Code BreakingAuthor(s): Darrell MorganSource: Mathematics in School, Vol. 35, No. 3 (May, 2006), pp. 28-29Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215914 .

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by Darrell Morgan

At Cwmtawe Comprehensive we have a key skills day, during which year 6 pupils are invited from our feeder schools. About 180 pupils were invited from 13 primary schools. They were split into two groups of mixed abilities from different schools. Each group of ninety pupils then took part in two activities. The first was a business enterprise activity where the pupils had to set up a company, design, manufacture, cost and produce a product. The second activity was a code breaking activity designed by the maths department.

MURDER IN THE MATHS DEPARTMENT INTRODUCTION CARD

A Murder has been committed in the Maths Department at Cwmtawe School.

Your job is to decode the clues to find

(a) the identity of the murderer,

(b) the murder weapon used

(c) the room in which the murder took place. The seven suspects are: Mrs Cavendish Mr Crane Mr Davies Mr Hicks Dr Hopkins Mr Morgan Mr Powell

The possible murder weapons are:

Metre ruler Chair Scissors Compass Text book Pencil Stapler The room in which the murder was committed could be: M1 M2 M3 M4 M5 M6 M7

If you crack all the codes in the time limit available then you can invent a similar game or design a code of your own.

Each session was to run for an hour and a half. This would give time for break, lunch, a tour of the school and a plenary session before the buses arrived. In the maths department we decided to work on code breaking since we thought that it would be an interesting topic for the pupils and would incorporate group work, creativity and problem solving. Each teacher in the maths department was responsible for 15-20 pupils. The pupils were split into groups of two or three; we felt that groups of four or more would remove some pupils from the work. The groups used were friendship groups to make the pupils feel comfortable. The scene was set (there is much scope here, including the possible use of fancy dress next year) using the introduction card; the added advantage of this card was that it could be used to record information gained when solving each clue. We photocopied each clue onto different colour cards. All the pupils were given clue 1 and the idea was to give them as little help as possible when solving clues. As soon as a group

solved a clue they showed their solution to the teacher and picked up the next clue. The clues increase in difficulty and pupils are introduced to the idea of a key for solving codes quite early on. This is then removed and they have to find their own key to solving the later clues. Most pupils sorted things out for themselves with minimal teacher input. Some groups needed a little help to get started on clue 1, others needed some prompting with clue 5 ("well you solved clue 3 using the alphabet forwards"). Clue 6 did slow most groups down, which helped with the competitive aspect, and pupils were encouraged to come back to the fifth word. Any groups that solved all the clues were then encouraged to design a similar problem using their own ideas for codes. The project proved to be very successful, with all pupils enjoying themselves, working together and determined to solve the problem. We will keep the same format for next year but incorporate more mathematical language into the clues.

Code 1

The first code uses the following key:

A BC J K L

D E F M* N *O V T Z 'X

G H I U Y

You need to work out how to use the key above to decode the following message.

Code 2

The second code uses the following key:

5

4

3

2

1

A B C D E

F G H I J

K L M N O

P Q R S T

U V W X Y/Z

1 2 3 4 5

28 Mathematics in School, May 2006 The MA web site www.m-a.org.uk

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You need to work out how to use the key above to decode the following message.

(5,2) (3,4) (5,5) (3,3) (1,1) (3,2) (4,5) (5,5) (3,2) (5,5) (3,2) (4,5) (5,3) (5,5) (4,2) (4,3) (5,3) (5,2) (3,4) (1,5) (2,1) (5,5) (1,5) (4,3) (5,5) (4,4) (4,3) (5,2) (3,4) (5,5) (4,4) (3,2) (4,3) (1,5) (3,3) (5,5)

Code 3

There is no key provided for this, or the following codes. You will have to work out the key for yourself.

20, 8, 5 18, 15, 15, 13 14, 21, 13, 2, 5, 18 9,19 15,4,4

Code 4

Can you decode the pictures to solve this clue?

Code 5

7, 19, 22 14, 6, 9, 23, 22, 9, 22, 9 23, 12, 22, 8 13, 12, 7 19, 26, 5, 22 26, 13 13 18, 13 7, 19, 22, 18, 9 13, 26, 14, 22

Code 6

The only clue to helping you decode this message is that it was received by mobile phone.

8, 4, 3 7, 6, 6, 6 6, 8, 6, 2, 3, 7 4, 7 4, 7, 3, 2, 8, 3, 7 8, 4, 2, 6 8, 4, 7, 3, 3

Code answers

Code 1. The room number is a factor of twenty. Code 2. The murderer does not have an e in their name. Code 3. The room number is odd. Code 4. The murder weapon is the compass. Code 5. The murderer does not have an n in their name. Code 6. The room number is greater than 3.

With thanks to Maria Edwards for the organization of the day. P

Keywords: Codes; Key.

Author Darrell Morgan, Cwmtawe Comprehensive, Parc Ynysderw, Pontardawe, Swansea SA8 4EG. www.thejoyofmaths.co.uk e-mail: d.morgan27@ntlworld.com

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Mathematics in School, May 2006 The MA web site www.m-a.org.uk 29

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