STMC Training Supported by Rolls-Royce plc

The Further Mathematics Support Programme Our aim is to increase the uptake of AS and A level Further Mathematics to ensure that more students reach their potential in mathematics. The FMSP works closely with school/college maths departments to provide professional development opportunities for teachers and maths promotion events for students. To find out more please visit www.furthermaths.org.uk

Problem-Solving In addition to organising the STMC competition, the FMSP provides additional support for developing problem-solving skills: Year 10 team Maths Feast in Feb/Mar Supporting students doing STEP/AEA/MAT Problem-Solving CPD for teachers Problem-Solving resources for students

Aims Become familiar with the rules of the competition Develop strategies for improving your score on each round of the competition Experience the fun of tackling challenging mathematics problems as part of a team

Overview of Competition Organised by the Further Mathematics Support Programme and the UK Mathematics Trust Sponsored by Rolls-Royce plc Provides enrichment and challenge to teams of senior students in the UK In 2016-17 there were 65 regional heats with 1296 teams entered in total The winners were Ruthin School with RGS Newcastle winning the Poster Round (which is unique to the final).

Summary of Rounds in the Heats Round 1 Group Round 40 minutes 10 questions = 60 points in total Round 2 Cross Number Round approx. 60 squares = 60 points in total Round 3 Shuttle Round x 4 8 minutes each 15 points each

The Group Round Teams have 40 minutes to answer 10 questions, worth 6 points each. These are marked right or wrong, so score 6 or 0 points for each question (correct answer only). Units are not required. Teams should form their own strategy as to how to divide up the work.

The Group Round What would be a good approach to maximise your score on this round? Separate the questions and share out Find ones you can get going on quickly Try using particular numbers in place of algebra to get some insight Maybe start with a simpler example Try looking for patterns Work in pairs to try ideas and check calculations Simplify algebra, and simplify numbers

Mini Group Round 5 questions in 20 minutes Maximum score = 30

The Cross Number Round Teams split into pairs, with desks separated and the teacher sits between the pairs. One pair is given the Across clues and an answer grid, the other pair the Down clues and a grid. Teacher looks after the master answer grid. Pair 1 Pair 2 Teacher Desk

The Cross Number Round 1 point for each correct digit on the master answer grid. When students have solved a clue they ask for the answer grid and write in the digits. The teacher immediately checks each digit of the answer. If it is correct, it is ticked. If it is wrong, there are no second chances, it is crossed out and the correct answer is written in. The correct answer is then shown to both pairs so that they can update their grids. Both pairs must have only correct information on their grids.

The Cross Number Round What would be a good approach to maximise your score on this round? Find the clues that can be solved straightaway, which do not depend on other clues. Put just one digit at a time if you wish, rather than a whole answer to check if you are on the right lines. Sacrifice a square (and a point), if you are stuck, by guessing a digit. You will be told the correct answer if you are wrong, which may help you solve the clue. Write down a list of possible answers – often there may be 4 or 5 possible answers with the right number of digits.

The Cross Number Round It may sometimes appear that there is more than one answer to a particular clue but every answer is uniquely specified although it may depend on clues the other pair have. You are not allowed to communicate directly with the other pair but you may, through the teacher, ask the other pair to try to work on a particular answer that you need. You cannot share any other information with the other pair or ask any questions about definitions etc. Continue to work until you finish or time runs out. Fill in all the blank squares with digits – you have a 1/10 chance of being correct!

Glossary Some terms and sequences that it would be useful to learn are: Fibonacci Numbers Triangle Numbers Cubes Primes Prime Factors Consecutive Sum and Product Integer

Mini Cross Number 32 digits to find in 20 minutes Maximum score = 32 Round 2 Mini Cross Number 32 digits to find in 20 minutes Maximum score = 32

The Shuttle Round Teams split into pairs again, with desks separated and the teacher sits between the pairs. The pairings can be different to those used for the Cross Number. Each Shuttle consists of 4 questions. The answer to question 1 gives the starting value for question 2 and so on. Teams have 8 minutes to solve all 4 questions. There are 4 Shuttles in this round alternating as to which pair receives Questions 1 and 3 and which receives Questions 2 and 4

For the first Shuttle, pair A works on Questions 1 and 3 and pair B works on Questions 2 and 4. When pair A solves question 1 they write the answer on the answer sheet and it is passed to pair B to work out the answer to question 2. And so on. Teams hand in the Answer Sheet only when they have written an answer for all four questions. The teacher then starts marking at Question 1 and stops marking at the first incorrect answer, ignoring any subsequent answers given. The Answer Sheet is then handed back to the pair who answered incorrectly for another attempt.

If the Answer Sheet is handed in again then only 1 point is available for the question that was previously answered incorrectly. Teams may have as many attempts as they wish at this question. Correct answers to later questions will still earn 3 points each. There is a whistle after 6 minutes. If a team has handed in an Answer Sheet with 4 correct answers (first attempts only) before this whistle they earn a bonus of 3 points in addition to the 12 points available for the 4 other answers. A final whistle is blown after 8 minutes. Teams must stop working and hand in their Answer Sheet.

What would be a good approach to maximise your score on this round? Decide on the best pairings for this round. Pairs should do some preparatory work before they receive the answer to the previous question. No communication is allowed between pair A and pair B except that on the Answer Sheet. Only answers may be written on the Answer Sheet and it must not be used to ask questions or pass information to the other pair. If a pair realises that they have answered a question incorrectly they may ask the teacher to retrieve the Answer Sheet and then change their answer. If a pair realises that the other pair has given them a wrong answer they can return the Answer Sheet with this answer circled.

Round 3 Shuttle Round 2 shuttles of 4 question For each shuttle you have 8 minutes Maximum score = 30

Further Help and Practice Questions and solutions are available for all previous heats and finals on the FMSP website www.furthermaths.org.uk/?section=resource s&page=stmc_materials

The Further Mathematics Support Programme To find out more please visit our website www.furthermaths.org.uk