Transcript File - The Mathematics Shed

THE CRYSTAL MAZE
Get into teams of 4
The Crystal Maze is split into four zones based on four ancient
cultures that made important Mathematical discoveries
Each zone has three puzzles:
A physical puzzle that requires you to make something
A skill puzzle that uses some of the number skills you have learnt
A mystery puzzle - something slightly different to the usual!
For each puzzle:
3 crystals are awarded to the team that finishes first
2 crystals are awarded to the team that finishes second
1 crystal is awarded to the team that finishes third
Each crystal counts as a 5 second head-start on
a final puzzle to be revealed after the rest...
GREEK
INDIAN
EGYPTIAN
CHINESE
physical
skill
mystery
Plato is best known for his identification of 5 regular solids now
known as the Platonic Solids, made from one regular shape each:
Tetrahedron
Octahedron
Cube
Dodecahedron
Icosahedron
Use the straws and play doh to make
an icosahedron (hint – it has 20 sides)
Euclid is known as the ‘father of geometry’ and laid down
the rules of geometry still used today. He also wrote about
primes and proved that there an infinite number of them...
Take the first n primes,
multiply them together
and add one to obtain
a new prime.
Eg using the first 3 primes 2,3 and 5
2 x 3 x 5 = 30
30 + 1 = 31 is prime
Without a calculator, evaluate the prime
given by this method, using the first 8 primes
2  3  5  7  11  13  17  19  1 = 9699691
The Greeks knew of several rules for the area of a triangle.
Hero worked out this formula for a triangle with sides a, b and c
Area = ss  as  bs  c where s  a  b  c
a
b
2
c
Find the area of a triangle with sides of 4, 13 and 15cm
s
4 1315
 16
2
Area  16 12  3 1
 576
 24
physical
skill
mystery
Egyptians realised that the volume of a pyramid is a third
of the volume of a cuboid with the same base and height
Eg
volume of cuboid = 2 x 2 x 3 = 12
so volume of pyramid = 4
3
2
2
Cut out the nets, fold and
stick to make 3 pyramids.
Then fit all 3 together to
make a cube!
The Egyptians liked to keep things simple
They only liked to use unit fractions - with one for the numerator.
Eg
3
8
 
1
4
1
8
5
6
Eg
 
1
2
1
3
7 can be written two ways as an Egyptian fraction:
24
7
1
1
7
1
1
24
12
4
24
6
8

 
Find three ways to write
1
60

1
10
1
30


7
as an Egyptian fraction
60
1
12
1
20

1
15
Egyptians used symbols to represent numbers:
Solve this problem, giving your answer in the Egyptian style!
1572  3  524
524  5  2620
physical
skill
mystery
Indian mathematicians were the first to develop
the concepts of zero and negative numbers
Cut out and position the numbers so that every circle add up to zero
-1
5
-3
2
7
-4
-2
3
-6
1
4
6
-5
0
Indian mathematicians were the first
to develop a proper decimal system
Use 8 8s in an addition sum to make 1000
888 + 88 + 8 + 8 + 8
Indian Mathematicians knew how to quickly add up
difficult-looking sums like 13  23  33  4 3  ...  993  1003
(the answer is 25502500 by the way)
Possibly related, how many squares can be fitted into the grid?
There are:
5 x 5 ways to fit a 1 by 1 square
4 x 4 ways to fit a 2 by 2 square
3 x 3 ways to fit a 3 by 3 square
2 x 2 ways to fit a 4 by 4 square
1 x 1 way to fit a 5 by 5 square
12  22  32  4 2  52 = 55 squares
physical
skill
mystery
Tangrams are an ancient Chinese puzzle
Starting with a square made up of 7 pieces…
you must arrange them to make something else
Cut and rearrange the square
to make a parallelogram
Chinese mathematicians found ways
to deal with many problems at once
I have a bag of sweets
If I share them between 7 people there are three sweets left over
Could be 10, 17, 24, 31, 38, 45, 52, 59, ...
If I share them between 5 people there are two sweets left over
Could be 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, ...
If I share them between 3 people there is one sweet left over
Could be 4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,...
What is the least number of sweets in the bag?
52 is the first number in all 3 lists
Chinese Mathematicians were intrigued by magic shapes...
Magic squares
Any line of 3 adds
to the same total
Magic circles
Magic triangles
Any side adds to
the same total
Any diameter or circle
adds to the same total
7
Use the digits 1 to 9 to
make a magic triangle
where each side adds to 23
3
6
4
9
7
or
6
2
1
5
5
1
8
9
3
4
2
8
-1
-3
2
7
-4
-2
3
-6
1
4
5
6
-5
0
1
2
3
4
5
6
7
8
9
Solutions
Greek
Indian
Physical
Physical
Skill
9699691
Skill
Mystery 24
888+88+8+8+8
Mystery
Egyptian
Chinese
Physical
Physical
Skill
Mystery
1
60

1
10
1
30

1
12
1
20

1
15
Skill
52
Mystery
55
Final challenge