1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.
  2. Hi Guest, welcome to the TES Community!

    Connect with like-minded education professionals and have your say on the issues that matter to you.

    Don't forget to look at the how to guide.

    Dismiss Notice

2013 Numeracy results. Is 5.00 not a whole number??

Discussion in 'Primary' started by emillers, Jun 28, 2013.

  1. ShadowMan

    ShadowMan New commenter

    Nomad - don't be so silly. Is 5.00 a whole number or not?
     
  2. mystery10

    mystery10 Occasional commenter

    Yes it is. The more I think about this question the sillier it all seems. Maybe it should have said round to 0 d.p. Ito be crystal clear. Losing two marks seems tough. Wonder what happened in the trials for this item?

    What was the exact question wording?
     
  3. nomad

    nomad Star commenter

    Oh dear. There speaks the voice of mathematical ignorance.

    A decimal may have both a whole-number part and a fractional part. The whole-number part of a decimal are those digits to the left of the decimal point. The fractional part of a decimal is represented by the digits to the right of the decimal point. The decimal point is used to separate these parts.

    So, to answer the question (again...), the digit 5 in 5.00 is the whole number while the .00 is the fractional part of that number. The fact that the value of the .00 part is zero does not stop from being the fractional part - it is just that it is a fractional part with a zero value.

    in itself, but it contains the whole number 5 with a zero value fractional part.

    To a laymen that may not be important but to a mathematician it is.

    is a difference) between the numbers 5 and 5.00

    To give an approximate parallel in English, that fact that a group of words which make sense when read in sequence start with a capital letter and end with a full stop does not make it a sentence. It may be a sentence, but then again it may be a clause or a gerund. To a layman it may not be important, but to a language teacher it is.

    Believe me, 5.00 is not a whole number in itself, but the fact that it is not has little relevance to whether a Year 6 pupil knows how to round numbers up.
     
  4. asnac

    asnac Lead commenter

    The actual paper is not online yet. Can anyone provide the exact wording of this question, or a photo of the page?
     
  5. ShadowMan

    ShadowMan New commenter



    If it contains a zero fractional part then it does not have a fractional part and is a whole number. That's what zero means and that's what whole number means.



    Please explain what is the difference between 5 and 5.00 - other than the fact that it takes longer to write the second, identical number.



    Incidentally, you may like to know you are not talking to a layman.
     
  6. ShadowMan

    ShadowMan New commenter

    Presumably, if your pupils are asked the following:

    3.2 + 4.5 Write your answer as a decimal.

    You would mark 7.7 as incorrect because they have written it as a whole number and a decimal instead of just displaying the decimal part. What nonsense.
     
  7. nomad

    nomad Star commenter

    ShadowMan, I have already explained the difference between 5 and 5.00

    A decimal may have both a whole-number part and a fractional part. The whole-number part of a decimal are those digits to the left of the decimal point. The fractional part of a decimal is represented by the digits to the right of the decimal point. The decimal point is used to separate these parts.

    I suspect that I am.


     
  8. nomad

    nomad Star commenter

    "3.2 + 4.5 Write your answer as a decimal."

    Incorrect use of language. Layman's language, in fact. It should be "write your answer in whole numbers and decimals" or "Write you answer in decimal notation". However, it would not be necessary to ask them to do this, since the requirement to add 3.2 and 4.5 implies that an answer in whole numbers and decimals is expected.
     
  9. nomad

    nomad Star commenter

    Anyhow, back to the KS2 SATs paper.

    I suspect that, if the examiner wanted the pupils to demonstrate whether they could round up to the nearest whole rather than demonstrate that they could tell the difference between a whole number and a whole number with a decimal fractional part, they should have used money as an example.

    "Round £5.01 to the nearest whole pound" would, in all likelihood, have produced more £5 answers than £5.00 answers from the pupils, and queries from their teachers.
     
  10. Milgod

    Milgod Established commenter

    Although Nomad is putting across valid sounding points I think Shadowman summed it up.

    If there is no fractional part to the number (5.00) then it doesn't have a fractional part. It is therefore a whole number.

    Even if you write the number 5 by itself, the .000000000000 and so on are still there. We just didn't write them. It doesn't change anything.
     
  11. nomad

    nomad Star commenter

    Sorry, Milgod, but this is incorrect. 5.00 DOES have a fractional part, but of zero VALUE.

    Take the year in which you joined TES - 2006. That figure does have a hundreds part and it does have a tens part, but both are of zero value. There is a difference between 'does not exist' and 'does exist but has a value of zero' in mathematics.

    Whole numbers are shown on the left hand side of the decimal point and ONLY on the left hand side of the decimal point. Hence 5 is a whole number whereas 5.00 is not (technically), since 5.00 is shown to have a fractional part albeit of zero value.

    All of this may mean bugger all to a layman, nor indeed to an 11 year old child. However, to a mathematician it does make a difference.

    When I am completing the school's monthly tax returns for the IR, I cannot ignore a purchase because, as a school, we paid no VAT on that purchase. I have to show that purchase with a tax return of 0% VAT. Again, it may mean bugger all to a layman, nor indeed to a headteacher. However, to an IR accountant it does make a difference.

    Basically, the difference between 5 and 5.00 is mathematical semantics. The value of each may well be the same but the numbers and the way they are written and what this implies is different. In a similar way, albeit rather clumsy, the value of the square root of 9 and the number 3 may well be the same, but the numbers themselves are different.


     
  12. ShadowMan

    ShadowMan New commenter

    You may have your own special definition of 'decimal' if you choose. But every definition of 'decimal' I have looked at in the last few minutes regards 7.7 as a decimal. It is not at all confusing to regard it as such. To claim that 7.7 is not a decimal but is a whole number and a decimal is pedantic beyond reason.

    Likewise, to claim that 5.00 is not a whole number but is a whole number with a fractional part is even more absurd.

    It is whole number with a fractional part that happens to have a value of zero. And what is a whole number: a number with a zero fractional part.

    I have never heard of your own special definition of whole number i.e. numbers written to the left of the decimal place. That's just silly.
     
  13. ShadowMan

    ShadowMan New commenter

    So is £5.00 not whole pounds?
     
  14. ShadowMan

    ShadowMan New commenter

    If you cannot see the dissimilarity between the relevance of a '0' in 2006 and a '0' in 5.0000000000000 then you, my friend, are a layman.
     
  15. nomad

    nomad Star commenter

    Poor lad!

    http://www.mathgoodies.com/lessons/decimals/introduction.html read the section "So why do we use decimals?" There is a whole host of other mathematical sites out there with the same definition.

    Shadowman, I am not suggesting that you understand the difference. You clearly do not and, I suspect, are not intellectually equipped to do so. What you can try to do is appreciate that mathematicians do not consider 5.00 to be a whole number by itself, but consider it to be a whole number (5) together with a zero-value fractional part.

    In any event, when rounding to whole numbers, the fractional part and the decimal point are not shown, since these do not form part of a whole number.

    Just for you... http://www.dummies.com/how-to/content/how-to-round-decimals.html Note the instruction on line four.






     
  16. harsh-but-fair

    harsh-but-fair Star commenter

    Now I remember why so many children get turned off maths at school ...
     
  17. nomad

    nomad Star commenter

    I was trying to demonstrate a mathematical point to Milgod, but I can see that you have not appreciated the difference between 'does not exist' and 'exists, but has zero value'.

    For what it is worth, Shadowman, I am a Masters degree-holding mathematician. I do, actually, know what I am talking about whereas I know that you do not.

    Now, to get back to the SATs papers, the marking schedule is correct, although I cannot see the necessity of imposing this level of rigor on Year 6 pupils.


     
  18. ShadowMan

    ShadowMan New commenter

    You said:

    And your website: http://www.mathgoodies.com/lessons/decimals/introduction.html says:

    A decimal is any number, including whole numbers, in our base-ten number system.

    One would appear to be contradicting oneself.


     
  19. nomad

    nomad Star commenter

    Indeed, Harshy. If I had taken this year's Year 6 SATs as an 11 year-old pupil and been told that I had failed to cross the Level 4/5 threshold because the examiner did not consider 5.00 to be an appropriate answer to rounding 5.01 up to the nearest whole, I should probably be put off the subject for life. An answer of 5.00 is quite good enough at the age of 11.
     
  20. ShadowMan

    ShadowMan New commenter

    Incidentally, your second site, for dummies, also uses an 'incorrect use of language'. Dear oh dear.
     

Share This Page