In each area, OFSTED selected 15 schools for inspection - five of the highest achieving, five in the middle, and five of the lowest achieving. Sylvester primary is among the first group, even though many of its pupils come from deprived backgrounds - one in two of its 490 pupils receives free school meals and six out of ten qualify for a clothing allowance.
Headteacher Tony Halpin says: "At key stage 1 in the national curriculum tests 95 per cent of our seven-year-olds are at or above the national average. And at key stage two, 26 per cent are reaching level five, against a national average of just seven per cent."
The St John's estate, which the school serves, has been identified in a local health authority survey as having one of the highest levels of deprivation in the area. The school itself presents an unprepossessing front - inside much of the paint is peeling, and the leaky roof provides an ineffective barrier to the heavy Liverpool rain.
But the atmosphere in the school is far from depressing. The walls are brightly painted and pupils walk the corridors in orderly lines. The staff are also extremely well-motivated and there is a positive learning ethos.
Keith Lloyd, head of OFSTED's primary team and co-ordinator of the numeracy survey, chose the school for inspection. He did his first teaching practice in Knowsley so this is, for him, a trip down memory lane. He is impressed by Sylvester's performance, and says the school is likely to be written up as a case study in the final report.
Mr Halpin puts part of the school's success down to expectations. He says: "We expect our children to be as good as any others in the UK. We have no excuses. The children might have a different baseline of knowledge before they come to school, but then we've got them. I have responsibility for these children from the time they come into our nursery at age two-and-a-half, so I can't blame anybody for any shortcomings. When the children come in without much experience, we give it to them. We structure their learning from a very early age."
Mr Halpin says this structure is responsible for the school's success in maths.
He says: "We don't have an off-the-shelf maths scheme. We decide what we want to teach - so we pick and dip into a variety of textbooks. If there isn't a clear scheme of work you can spend all your time and energy thinking 'what should I teach?'.
"The staff are very proud of our maths scheme - they wrote it, they own it and they put their energy into teaching it. That is at the centre of our success. "
Mr Lloyd believes the reliance on ready-made commercial maths schemes lies at the heart of our failure to teach maths well in many primary schools.
He says: "Some schools never abandoned whole-class teaching. But the weaker ones have placed too much emphasis on individualised learning in mathematics. Children in such schools follow published schemes, working at their own pace and at their own level. Children work in isolation from the teacher and the pace is slow. It's difficult for children to interact with the teacher in a mathematical way and for the teacher to teach them directly.
"It's difficult to manage 30 children, all working at different levels, often on different mathematical topics."
The class teachers at Sylvester, headed by maths co-ordinator Mark Hilton, have compiled their own maths scheme, which involves a great deal of whole-class teaching.
Julie Clayton takes the year two maths group. She says: "The yearly scheme splits maths into the various areas demanded by the national curriculum. It specifies the way our school aims to teach maths. Then within each topic it also states learning objectives and identifies any resources we might need. From this we make an individual structure plan, taking account of almost every minute of each lesson."
The scheme is constantly revised and updated, so each new class teacher has an instant reference for every stage of the teaching.
At key stage 2, the school is experimenting with setting in maths. "We're lucky to have found the resources to employ a floating teacher. It means we can split the 45 children in this year's two classes into three groups," says Mark Hilton.
The children are allotted to a particular group on the basis of the national curriculum tests and the school's own tests in year five. Mr Hilton says: "It works well because as a teacher I get around to each individual pupil. You can also teach at a level that's appropriate to each group."
Each class has four of these sets a week, as well as a fifth day of whole-class practical maths. "We have a special room with box assignments set up like mini-experiments, so the children can do some hands-on maths, looking at topics such as length, time and capacity. It's fun for them and it adds variety to what they're learning," says Mr Hilton.
One of the problems with primary level maths has been a lack of expertise on the part of some teachers. "If there is a particularly bright 11-year-old who's streaking ahead, the teacher sends the child to me and I point him or her in the direction of the resources room, which has hundreds of books that can be used for this type of child," Mr Hilton says.
He regularly attends maths courses - he has just come back from a conference, and feeds back ideas and new ways of making maths exciting to the other teachers. There is also in-school training and "team teaching" days, when Mark will sit in on classes to identify problems. Curriculum time is devoted to this every week.
Mr Halpin says good teaching lies at the heart of the school's success in maths. He says Sylvester may well be held up as a beacon of excellence when the numeracy survey is published later this year.
As Mrs Clayton says, "If the children are not enjoying the lesson or there's not the understanding, it's a reflection of my planning and my work. If they start to feel lost and confused, that negativity carries on into the secondary level. It's now - at the primary stage - that I can give them the one-to-one attention that will make them excited about maths."