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Finger counting

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320318.  Sat Apr 19, 2008 3:59 pm Reply with quote

mckeonj wrote:
and July -3 is May.

In what sense? :-s

320322.  Sat Apr 19, 2008 4:03 pm Reply with quote

The complements are aparrently now called "number bonds", by school type people.

320363.  Sat Apr 19, 2008 5:18 pm Reply with quote

Oh, goody, one of my hobby horses.

I never came across 'compliments' or 'number bonds' until I helped out in an adult numeracy class. Having been made aware of these ideas the whole concept of numeracy and its relevance to todays world became questionable. I see no need for anyone to be able to instantly give the result of 4 times 7 or being able to use paper and pen to discover a value for 27 times 36.

(An aside, there may well be an affect on educational attainments that learning such skills develops, but I'm not aware of any definitive research to support this.)

Oh, and don't get me started on the national curriculum for numeracy, which has room for improvement.

320365.  Sat Apr 19, 2008 5:26 pm Reply with quote

Ah, Southpaw, that does make more sense. A mapping from digits to letters, then padding to make words, eh? Sounds odd to me, but I guess it's just a matter of practise. Seems like it'd get a bit awkward with repeated digits, though.

How about this for a compromise: convert the number to binary, then map 0s to vowels and 1s to consonants. You couldn't pad the word of course, but you'd have a fair few choices for most combinations. Repeated digits would still be a bit awkward though. Hmm.

As for these 'complements', I don't think I've ever heard them called that. Or anything, for that matter. Actually the first thing that sprang to mind was conjucates, though that's a rather different thing (and of less use to most people).

Can't do simple things with weekdays or months quickly though. It takes me ages just to remember what order the months come in. And how many days are in each. Heck, I can't even do alphabetical order quickly.

320448.  Sun Apr 20, 2008 3:40 am Reply with quote

npower1 wrote:

Oh, and don't get me started on the national curriculum for numeracy, which has room for improvement.

MrsP writes:

I understand there are problems with the National Numeracy Strategy as it didn't give you much scope for cross-curricular linking. The new Primary Framework seems to be approaching things differently.

320486.  Sun Apr 20, 2008 4:58 am Reply with quote

Simon and MrsP,

I did a Google search on 'Primary Framework Numeracy'. I found what looks like an official site. I was not impressed.

(1) it mixes numeracy and mathematics - I consider these as totally separate. Yes, you can learn some maths from becoming numerate but the objectives of each are different. Becoming numerate helps in dealing with the every day world; learning maths is learning logical thinking.

(2) it is aimed at year 6. By this age (10/11 years old) most children should have achieved fluency in numeracy.

320625.  Sun Apr 20, 2008 9:40 am Reply with quote

npower1 wrote:
I see no need for anyone to be able to instantly give the result of 4 times 7 or being able to use paper and pen to discover a value for 27 times 36.

And I see no particular reason for them to know who William the Conqueror was, nor when World War II took place. And why bother learning where China or Paris are on a map? What good will reading Shakespeare do you? Should you really bother studying where to put apostophe's? Who really needs to know the laws of gravitation?

Any subject is going to look useless if you boil it down to a list of silly facts. That doesn't mean there's no reason to learn those facts, just that the facts themselves aren't really the point.

As for mixing numeracy and mathematics, as far as I can recall school level maths hardly contains anything I would recognise as actually being mathematical - it's nearly all about numeracy, at least up until the end of GCSEs. You can't really do maths until you've comfortably numerate, so it's hardly a surprise. I think a spot of number theory would fit nicely, but nobody asked me.

My point, if I can remember it, is something along the lines of, 'school maths may be useless, but that's not the point, so who cares?'

323747.  Thu Apr 24, 2008 8:22 am Reply with quote

I didn't know the 99 one, but I'll definately use it with some of my lower ability children who still have trouble with numbers over 10. Thanks! :-)

Mrs.P, dear Mrs.P,

You've made my day.
I'm so pleased to think that something I found "QI" is going to be used to help children who get stuck with their bigger numbers. Curiosity is nothing if the stuff you pick up can't be used to create fun ways to help people learn. Like I said; how I wish someone had told me about counting to 99 on my fingers when I was at school. It may not open the flood gates of mathematical genius, but it really will help dispel the fear that some children have of big numbers and how they work. It puts large numbers literally in the palm of their hands, and that will give them confidence.

Hurray for Mrs.P.

356794.  Mon Jun 09, 2008 9:45 am Reply with quote

Southpaw wrote:
Yes, though perhaps I wasn't precise enough in my naming it the peg system. What I actually mean is the Major Mnemonic System, a form of peg system. This involves assigning a (logically suitable) letter to the numbers 0-9, then using these letters to form a memorable word or set of words. Par example:

0 - z (and by extension s)
1 - l
2 - n (as n has 2 downstrokes)
3 - m (as m has 3 downstrokes)
4 - r (fourrrr)
5 - f/v
6 - b
7 - T
8 - gh and j
9 - g

For example, I happen to know that the hectarage of the parish of Chailey in West Sussex is 2491.32ha. I remember this with the phrase 'Energy Lemon', derived from NRGLMN.

Personally I find this kind of word play/visualisation easier to remember than binary, though of course it's horses for courses.

I remember things by 'remembering' them or if that may not work i use a pen and paper to make marks (eg numbers) which i can then later 'translate',

hope that helps


510505.  Mon Feb 23, 2009 7:25 am Reply with quote

mckeonj wrote:
There is another finger counting method taught in India by which the thumb and fingers of one hand can be used to register and operate on numbers up to fifteen; by counting phalanges.
A phalange is one section of a finger or thumb.
Pretend for the moment that the thumb is the first finger and has three sections, not two; also pretend that you don't need to calculate with numbers less than three.
Hold up one thumb for 3, and use the tip of that thumb as a pointer to count the phalanges on the index finger; 4, 5, 6; middle finger; 7, 8, 9; ring finger 10, 11, 12; ear finger; 13, 14, 15. Learn and remember the numbers for each phalange.
Now you have a built in calculator.
A couple of side notes:
A calculus is a pebble, as kept in the shepherds purse.
Herd animals are counted in sets of twenty; a score on the tally.
Shepherds use a set of counting words, such as 'yan tan lethery pethery pimp'; this was explored in an earlier thread with the interesting title bumfit post 185154

I used when I was a small kid (and didn' t like math too much :D ) a tool for counting, adding and solving small math problems. Arithmetic, in general. It was about a small machine (with horizontal "wires" )with small balls displayed on each one of them. When doing the math addition of natural numbers, the kid would have moved, from right to left, as many balls as possible, to reach the sum. It was a practical math teaching for a 10 years old kid. :D

510838.  Mon Feb 23, 2009 5:44 pm Reply with quote

You wouldn't need paper and pencil for 27 times 36 - it's just 36 times 10 twice plus 36 times 5 (half the amount) once, plus 72, so 360 plus 360 plus 180 plus 72, which is pretty straightforward.

510865.  Mon Feb 23, 2009 6:15 pm Reply with quote

Surely you can count to over 1000 just using your fingers and thumbs.

I've just counted to 33 with one hand.

Binary (one of those weird bases) isn't as much fun though.

521819.  Sat Mar 14, 2009 11:45 am Reply with quote

I never heard of those compliments, but i used something similar to learn my 9 times table when a was younger.

You may have noticed that every multiple of 9's digits add up to 9
e.g. 9x8 = 72 7+2 = 9

if you can figure out the 10s (x-1) then you can figure out the units


522760.  Mon Mar 16, 2009 6:07 am Reply with quote

There are only 10 types of people in the world - those who understand binary and those who donīt.
It may be an old joke, but I like it because it can only be told in written form - not by speech.

Hooray, indeed, for Mrs P (320448 and 323747), but I canīt help thinking that her spelling could be better. If you can pronounce "infinity" and "finite" as most people do, then you should have no trouble spelling "definitely", and all the other similar words derived from "finire". I justify my pedantry on the grounds that she is a teacher, and she may confuse young minds. :-)

I would like to agree with those who say that learning stuff is easier, generally, than learning lots of special short cuts. I mean, Jennyīs example is not exactly straightforward, is it? It works for 27x36, but for 43x73 youīd have to do something different. 27x36 can be factorised to 9x9x3x4, which is 81x12, which is 810+162 =972.

This forum is one of the best I have come across. Mistakes are few and far between. (I mean in grammar, spelling and punctuation.) My opinion is probably unpopular in many quarters, where itīs the message that counts. But I feel that posts littered with mistakes are a sign of lack of respect of the writer for himself and for the reader. The attitude is, "This will do. I canīt be bothered to hit the "Preview" button and check for mistakes," which means you arenīt bothered about what people think of you (after all, youīll never meet them). And it means, "I donīt care if you do have to read bits twice to understand what Iīm writing about. Youīll get there in the end." When I read: "Your reading too many trashy novels," I have to go back and read it again, because I am expecting something like, "Your reading must be improved." Some rules of grammar can be ignored, such as not beginning a sentence with a conjunction or ending one with a preposition, and not splitting infinitives, because they make little sense (to me, perhaps). Some rules of punctuation are preferred by some and not others - the Oxford comma, for instance, and punctuation concerned with quotation marks at the end of sentences. But I believe that the correct use of apostrophes is quite straightforward and does perform a useful function. And spelling is fairly fixed by now. Itīs "complementary" numbers, not "complimentary". Think of them as "completing" the sum to 10, and it should not be a problem. Am I being too judgemental?

522849.  Mon Mar 16, 2009 11:40 am Reply with quote

grabagrannie wrote:
Am I being too judgemental?

Not by the standards of this forum, but on the other hand if you take it too seriously you're likely to be very disappointed.


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