"OK," says Margaret Rose, maths co-ordinator at Timberley primary school, Birmingham, writing up a quick number grid on the blackboard, "we're going to play four in a row." Hands start shooting up in the air and waving frantically and cries of "Yes!" go up from the eight to nine-year-old True Blues and Dirty Yellows of Year 4.
"You can use the four rules - add, subtract, multiply and divide, " Ms Rose reminds the children. "So, what can you say about these numbers? Alan,you look keen."
For the Yellows, Alan stands up. "You can use 2 and multiply by 10 to make 20," he says, indicating three contiguous squares containing those numbers. "Is that right?" asks Ms Rose. "Come on, the rest of you, use your thinking to see if it's right. Thumbs up or thumbs down?" Thumbs go up. "Right it is, so there's some squares for the Yellows. Now, who else has been planning ahead to say what you think you can do with the numbers? Remember, you can go up and down or side to side. And when you've got four in a row, you've scored a goal."
The hands start waving and the number combinations come thick and fast. Forty plus 20 is 80 - thumbs up or down? Ninety times two add 20 equals 200. "Two points there for your team for using two different rules. More operations means more points, remember!" Eighty take away 40 equals 40; 28 add zero is 28. Yes! Four ina row!
There is a gentle roar and Margaret Rose starts her football rap: "Coming up to the goal and Collymore swerves and flicks it past Pallister, and Yorke heads it past Schmeichel, who just misses it and it hits the crossbar and in - it's a goal."
Groans from the Blues. "No."
"4-3-2-1: A goal for the Yellows!"
Yellows all punch the air and cry, "Yes!".
Suddenly, the visitor realises why maths is now "best subject" at Timberley and Nicky and Kerry are bursting to tell all about "these great games we play". The children don't know that they are part of a national drive to improve the nation's numeracy. But Kerry knows that her mum likes taking her shopping, to see if she can add it all up, and Nicky keeps thinking about how multiplying and adding are so much easier than subtracting and dividing. After each pupil has had a go at four in a row and each goal has been celebrated, an extra question is asked. "Who wants the glory?" asks Ms Rose. Lots of takers from the Yellows, and when there is another rousing cheer, Jamie volunteers to solve 30-6=24.
"Are you warmed up now?" asks Ms Rose. "Yes!"
"Are you ready to do some work?" "Yes!"
"Is maths fun?" "Yes!"
The group sessions
It's 20 minutes into the numeracy hour and there is no sign of flagging interest.
Before the class divides into three ability groups, Margaret Rose introduces today's theme, which is money, how you write it down and how you work out change from your shopping. She writes 406p up on the blackboard and urges the class to see who "for one house point" wants to turn this into a figure with the pound sign. "Hands on desks, now hands up!You can all do this with your eyes closed." There is an eager hum like an audience at a pub quiz. "Okay, Natasha, tell us." Natasha says "#163;4.06". Ms Rose beams. "Is that right? Thumbs up or thumbs down? Thumbs up it is. One house point. " There is a rustle of appreciation and, as the worksheets from the national numeracy project are handed out, much eager scanning and nudging.
While the large groups work in pairs, Ms Rose circulates. On the lowest ability table, there are trays of plastic money to help calculation with buying simple meals in the canteen. On the middle table, some straightforward sums - take #163;2.98 from #163;5 - and a decoding question at the end which needs all the individual answers. "Anyone who can decode it gets five house points. " On the top table, there are problems to be solved and the requirement that children think of what operations they are using, to help them become aware of algorithms (patterns for solving problems).
The children have devised their own ways of working together, from Rupinder and Kelly, who are counting on each other's fingers, to Alan and Curt, laying out money side by side, and on to Jamie and Danielle who are reading out problems and discussing them: "You do that one just like the first one." Adds Nicky, nearby: "You could use multiplying instead of adding for that one." This is maths in action - an intense cognitive and social activity giving great enjoyment and sense of achievement.
Not surprising, then, that, as the 20 minutes of paired working draws to an end, along with the stretching and rubbing of eyes there is also a pleasant hum of completion. "Did you get #201;?" pairs are asking each other.
The whole class plenary
Ms Rose comes up to the front again. "So," she asks, "what answers did we get?" Once more the hands wave in the air. Once more the thumbs go up and the house points are added. But this time the children get to explain how they got the answers, whether they rounded up or took away, how they used multiplying and why not adding.
For the visitor, the really interesting thing is that children of all abilities are equally interested in each other's answers. The process itself, it seems, is fascinating, even if the finer points are hard - or too easy - to grasp.
As we come out of the classroom, Ms Rose is smiling. "They are so much better, and so much more confident. They can see now that problem-solving is not daft, and that they can do it. And they can talk about it with each other, without feeling foolish."
Back in the office, we pore over the numeracy test sheets. They show a marked improvement. "We do honestly know it's due to the numeracy programme," says headteacher Jane Walker.
So, of course, does Kerry's mum.