Maths - do any children get consistently 100% on hard maths?

[MonkeySea]

My son likes maths, is in Y6 and regarded as very able. However while he's obviously very good at it, he doesn't do perfectly. E.g., in the Primary Maths Challenge, he got 21/25, where 23 was the bonus round mark. I had him do a couple of the PMC bonus round papers, and he got 19/25 on 2012's paper (which would have been bronze out of the bonus round entrants), and 20/25 on 2011 (silver).

Obviously quite creditable, but he's clearly not the highest echelon. Is it possible to get there? Or is he just a case that he's a three-sigma student, but never six-sigma, so to speak?

A boy at my son's school got full marks. My DS is not in the top set for maths but has won silver medals twice. DD in set 4/5 got silver twice in primary & in senior school.

A girl in my daughter's year at school got a sum wrong at maths last year. This was the first time she'd ever got a sum wrong, in the past she only didn't get 100 % when she didn't finish papers. She has got through to the second stage of the maths challenge & has been in the top 50 nationally for the year above.

Some people are at a different level.

How challenging did he find the questions? My DSS is very good at maths but will frequently make silly mistakes with the easier questions as he's too blaze about it!

Lost marks could either indicate that he doesn't know the material well enough (and, talent or not, there are some principles that just have to be learnt the hard way) or that he's finding the material too easy and not giving it his best shot.

Either way, if this is his interest, I think he can find a way to 100%

My DS2 (now yr 7) never achieved full marks because he was always careless with the easy questions. He's always better at hard maths. Fortunately this dynamic is much better recognised at his secondary school.

There could be up to a year difference in age for all those taking the test. At 10/11 this makes a big difference.

Also the questions tend to require thinking about maths rather than simply knowing the facts. A good practice for this is the nrich website.

Are the ones he gets wrong using the same principles as the ones he gets right? That would indicate he is lacking in 'exam technique' or he isn't concentrating properly (too easy, not bothered, bored, rushing?)

Or do the ones he gets wrong require different skills/knowledge than the ones he gets right? That would indicate he is doing as well as his knowledge (and possibly ability) will allow.

Either way he's doing well.

I'm pretty good at maths. In my experience it is difficult to get 100%.

I managed a few times at school, but not often. In my Open Uni last year I got 100% in one of the 4 tests and over 90 in another. Despite only studying 75% of the course due to work commitments I ended the year with 89%. This year I have only got the results back from one test and I achieved 96%.

Because there are do many marks, you can be on the right track entirely but lose a mark for putting 5-3=8 at some point in the middle of calculation.

It is good practice to do the calculations in small steps rather than to try to do too much in each step. If you break things down then it can be easier to see where you went wrong and you are likely to lose fewer marks if the examiner can see exactly the point at which you made a mistake.

Dh is very good at maths. I'm good, (Oxbridge maths degree) but he's one step above. He got 100% in all his school maths exams, including further maths Alevel, except once when he got one wrong when he misread the question.
Maths is something 100% is possible. Dd1 got 100% on her SATS paper last year, and wasn't the only one from their school. She's very careful and precise. Dd2 won't get 100% although she's at least as good at maths because she's not careful and will probably make silly mistakes.

You do get the extra brilliant person. Like the person I knew at Uni who got one of the top 1st in the year-he could have halved his marks and still got a comfortable 1st. He also was 2 years younger than everyone else, did the degree in 2 years rather than three, English wasn't his first language (wasn't even his second language) and for a rest in his third year (you can't graduate until you've done 9 terms) he did a History degree in one year-and also got a first.
Despite this he was both "normal" to talk to, and very pleasant with a lot of outside interests.

I think part of the problem at this age (maybe especially with boys) is to train them that if they have time left over they check their work and go over the paper.

Ds got 100% in both his level 5 and level 6 SATs last summer - he found the work easy and had plenty of time so double checked. Previously he rushed the work and would read a book.

He didn't manage 100% in primary maths challenge as he found he could not do all the questions, but got a silver medal, so not bad. He would have got full marks on the easier questions.

You can get 100% in maths - one of the few subjects you can! but practice helps to speed you up. Last year (Y5) DS got bronze in the PMC. This year (after loads of practice for various entrance tests) he got gold and top of his year - his maths has clearly gone up a notch. He refused to practice for the bonus round (tested out) so who knows what he got in that.

I was one of those children who always got close to 100% so I tell him he has a lot to live up to :)

I used to love getting 100% - I was good at Maths and also very precise.... I see at my DD primary school y6 that there are a handful of them (including one at GCSE level) who are always jostling around the 97-100% mark - looking through DD paper it's always a careless mistake not the maths that loses marks, and I suspect it is the same for the others... She's aiming for 100% but of course checking through (she often has time to do this 2 or 3 times) they often visually make the same mistake they made first time - I think it's tougher to catch mistakes at this age, than to do the sum in the first place. So far only 2 of them managed 100% once each.... it's rare but yes, possible!

Love any tips about how to get it consistently - this thread has got me thinking - I might suggest she does it slightly more slowly (ie less likely to make mistake in first place) or actually SLOWLY does her checking, reading silently aloud to engage brain??? Other ideas people?

We've done a lot of exam practice this year in the run up to the pre-tests, and DS got a gold medal in PMC.

For him, the key was slowing down so that he checked as he went along - he was very poor at going back once he'd finished. 'I don't like rubbing things out - it seems a waste of energy'.......

DS pretty much consistently gets 95% on school maths exams. Never 100%.

I didn't think the PMC bonus round questions were excessively difficult, with the higher levels (JMO, IMO), the start getting less trivial.

Here's the paper he did:

www.m-a.org.uk/resources/PMC_Feb_2011_Finals.pdf

He got q12 wrong, putting 4, whereas the answer comes out fairly simple if you draw it on a piece of paper, it's a sort of Maltese cross.

He also got q15 wrong, putting 19 I think missing the two 7s required for 77. A bit of a classic brainteaser that one.

He also got qs 21, 22, and 24 wrong. q21 is easy if you write it out as algebra. q22 possibly a bit wordy/confusing? He said he didn't understand q24, so I guess too wordy again.

I had him do the JMC 2012 paper as practice (he's too young for it at the moment), he got 79, which is a silver, which is obviously good for his age. He made a couple of silly mistakes on the numerical questions, i.e.,

"What is the smallest four-digit positive integer which has four different digits?"
A 1032 B 2012 C 1021 D 1234 E 1023

"Which of the following has exactly one factor other than 1 and itself?"
A 6 B 8 C 13 D 19 E 25

and he got pretty much all the shape/geometry type questions wrong.

I was going to ask his maths teacher if he could do the JMC, but I didn't realise that he had already done the PMC and not got through to the Bonus Round, so it perhaps seems less of a reasonable request. However I would say that the PMC seems to be a lot more wordy, and I'm sure that is confusing him, as he does have Aspergers.

Just out of curiosity what is the answer given for your 2nd question ?

I make the number of prime factors including copies to be:
A 2 B 3 C 0 D 0 E 2

ie none of them =1, and if you exclude copies B and E are both 1.

I always made silly mistakes. I got 96% in my mock O-level because of silly mistakes, namely 1+1=1 and 2x3=5

DS is the type of child who will get 93-96% in any Maths test - from Level 1 all the way up to Level 7. Always makes 1 silly mistake...

(PMC levels, btw, are 'school specific' - as far as I remember, the medals are awarded to the top marks in the school, not the top marks per se. It's only once they get onto the 'out of school' rounds that 'absolute' levels become meaningful. DS obtained gold medals in both Year 5 and Year 6, but I'm interested to see what he will get on the 'absolute level marked' JMC this year)

Cumfy:

6:
2,3

8:
2,4

13:
(none)

19:
none

25:
5

So it's E.

Teacherwith2kids:
You typically need to score 23/25 to get to the bonus round (about 1000 get through I think), which then has medals for about half the candidates.

I was good at maths at school - I could get 100% on school tests and got a certificate in the thing you do after the senior maths challenge, but my friend was still clearly streets ahead of me and I don't think that extra practice would have got me to her level.

Monkey, so E was given as correct answer.

But B is also "correct" as prime factorisation of 8=2x2x2. ie 2 is the only prime factor of 8.

It doesn't say prime factors.

there is a variant of this which asks which numbers have ODD numbers of factors - only squares have these as they have two + 1. I have to admit I had never thought about this before - I think it came up in a London Consortium paper. So practicing different papers will help here.

Agree that 8 has 1, 8, 2, 4 so doesn't count.

According to the Primary Maths Challenge website "An amazing 268 pupils scored 25/25." out of 70 000 entries. So that would be somewhat less than 0.5%.

My dc's school doesn't take part in pmc but does do hard maths

Dd1 went through a phase of high 90s but it was always the easy questions she got wrong -decimal in the wrong place, rushing reading the questions and assuming they are going to ask something they don't

Her teacher actually got her doing some easier maths papers, dd understood why and that he was trying to make a point

Did her a huge favour in the entrance exam she has just taken and she got 100% in the level 6 practise she has just done

Don't know about the primary maths challenge, but for the secondary maths challenges the UKMT emails out monthly mentoring sheets with tricky problems for the most able to give them practice on the sort of thinking which will help them in the challenges.

www.mathcomp.leeds.ac.uk/mentoring/junior/

For standard school exams, not much difference between getting 95% and 100% - everybody is bound to make a few careless mistakes even if they totally understand the material.

Things like the PMC/SMC etc are a bit different and are slightly different from the JMC, BMO etc - people do very well in the latter without necessarily having got 100% in the former. Those are different again from e.g. doing well at maths at Oxbridge, ending up as a top class maths researcher and so on. There are definite correlations certainly but plenty of exceptions too.

Important thing at this stage is if he enjoys maths to encourage that!

Having just read this thread, I had no idea that the Primary Maths Challenge carried so much weight. DD bought home a certificate a few weeks ago, I put it on the fridge and thought nothing of it. Now, reading this thread, maybe I should have made a bit more fuss of her. The school have gone to town with her results but I really didn't have a clue...perhaps I should have googled it.
Anyway, I've now learnt that DD is a bit better at maths than I thought as she got a gold as a Year 3. I'm guessing she didn't make the next stage though.