The UK Mathematics Trust and the Further Maths Network

United Kingdom Mathematics Trust/Further Mathematics Network Senior Team Challenge Final

On Thursday 7th February, teams made up of students from years 11, 12 and 13 in the following schools and colleges competed in London to become the first national winners of the Senior Team Challenge.

Bristol Grammar School	Queen Mary's Grammar School
Culford School	RGS Worcester & The Alice Ottley School
Dame Alice Owen's School	Royal Latin School
Eton College	Solihull School
King Edward VI Camp Hill Boys' School	St Olave's Grammar School
Lancaster Royal Grammar School	Tadcaster Grammar School
Lancing College	Torquay Boys' Grammar School
Loughborough Grammar School	Watford Grammar School for Girls
Pates Grammar School	Woodhouse College
Peter Symonds College	Yarm School
Queen Elizabeth's Grammar School

Well over 300 schools and colleges entered the competition. Finalists had qualified by winning a regional heat. The historic Clothworkers' Hall was a fitting venue for the first final of what is already proving to be a prestigious event.

Teams competed in three rounds; one in which they worked on questions together, one in which the teams were divided into two pairs to complete a mathematical crossword, and one a mathematical relay. Scoring was close throughout the day and most teams still had a good chance of winning coming into the final round.

In addition to the main event, a separate competition was held in which teams were given 50 minutes to produce a poster entitled 'How would you you judge a freehand circle-drawing competition?'. The standard was excellent and the eventual winners were Loughborough Grammar School. A poster based their winning entry is being produced to be distributed to schools and colleges.

The overall winners of the competition were Torquay Boys’ Grammar School. Marcus du Sautoy presented them with their trophy and prizes. This year’s competition has been an enormous success. Demand for places in the competition exceeded our most optimistic predictions. The level of support for the competition in schools and colleges should ensure that it will thrive for many years to come. Plans are already in place for a bigger competition next year with many more schools and colleges involved.

Thanks to everyone from the Further Mathematics Network who has been involved in the competition. A huge amount of effort went into making sure that teachers and students had a fabulous experience at the heats and final.

Thanks to our partners in organising the competition, the United Kingdom Mathematics Trust, for all their great work. Our collaboration with UKMT has been entirely positive and we look forward to it continuing for many years to come.

Thanks also to all the teachers who were involved in the competition, many of whom gave up a large amount of their own time to support their teams.

Information about how the competition runs and this year’s questions

Each heat and the final lasts approximately three hours.

Each team must consist of four year 11, 12 or 13 students with no more than two from Year 13.  Each team must be accompanied by a responsible adult who must stay throughout the duration of the competition.

There are three rounds:

The Group Round: ten questions which the teams have around 40 minutes to solve.  Teams must decide their own strategy: work in pairs, as a group or individually.
2007/8 Regional Stage questions
2007/8 Final questions

The Crossnumber Round: a mathematical crossword puzzle with one pair from the team solving the across clues and the other pair the down clues.
2007/8 Regional Stage questions
2007/8 Final questions

The Mini-relay Round: individual members of the team have to answer mathematical questions which they can begin work on immediately but information passed from other members of the team is needed to solve them completely.
2007/8 Regional Stage questions
2007/8 Final questions

Solutions for 2007/8 Regional Stage
Solutions for 2007/8 Final

Further details:

The Group Round (approx 40 mins).
6 marks are awarded for every correct answer, no partial marks are awarded.

The Crossnumber Round (approx 40 mins).
Teams divide into two pairs. One pair is given the across clues, the other pair the down clues. It is the pupils’ responsibility to put an answer in the right place on their answer grid. The teacher immediately checks each digit of the answer. If it is correct, tick it, and it gets a mark. If it is wrong, there are no second tries, cross it out and write the corrected answer in, but it does not get a mark. Then show the correct answer to both pairs so that they are up-to-date. They can put just one digit at a time if they wish, rather than a whole answer. They can sacrifice a square if they are completely stuck by guessing and being told the answer. They are not allowed to communicate directly with the other pair but they may, through the teacher, ask the other pair to try to work on a particular answer that they need. They cannot share any other information with the other pair or ask any questions about definitions etc. It may sometimes appear that there is more than one answer but every answer is uniquely specified although it may depend on clues the other pair have.
1 mark is awarded for every correct digit on the answer grid.

The Mini-relay Round (3 Relays – 10 mins each).
Team sit on chairs one behind the other. The teacher then sits on a chair facing the front student. Each member of the team will be given a question which they can start working on using the paper provided. The team member furthest away from the teacher is given Question 1 etc. Question 1 can be answered without any additional information but each of the other questions requires the previous answer before it can be answered unambiguously (e.g. The answer to Q3 will depend on the answer to Q2 etc.) As soon as the first team member has an answer to Q1, this is written on the record sheet and passed over the shoulder of the second team member. The second team member can then finish off working on Q2. This answer is then recorded and passed to the third team member and so on. Note that the questions are devised in such a way that some preliminary calculations can be carried out without knowing the previous answer and all individual team members are encouraged to start working on their question as soon as they are told to start. If a team member, based on knowledge of their question, knows that a passed on answer is incorrect (e.g. they know that the received answer should be a square number) they can pass it back to the previous team member.If a team member realises they may have passed on an incorrect answer then, providing that the fourth team member has not asked for the sheet to be marked, they can ask the teacher to retrieve the score sheet; Once all questions have been answered the fourth team member shows the record sheet to the teacher who will then mark their answers.

Correct answers to questions 1, 2 and 3 score four points; a correct answer to question 4 scores 8 points. Mark the questions in order until one is wrong or they are all correct. If one is wrong hand the sheet back to the competitor who submitted the wrong answer. When the sheet is marked a subsequent time only half marks (i.e. 2 for Questions 1, 2 or 3 and 4 for question 4) may be given for that question. Subsequent answers may still receive full marks. If the team fails to finish in the time given, marks will be allocated for any correct answers as normal; A maximum of 20 points (4+4+4+8) are available for each mini relay, and there are three parts to this round thus giving a total possible score out of 60.