Do you know what 30 less than the first Fibonacci number over 100 is? Can you find two numbers whose sum is 1 and product is 425? Is it possible to have a triangle whose angle sizes are three square numbers? Tackled individually, these questions could put you off maths for life - but done collaboratively, your interest in maths is likely to be ignited, not extinguished.
Teamwork wins hands down every time because working together everyone achieves more, a fact gloriously illustrated by the 100 pupils who took part recently in the UK Team Maths Challenge regional final at the City of London School. The challenge is a minds-on competition for enthusiastic and able mathematicians and this was one of 44 regional finals involving 1,200 schools across the country.
Agile, alert and ambitious minds assemble for a day of maths and mingle together to work at four events. The first is the group round, in which each team of four - two Year 8s and two Year 9s - compete against the clock to answer 10 maths questions. The second round is "cross number", where two members of the team work on across clues and two on the down clues. In the "head to head" round, pupils compete directly against another school to unearth a mathematical rule. The day finishes with a nail-biting relay fusing mathematical ability with speed and fun.
The challenge is a hive of activity, with pupils bursting to tell each other their experiences: "How did you do that?", "I did it like this", "Oh, that's a good way. I tried this." Great minds don't think alike, they do it differently. They also need a space and forum to think and breathe in a devoted day of maths, and that's what the event provides: a demanding, friendly, calculator-free day to showcase creative and critical thinking, problem-solving and plenty of thought friction.
The UK Team Maths Challenge is maths at its best, because it is interactive, collaborative and formative. Most challenges are dull, sedentary, mothballed and solitary exercises - but this one is vibrant, dynamic and active. It is an excellent example of self and peer assessment in action, providing valuable talking points and enabling students to express themselves.
The day starts with sample warm-up questions to help pupils relax and settle into the day - a sensible idea, as there are more than 25 schools here, meeting together for the first time. This can also work to the benefit of the children, as Elissa Nelson, head of Year 11 at Farnborough Hill School, says: "It's good for children to work in an unfamiliar and unknown environment."
Teachers accompanying pupils are not allowed to sit with them. This isn't intended to be draconian but is done in a spirit of fairness. Teachers "adopt" a team from another school and spend the day with them. After a full briefing, the teachers are kept busy and fully involved, helping the day run smoothly and overseeing the activities. The day is also a great opportunity for teachers to get to know their pupils better, as Ms Habanyana of St David's School in Ashford found "It's interesting to see the way they break down the numbers and play around with them. We don't always get a chance to do that."
Through exploring and unpacking maths, pupils can see for themselves what they know, what they don't know and, more importantly, what they partly know. Lydia Keegal, 12, says the opportunity to work in a group enabled her to "learn from everyone's input". Even if ideas aren't right every time, as Laura Kent, 13, points out, the activities "help you to learn from others' mistakes" and to do so without embarrassment.
The children soon realise their team members are good at different things.
For many, the learning curve is steep. The problems are designed to ensure a level of success for everyone but with a level of challenge for the brightest.
Teacher Suzanne Shakes of St Joseph's College, whose motto is "maths is fun", is fully supportive of the event as a fun day where pupils learn to work in a team: "The children enjoy the day, it's healthy competition and great for confidence building." Sorabh Patel, aged 13, found the team aspect a far more enjoyable experience than working independently, because "we can put our ideas together and bounce off each other."
It's not just the maths that gets a good work-out. Byrone Mitchell, 13, found the activities helped him "improve his thinking and concentration" and Kathryn Ticehurst, a learning support assistant at Edgbarrow School, points out the social spin-offs: "Children learn a lot by mixing with other pupils and adults they have not met before."
Terry Heard, the UK Mathematics Trust representative running the event, describes the challenge as "an enjoyable day's mathematics, different from the normal routine". Pupils work hard and everyone receives a certificate of participation to acknowledge their efforts.
At the end of the competition the biggest smiles were from the Notting Hill and Ealing High School team (13-year-old Saoirse Bryar, Johanna Preston, aged 12, 14-year-old Jessica King, and Elisabeth Matthews, aged 13), who came out on top and now compete at the final on 3 July at the Camden Centre, London. Teacher Arna Perie-Matthews is overjoyed. "I am delighted for the girls. Our prime intention was to enjoy ourselves and this will encourage them to continue enjoying maths."
The image of maths being a boring, individual subject akin to ploughing a field couldn't be further from this reality - it has the potential to be vibrant, interactive and collaborative, oozing with talk, excitement and adventure.
l If you're looking for a group-based maths competition that integrates cognitive activity with excitement and enjoyment, sign up for the 2007 Team Challenge at www.ukmt.org.uk