.
My method varies depending on the numbers involved. If you'd asked me 13 x 25, for instance, I'd have done 1300/4 = 325. If it had been 13 x 26, I'd have done 2 x (13^2) = 2 * 169 = 338. I think the skill lies as much in identifying which method to use as in the actual calculation.
>>> In Peter's 13x27 example, I would be saying to myself "seven threes
>> are twenty-one" for the first step.
>> Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7),
>> which is the same as 20 squared minus 7 squared, which is 400 minus
>> 49, which is 351.
>Oh that's good. I'd do 12x24 = 2x12x12 = 288. Plus another 24, plus
>13x(27-24) = 39. Total = 351
13 x 27 = 13 x (3 ^ 3)
= 13 x (3 x 3 x 3)
= (13 x 3) x (3 x 3)
= 39 x 9
= (40 - 1) x 9
= (40 x 9) - 9
= 360 - 9
= 351
>On Tue, 13 Nov 2012 13:15:45 +0000, the Omrud <usenet.om...@gmail.com>
>wrote:
>>I had no choice but to learn my tables by rote - we chanted them in >>class when I was about five or six. Thank goodness for that, I say.
>Absolutely. And children usually like learning things by heart,
>anyway: their play and socialisation require it.
Yeah...give 'em something repetitive and meaningless to repeat until they're
numb between the ears...kids love that...and if you can throw in some kind of
irrelevant association to a set of colors, do that too, because they just eat up
that kind of stuff....r
>> >> "Show your work" to me means just show your answers. "Show your
>> >> working (out)" means explain how you got from the question to that
>> >> answer and prove that you didn't copy it from Perkins.
>> > That doesn't prove you didn't copy it. You could have copied his
>> > working as well.
>> Yes but it's much, much more obvious. Trust me, I've marked
>> undergraduate lab work.
> There's an art to copying. You don't copy it verbatim. You rework
> things slightly and phrase it differently. Sometimes it can even be a
> good idea to introduce deliberate mistakes if you're under any
> suspicion. I've done it a few times and never been found out. (I used
> to let people copy my work as well, so I didn't feel bad about it.)
I don't think I would have enjoyed (or felt entitled to) my grade had I gotten it by copying, even if I weren't caught.
From the other side of the desk - a LOT of copying is blatantly obvious, largely because it's word-for-word. If you know your students - a good bit of the rest stands out because it's so atypical of said student's usual work. That's harder to prove, though.
"Cheryl" wrote in message news:aghdbcFktqrU1@mid.individual.net...
> On 2012-11-14 4:27 AM, Guy Barry wrote:
> > There's an art to copying. You don't copy it verbatim. You rework
> > things slightly and phrase it differently. Sometimes it can even be a
> > good idea to introduce deliberate mistakes if you're under any
> > suspicion. I've done it a few times and never been found out. (I used
> > to let people copy my work as well, so I didn't feel bad about it.)
> I don't think I would have enjoyed (or felt entitled to) my grade had I > gotten it by copying, even if I weren't caught.
Maybe I shouldn't call it "copying", then. I certainly wouldn't have been able to complete one particular project in my Master's degree if I hadn't been able to look at another student's work. (It was an area I wasn't remotely interested in, and I just wanted to get through that part of the course quickly so that I could concentrate on the areas that I wanted to.) But it was all in my own words.
> From the other side of the desk - a LOT of copying is blatantly obvious, > largely because it's word-for-word. If you know your students - a good bit > of the rest stands out because it's so atypical of said student's usual > work. That's harder to prove, though.
Well they haven't done it very well then. I never copy things blindly. I work through the problem myself, but use the other person's solution as a guide to how to do it. At least I learn something that way.
>>>> In Peter's 13x27 example, I would be saying to myself "seven threes
>>> are twenty-one" for the first step.
>>> Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7),
>>> which is the same as 20 squared minus 7 squared, which is 400 minus
>>> 49, which is 351.
>> Oh that's good. I'd do 12x24 = 2x12x12 = 288. Plus another 24, plus
>> 13x(27-24) = 39. Total = 351
> 13 x 27 = 13 x (3 ^ 3)
> = 13 x (3 x 3 x 3)
> = (13 x 3) x (3 x 3)
> = 39 x 9
> = (40 - 1) x 9
> = (40 x 9) - 9
> = 360 - 9
> = 351
On 14 Nov 2012 00:43:38 -0800, R H Draney <dadoc...@spamcop.net>
wrote:
>Mike L filted:
>>On Tue, 13 Nov 2012 13:15:45 +0000, the Omrud <usenet.om...@gmail.com>
>>wrote:
>>>I had no choice but to learn my tables by rote - we chanted them in >>>class when I was about five or six. Thank goodness for that, I say.
>>Absolutely. And children usually like learning things by heart,
>>anyway: their play and socialisation require it.
>Yeah...give 'em something repetitive and meaningless to repeat until they're
>numb between the ears...kids love that...and if you can throw in some kind of
>irrelevant association to a set of colors, do that too, because they just eat up
>that kind of stuff....r
You _don't_ give 'em anything meaningless, and you don't let them get
numb between the ears or anywhere else. Repetition is a learning tool:
it's how they learn all the things we don't teach them, including the
things we don't want them to learn. It's how grown-ups learn things,
too.
>>>>> In Peter's 13x27 example, I would be saying to myself "seven threes
>>>> are twenty-one" for the first step.
>>>> Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7),
>>>> which is the same as 20 squared minus 7 squared, which is 400 minus
>>>> 49, which is 351.
>>> Oh that's good. I'd do 12x24 = 2x12x12 = 288. Plus another 24, plus
>>> 13x(27-24) = 39. Total = 351
>> 13 x 27 = 13 x (3 ^ 3)
>> = 13 x (3 x 3 x 3)
>> = (13 x 3) x (3 x 3)
>> = 39 x 9
>> = (40 - 1) x 9
>> = (40 x 9) - 9
>> = 360 - 9
>> = 351
>> ....r
>You people make me sick.
Me too. Particularly as it's just twenty thirteens plus seven
thirteens. Mountains are here being constructed from molehills.
>> In Peter's 13x27 example, I would be saying to myself "seven threes
>> are twenty-one" for the first step.
> Here's how I'd do 13 x 27 in my head: it's (20 - 7) times (20 + 7),
> which is the same as 20 squared minus 7 squared, which is 400 minus 49,
> which is 351.
I'd have a heart attack if I had stuff like that going on in my head.
The only mental arithmetic I could do quickly was with darts scores, and I don't play any more.
> On Nov 14, 2:16 am, Robert Bannister <rob...@clubtelco.com> wrote:
>> On 13/11/12 6:05 PM, Guy Barry wrote:
>> doing sums. In Peter's 13x27 example, I would be saying to myself "seven
>> threes are twenty-one" for the first step.
> Oh, I see, long multiplication. Wouldn't it be easier to add 270 to 81
> (81 arrived at by subtracting 9 from the 90 you get from multiplying
> 30 by 3)?
>> On Tue, 13 Nov 2012 13:15:45 +0000, the Omrud <usenet.om...@gmail.com>
>> wrote:
>> >I had no choice but to learn my tables by rote - we chanted them in
>> >class when I was about five or six. Thank goodness for that, I say.
>> Absolutely. And children usually like learning things by heart,
>> anyway: their play and socialisation require it.
> I don't recall that most of the children I was at school with enjoyed
> learning their times tables. (I knew mine before I went to school, but
> then I was a precocious little brat.)
> Here's something I've never understood. We don't teach addition tables
> by rote, and yet children usually seem to pick them up all right. How's
> that?
Do they? I wasn't aware of that. We certainly did learn which combinations of two numbers made ten - I can remember us learning that when we were about eight or nine. Later, I quickly learnt the combinations for fifteen for crib.
>> "Show your work" to me means just show your answers. "Show your working
>> (out)" means explain how you got from the question to that answer and
>> prove that you didn't copy it from Perkins.
> That doesn't prove you didn't copy it. You could have copied his
> working as well.
He used to cover his working in blots deliberately.
> "Show you're working" would mean "demonstrate that you are currently doing
> something." "Show your work" means show the process by which you arrived
> at your answer. "Show your working" would be an obvious typo for "Show
> you're working."
They would also sound different out here on the Left Coast.
