MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
Country
name
Italy
Nome of the
material
JULIUS CAESAR CIPHER
Which
subject of
mathematic
s is related?
Numbers, corners and sentences .
Subject objectives:
- reflecting about angles and their construction using the goniometer
- make the subdivision of a round angle in submultiples
- memorize prime numbers
Aims of the
game
- reflecting about prime numbers and their use in common life to encrypt messages or
personal passwords.
Transversal objectives:
-improve the control over their own learning, the attention span and the cooperation
level
-get the students used to increase the precision and shared rules
Tools and
equipments
How many
people
played
with?
-
To make the Cipher we need cardstock, goniometer, scissors, set square and
compass.
-
Everyone must realize his cipher machine that it is possible to use in groups of two
or more students
o
o
o
o
o
o
Please thick
appropriate
box:
(Age range)
Pre-Primary Schools
Scuola Primaria
Secondary School
High Schools
Special Needs Schools
Other (please specify)
The Cipher machine is based on Julius Caesar cipher.
He used to send a messenger with an encrypted message.
If the messenger was caught, his plans were safe because nobody could understand the
message.
He used to transpose the Roman alphabet of three letters in his messages; there was
only one translation key. More years later Leon Battista Alberti invented another cipher
machine with which was possible to change the encrypted and decrypted key of cipher.
The use of encrypt messages was safer (Fig.1).
How to
play?
We constructed this instrument using prime numbers and the English alphabet.
Building cipher machine:
1)
2)
3)
4)
5)
6)
Using compass construct two circles;
Using scissor, cut the biggest circle
Using goniometer dividing every circles in angles of 10°, so it’ll be possible to use
35 letters and 35 prime numbers
Overlap the circles and , using a rule, draw lines from the center to the points that
correspond to every angles, in every circles (Fig. 2)
The circles will be divided into segments (Fig.3)
Write a prime number in the segments of the inner circle and letters in the
segments of the external circle. So to a segment with a prime number will
correspond a segment with a letter. Use the first prime numbers according to the
increasing order (Fig.4)
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
7)
8)
9)
Fix the center of concentric circles with a screw (Fig.5)
You can decide the key cipher : for example if you can use a:7, you must rotate
your machine to correspond the segment with “a” and the segment with “7”,
consequently “b” will correspond to number “11” and “c” to number “13” …
You can use this instrument to play with prime numbers, encrypting and decrypting
your messages
Use of cipher machine:
1)
2)
3)
The teacher makes some sentences
The first group encrypts the messages and send them to the other group.
The receivers decrypt the messages using the cipher.
For example the teacher gives the sentece to a group: “Good luck” and the group
encrypt this message with a key A:5 into “23 59 59 13 – 43 83 11 41”. Than a member
of this group gives this sentece to another group with the key. The second group must
decrypt the message in “Good luck”.
Photos /
videos of
the game
Fig.1
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
Fig.2
Fig.3
MATHEMATICS GAMES TEMPLATE DOCUMENT FOR “I LOVE TO PLAY MATHS” PROJECT
Fig.4
Fig. 5
* Please write in English and do not forget to take photos and videos of the materials.