11+ maths papers are much less interchangeable than I thought (long, sorry)

[heiheiLondon]

A while back I asked here what to do about maths at home (www.mumsnet.com/talk/primary/5447855-y4-in-independent-school-almost-no-maths-homework-what-do-you-do-at-home). Then DD did the new St Paul's Girls' sample paper and asked me, "Why have I never seen any of these questions before?" and I went a bit further than I meant to.

The advice everywhere, including here, is "do past papers". What I didn't know was whether one school's papers actually prepare a child for another's, so I went through 65 of them: St Paul's, Latymer, City of London Girls, Sevenoaks, the CSSE, ISEB-style pretests, and the Primary Maths Challenge, which isn't an entrance exam but a lot of people use it for practice. I sorted every question by what it was actually asking a child to do.

A few things surprised me (two charts at the bottom).

• They overlap a lot, but the amounts are very different. Questions where you're handed a rule (a function machine, or a made-up symbol) and have to use it make up 12 of the 51 questions on the current St Paul's samples. In 541 ISEB-style questions they come up twice.
• The same topic can be a completely different job. Take multi-step and simultaneous equations: half of the Sevenoaks questions on them hand you an equation and ask you to solve it. The CSSE's most common version is a word problem where you have to write the equation yourself. The most common St Paul's version has no numbers in it at all, just symbols to substitute.
• Older papers from the same school aren't always the same exam. St Paul's changed format, and the current samples lean on the made-up symbol questions more than twice as hard as the older three-section papers you find on tutoring sites.

So my takeaway was: past papers, yes, but the ones for the exam your DC is actually sitting, and less faith in topic-by-topic books than I'd had.

Caveats: these are published sample and past papers, not live ones, and it's my reading of them rather than any data on how children actually do.

Has anyone found that practising one school's papers didn't really carry over to another's? Or the opposite?

(Full disclosure, since it's relevant: I'm building a daily maths app around this, called Halomath, and the two charts come from that. Not linking it, I'd just rather say so up front.)

OP used 'sample paper' and 'past paper‘ interchangeably, but in reality, they can be quite different. I believe actual past papers—such as those published by Manchester Grammar School—are a much more accurate predictor for future sittings.

What we did is aim for a fairly high
level paper in maths like Exams Paper Plus and work our way up towards higher scores. Such papers are usually hardest and a ‘super set’ of most schools’ papers.

closer to the actual exam it’s more worthwhile to get past papers of specific schools and try them out more for style, familiarity and timing.

maths can be done as a ‘single’ subject but you need to aim for the highest level of all the schools you are going for.

Fair point, and I should have been clearer. Of the 65, the CSSE ones are genuine past papers. St Paul's, Latymer and Sevenoaks are the schools' own sample papers, and the ISEB ones are practice papers in the ISEB format, since the real pretest isn't released. For St Paul's the school only publishes samples, so that's all there is to go on. Where a school does publish real past papers, like MGS, I'd go to those first. Even then it's worth checking whether the format has changed, which is what happened with St Paul's. I haven't looked at MGS yet, so I'll go through theirs next and post back here.

Agree completely on switching to the actual school's papers nearer the time, for style and timing. The "super set" idea is the one my numbers made me less sure about, though. Rounding and estimation, which is what the CSSE asks about most, doesn't come up once in the four Latymer papers. So a paper can be hard and still miss what a particular school leans on. Did you find the higher level papers covered most of what came up in the end?

Some interesting statistics. You didn't mention as much about how the PMC ties to a majority of the past and sample papers.
From our personal experience, the PMC and even the JMC (for Y7 & Y8s) are probably the best source of 11+ maths prep. The skills acquired while doing these types of problems give you the understanding needed to solve most 11+ questions.
For example, someone getting the equivalent of a silver in the bonus round of the PMC would be on track to be among the very top performers in any 11+ paper anywhere in the country. Hence I think these papers (PMC & JMC) are far more interchangeable than past and sample papers.

That's a fair challenge, so I went back and checked. The PMC ties in more than I'd made it sound: between 71% and 84% of each entrance exam's questions are on objectives that also come up somewhere in the PMC papers, and St Paul's is the closest match. Where it falls short is the routine methods: adding and subtracting fractions with different denominators is 12 of the CSSE's 443 questions and doesn't come up once in 356 PMC questions, and long multiplication and division appears on the Latymer and St Paul's papers but never in the PMC. So I'd agree it builds the thinking, but I'd still check the standard methods separately. That's overlap in topics, mind, not how children actually score.