Transcript Senior Team Mathematics Challenge

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 2014-15 there were 70 regional heats with 1150 teams
entered in total
 The joint winners were Hampton School, King Edward's
School, Birmingham and Harrow School with Dunblane High
School winning the Poster Round (which is unique to the
final).
The 2015 Winners –
Summary of Rounds in the Heats
 Round 1
Group Round
40 minutes
10 questions = 60 points in total
 Round 2
Cross Number Round
40 minutes
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
Round 1
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
Pair 1
Desk
Desk
Pair 2
 Teacher looks after the master answer grid.
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
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