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

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

  1. SansAtout

    SansAtout New commenter

    We have seen this before. Look at the mark scheme for the 2005 Year 5 Optional Test Paper - Q3, Paper B. The children had to round 7.75 and 5.51 to the 'nearest whole number'. The mark scheme says "Do not accept 10.00 OR 10.0 OR 8.00 OR 8.0". Admittedly, they had given an example of 6.01 being rounded to 6, so my Year 5s usually get this right. I do point out to them that the whole numbers are conventionally not written with a decimal component. Similarly, the 2006 Y6 test (Paper B, Q20) had a rounding question where the mark scheme again specified, "Do not accept 129.0 OR 7492.0 OR 51.0 OR any other equivalent answers with zeroes after the decimal point."

    And Nomad has explained the difference. In the context of rounding - for example, in real life measurements - 5.00 is not the same as 5. 5.00 is a number in the range 4.95 to 5.05 (exclusive), whereas 5 is a number in the range 4.5 to 5.5 (exclusive).

    I agree with the posters that it seems very pedantic to deny a mark to Y6 children when they clearly have a decent understanding of the concept being tested (rounding), but the mark scheme is correct, and we can't say we weren't warned.
  2. SansAtout

    SansAtout New commenter

    And of course, you've spotted my error - 5.00 in the context of rounding and measurement is a number in the range 4.995 to 5.005 (exclusive).
  3. nomad

    nomad Star commenter

    Not at all, Shadowman.

    You suggested the line "Write your answer as a decimal". As a decimal what?

    If you used the word as an adjective and mean "relating to the denary number system" then the line is redundant. The child must assume that the answer will be as a decimal number because the denary number system is the default in normal mathematics. Unless you had told the child that the question was asked in octal or hexadecimal (for example) then the instruction to "Write your answer as a decimal" is unnecessary. The child would automatically write the answer as a decimal number (7.7) .

    On the other hand, if you used the word as a noun and mean "... as a decimal [fraction]" then the line is incorrect as the answer cannot be given as a decimal fraction alone, but only in the form of a whole number and a decimal fraction.

    Mathematical semantics, again.
  4. nomad

    nomad Star commenter

    I did, actually, SansAtout, but since you are talking mathematical sense otherwise, I was not going to point it out.

    To be honest, as I suggested before, I really do not think that the pupils need to be given this level of rigor at the age of 11.

    Can they round numbers? Yes? Fine. Can they tell the difference between a whole number and a decimal fraction? Yes? Fine. Can they give an answer to a given degree of accuracy? Yes? Fine. But lets keep all three types of question separate.
  5. harsh-but-fair

    harsh-but-fair Star commenter

    No, in REAL LIFE 5.00 is the same as 5 - Only Maths teachers spend hours arguing about it.
  6. nomad

    nomad Star commenter

    To a mathematician, that IS 'real life, Harshy. [Goes back to watching 'The Big Bang Theory']
  7. ShadowMan

    ShadowMan New commenter

    I see.

    So the answer to Q3 on your site: http://www.mathgoodies.com/lessons/decimals/introduction.html is 'none of them' since none are decimal [fractions].

    Incidentally, you have not yet answered my question about £5.00. Is £5.00 five whole pounds?
  8. harsh-but-fair

    harsh-but-fair Star commenter

    I'm beginning to worry that you might be my son now, Nomad!
  9. cassandramark2

    cassandramark2 Lead commenter


    I feel very sorry for those borderline pupils who will be denied a higher level. I'd also feel incredibly frustrated were I to work to in a school where the floor target was missed.

    After noting the problem yesterday, I immediately mentioned it to my partner (secondary maths bod who had spent years marking KS3 papers) and he agreed that the question was flawed, in that the marking did not give credit for understanding of the concept but that, theoretically, the award of zero marks was correct.

    He thought it extremely harsh though, particularly when you see what dross is acceptable for the award of a mark on a foundation GCSE paper.

  10. nomad

    nomad Star commenter

    I agree, Cassandramark2. Your OH is right, as are several of my colleagues who are concerned that some Year 6 in their schools pupils have been short-changed this year, despite the mathematical correctness of the marking scheme. Pupils may well have given an answer which is correct in the concept being tested, but have been marked wrong on a technicality.

    I don't mark GCSE papers but do 'A'-Level maths papers, and those too seem to have an amazingly generous margin of allowable leeway in the award of marks.
  11. Milgod

    Milgod Established commenter

    At least there's some bloomin discussion going on for once. This place has been dead recently. Stupid TES with their stupid changes.
  12. ShadowMan

    ShadowMan New commenter

    Does anyone know if £5.00 is five whole pounds? Nomad is not answering. I'm about to go to Waitrose and I don't want to look a fool.
  13. Even the Royal Mail would have failed this question, I wonder what they are thinking including those decimal places on their £5.00 stamps? Clearly they should have rounded since it's a completely different number.


    Clearly 5.00 is equivalent to 5 in terms of value. And so it should have been accepted for at least a mark, especially when all of the numbers to be rounded also had 2 decimal places.

    So frustrating the impact a couple of mathematically insignificant 0s will have on that child who worked so hard! I never thought so much debate would be had on this matter!
  14. nomad

    nomad Star commenter

    As I have already pointed out (as have a couple of other posters), 5 and 5.00 are numerically equal in terms of value, although in terms of mathematical notation and mathematical concept are not one and the same. So, for the purpose of everyday shopping, since £5 and £5.00 have exactly the same monetary value, you will be ok when you to Waitrose.

    As far as I am aware, mathematicians tend not to moonlight behind a Waitrose till on Saturday afternoons, so you will not be laughed at for not knowing the difference.

    A bit too late for that, I'm afraid.
  15. ShadowMan

    ShadowMan New commenter

    I think it was me that pointed it out actually.

    But that's not what I asked.

    Is £5.00 five whole pounds?

    If I am asked what £2.50 + £2.51 to the nearest whole pound is, can I write £5.00?

    It's OK, Nomad. Your contempt for those you consider to be your intellectual inferior has already been established.
  16. nomad

    nomad Star commenter

    No, you cannot.

    £2.50 + £2.51 to the nearest whole pound is £5. You do not give any further information after the whole number. So, it is £5, not £5.00. Now, to a layman there is no difference, since the value of £5 and £5.00 are the same. To a mathematician, however, the £5 is the only correct answer, since the £5.00 gives not only the required whole number but also an unnecessary £0.00 decimal fraction.

    Not at all.

    The trouble is, ShadowMan, that you came onto this thread, arguing in a rude and aggressive manner from a position of ignorance. Now, if you do not know how to throw a punch, you do not get into the ring with those who do. Or, in the case of these fora, if you want to engage in an argument, you should make sure that you know what you are talking about. In this case you clearly do not! I am sure that you have areas of knowledge of which I am ignorant, but I would not engage in an argument with you until I was better informed. However, if you want to come onto these boards all mouth and no trousers, then you take what you get.

    A word of advice. If you not, then shaddup, listen and learn before doing so.

    Now, can we get back to the effect that this apparently silly marking schedule has had on these Year 6 pupils?
  17. ShadowMan

    ShadowMan New commenter

    Calling someone silly is hardly rude and aggressive. I can only assume you must be deeply insecure about your knowledge. And possibly rather lonely.
  18. tafkam

    tafkam Occasional commenter

    I can't add much to this debate other than the fact that I agree wholly and entirely with Nomad.

    5.00 is equivalent to, but not the same as, 5.

    5 is a whole number.

    Personally, it seems an unreasonable distinction to make on a question on a KS2 test, but it's is mathematically accurate.

    Then again, if it teaches KS2 teachers to teach 'whole numbers' as being numbers without fractional parts, then maybe it's no bad thing.

    Interestingly, I would say that there are "interesting" mathematical debates about whole numbers (are negatives whole?; is zero a whole number?, etc.) , but that this particular example is not one of them.

    It might not make it seem any less unfair, but it's true.
  19. So - has anyone written to the marking authority yet to complain?

    This is an example of the world gone mad.

    Mark 5.00 correct and be done with it.

    Could anyone guarantee that all Y6 teachers would know these differences?

    I certainly did not.

    I wonder what percentage of Y6 teachers will have taught these (splitting hairs in the circumstances) differences?

    'Pedantic' is an understatement I suggest.
  20. Milgod

    Milgod Established commenter

    Still not sure I see the difference. Haven't found one reference site that deals with the concept of there being zero 'fractional parts' to the number.

    Surely if you write the number 5, the .00 is still there it exists even if you write it or not. Not wanting to get into an argument again, but if somebody can find an actual reference that deals with this (not one that refers to fractional parts when there is an actual amount) then I would appreciate it.

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