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

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

Correct.

However, whole numbers exist ONLY to the left of the decimal point. So, if you have been instructed to round a number with decimal fractions to the nearest whole number, you only show whole numbers. The .00 still exists but in order to comply with the whole number instruction you do not show it.

2. ### frustumStar commenter

I think this one actually illustrates the difference. Answering orally, you might well say "five pounds", but you would definitely not say "five pounds and no pence" - because you know perfectly well that the accurate answer does involve pence.

I agree with others that 5 is correct and 5.00 is incorrect, and also that it's a little harsh to penalise this at KS2. It's the sort of thing that on internal KS3 tests I would usually have given half a mark.

The existence of previous questions with the same markscheme suggests that maybe experienced year 6 teachers shouldn't have been too surprised. (I wonder, though, if some teachers mark past paper questions without reference to the markscheme, and so miss out on picking up on subtleties they weren't aware of.)

3. ### emillers

Thank you for all your replies! I was away at the weekend and didn't realise how much of a debate I had started...

4. ### tafkamOccasional commenter

I think you'll find that any reference to "whole number" in a mathematical dictionary will normally refer to the natural numbers (i.e. those that we consider to be the counting numbers). We never count 5.00, always 5

http://www.mathsisfun.com/definitions/whole-number.html
http://www.mathsdictionary.net/home/w
http://www.amathsdictionaryforkids.com/dictionary.html
http://www.wolframalpha.com/input/?i=whole+number&a=*C.whole+number-_*MathWorld-
http://users.erols.com/bram/Udictionary.html
http://www.mathsphere.co.uk/resources/MathSphereMathsDictionary.htm

Perhaps teachers would prefer that the test ask instead for an integer?

5. ### HSXOccasional commenter

Nomad makes perfect mathematical sense. The question is flawed, but the mark scheme appears to be clear however and there are precedents for this type of question, as has been pointed out. Some of this thread has been written with incredible knowledge (as a masters level mathematician myself I've loved the debate) but agree that key stage 2 children shouldn't have this weight of accuracy needlessly placed before them. However I've been uncomfortable reading this at times - being unnecessarily nasty to others really isn't helpful or constructive. If I were you nomad, and you've made your point very clear in a number of ways, I'd let this drop for now as it's on the verge of becoming unhelpful.

6. ### CerviniaOccasional commenter

Maths can be amazing, fun and a joy to teach/learn. We really do the subject and kids an injustice when we introduce such pedantry and levels of mathematical accuracy to 11 year olds.

7. ### HSXOccasional commenter

Just remembered some else I was going to say nomad. To quote Mary Cooper (series 1, episode 4): Now you listen here, I have been telling you since you were four years old, it?s okay to be smarter than everybody but you can?t go around pointing it out.

Sheldon: Why not?

Mrs Cooper: Because people don?t like it.

Yes, Mummy.

Sorry.

I'd go with the mark scheme - although if available I might give something (but not much) for 5.00.

The reason I would be harsh on 5.00 is that it is expressed to the same number of decimal places as is the original 5.05 !

Anyone who writes the rounded value as '5.00' obviously has not realised what rounding is for - for what purpose it is done.

The purpose is to get rid of some decimals, i.e. to shorten the expression of the number so it easier to handle.

If you continue to write the same number of decimals as in the original you've approximated - but you haven't rounded.

Not a reasonable assumption - the contrary is true in fact. Year 6 children will have been correctly taught that 5.00 is identical in value to 5. A child who understands the place value of decimals and understands the process of rounding, might well write 5.00 unless his/her teacher has specifically taught them not to do so. This is why so many posters are bemused by the mark scheme as it doesn't acknowledge the understanding of these children.

11. ### bears1404

Given the level of debate and disagreement on here, is it even realistic to expect primary maths teachers to have this level of understanding? I'm a primary maths specialist and have contacted several colleagues today, all maths leaders at primary level, plus couple of county advisors. No one was 100% sure. Clearly only a specialist secondary teacher is equipped to deal with this. Can't believe no one picked up on this when the marking guidance went out - shows the slim grasp the exam setters have on the real world of teaching.

12. ### SansAtoutNew commenter

No, T34 is correct - if you write the rounded value as 5.00 you do not fully realise the purpose of rounding (or one of its purposes). There's lots of material out there explaining this - google 'exact numbers', 'significant figures' and 'measurements'. The problem is that this material is mostly aimed at first year undergraduate scientists and engineers! Our pupils will begin to meet some of the ideas in Y10, when they come across questions such as:

"If a mass of 5.0kg is pressing on an area of 2.5s square metres, what is the minimum and maximum pressure?" They are expected to work out Pmax = 5.05/2.45 = 2.06, rounded to 2.1 Pascals, where 5.05 is the maximum measurement that would be rounded to 5.0, and 2.45 the minimum area that would be rounded up to 2.5. Similarly, Pmin = 4.95 / 2.55 = 1.94, rounded to 1.9 Pascals. If the question had said 5.00kg , the maximum would be 5.005/2.45 = 2.04.

Another way of thinking about it is that if we round a measurement of 5.05 cm to the nearest cm, the measurement is still 5.05, but we are asked to round it to 1 significant figure, the whole number 5. The measurement is not 5.00cm - we have measured 5.05cm; but we have rounded it to 5cm.

OK - that's why the mark scheme is technically correct. And because I've seen this in previous mark schemes, I teach my pupils this.

But I entirely agree with everyone who thinks that awarding zero marks to the answer 5.00 is the height of pedantic stupidity on the part of the exam board. The purpose behind this is not something they will meet for at least another three years, and any child that answers 5.00 is showing that they know how to round, and that they know 5.00 equals 5 for most purposes.

The official mark scheme does not cover this this year. I presume that this was circulated to the markers as an amendment to the published scheme - can any KS2 maths markers out there confirm this?

13. ### Albert Tatlock

Great debate but the STA/ DFE will just turn it into Fish and Chip paper. They won't ever back down or admit they are being picky,pedantic and just plain obtuse. Pointless even trying to, trust me I have tried too many times. It's all just Foobar.

Cheers Albert

14. ### AnonymousNew commenter

Gosh nomad, you are so clever. You certainly know how many beans make 5!

15. ### nerllybird

I have no idea how to quote anyone on this stupid thing any more (heat getting to me). But I want to say that I agree with asnac about the teaching of maths in primary. In order that my Y4s might better understand tenths, I have repeatedly shown them various representations of them - including those where no whole number appears, and those where there is a zero in the hundredths or thousandths column. The point being that it is the digit in the tenths column which matters when we're looking at how many tenths there are. So far this approach has resulted in some much happier children with a better understanding of decimals.

So I agree with pretty much everyone else that the mark scheme is an ass.

Incidentally, I'm not too happy about teaching decimals using money. I see it suggested rather often on here, and I've had a debate about it in school as well. It's best, IMHO (because I am a mere NQT not yet even in charge of my first very own class) to teach decimals as numbers and then apply that knowledge to money, length, weight, capacity, etc. It's far too easy, when decimals are introduced via money problems, to call 0.50 'zero point fifty'. Which, of course, quite apart from going against accepted practice, causes difficulty when dealing with kilos and grams.

16. ### AlexCharlie

Will anyone bother to appeal this?

From http://www.mathsisfun.com/rounding-numbers.html

"What is "Rounding" ?

Rounding means reducing the digits in a number while trying to keep its value similar. The result is less accurate, but easier to use. "

There are no grounds for appeal. Mathematically the answer '5' is correct and '5.00' is not.

Period!

However, the fact that this issue appears to be so widely misunderstood suggests that there is material on which primary school mathematics leaders can run some CPD sessions.

19. ### mystery10Occasional commenter

Was it a 1 or 2 mark question?

I wonder if (gulp) it is the way that teachers are expected to make up all their maths exercises etc themselves that leads to this and similar issues where primary children are not that familiar with "conventions" that they could easily learn at that age?

Some teachers are pointing back to older test papers with similar questions and mark schemes which are worded the exact same way.

When I was a pupil ( an extremely long time ago) we would routinely have answered this kind of question from maybe year 4 upwards. The text book explained it, and there were questions and answers ready for the teachers to use ..... the teachers always marked in a pernickety way .... it was rare for anyone to ever get 100% in a school exam as there was always some aspect of mathematical presentation / convention that they were pulled up on.

But it wasn't done at the expense of understanding either.

I think primary teachers have got too much to prepare "from scratch". So things like this, which are relatively unimportant, slip through the net. It's a shame if it makes a grade boundary difference for a child who is deserving of the higher level.

If a whole two marks was lost with this, I think that is tough. It is the proportion of marks given to this that is too high if it was two marks.