the crystal maze
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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. - PowerPoint PPT PresentationTRANSCRIPT
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 learntA mystery puzzle - something slightly different to the usual!
3 crystals are awarded to the team that finishes first2 crystals are awarded to the team that finishes second1 crystal is awarded to the team that finishes third
For each puzzle:
Each crystal counts as a 5 second head-start on a final puzzle to be revealed after the rest...
GREEK EGYPTIAN
INDIAN 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
Cube
Dodecahedron
Use the straws and play doh to make an icosahedron (hint – it has 20 sides)
Octahedron
Icosahedron
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
1191713117532 = 9699691
The Greeks knew of several rules for the area of a triangle.
215134 s 16 131216 Area
576
csbsass 2cbas Area = where a b
c
Find the area of a triangle with sides of 4, 13 and 15cm
24
Hero worked out this formula for a triangle with sides a, b and c
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
2
2
3
volume of cuboid = 2 x 2 x 3 = 12
Cut out the nets, fold and stick to make 3 pyramids.Then fit all 3 together to
make a cube!
so volume of pyramid = 4
Eg
The Egyptians liked to keep things simple
Eg 31
21
They only liked to use unit fractions - with one for the numerator.
65
Eg 81
41 8
3
can be written two ways as an Egyptian fraction:
81
61
247
247
41
121
247
101
601 12
1301 15
1201
Find three ways to write as an Egyptian fraction760
Egyptians used symbols to represent numbers:
Solve this problem, giving your answer in the Egyptian style!
52431572 26205524
physical skill mystery
Indian mathematicians were the first to develop the concepts of zero and negative numbers
5
1-
6
05-
Cut out and position the numbers so that every circle add up to zero
-3 2 7
-4 -2 3
-6 1 4
Use 8 8s in an addition sum to make 1000
888 + 88 + 8 + 8 + 8
Indian mathematicians were the first to develop a proper decimal system
Indian Mathematicians knew how to quickly add up difficult-looking sums like 333333 10099...4321
Possibly related, how many squares can be fitted into the grid?
(the answer is 25502500 by the way)
22222 54321
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
= 55 squares
There are:
physical skill mystery
Tangrams are an ancient Chinese puzzleStarting 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
52 is the first number in all 3 lists
I have a bag of sweets
If I share them between 5 people there are two sweets left over
If I share them between 7 people there are three sweets left over
If I share them between 3 people there is one sweet left over
What is the least number of sweets in the bag?
Could be 4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,...
Could be 10, 17, 24, 31, 38, 45, 52, 59, ...
Could be 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, ...
Chinese Mathematicians were intrigued by magic shapes...
Use the digits 1 to 9 to make a magic triangle where each side adds to 23
Magic squares
Any line of 3 adds to the same total
Magic circles
Any diameter or circle adds to the same total
Magic triangles
Any side adds to the same total
7
89
6
251
34
7
89
5
324
61
or
5
1-
6
05-
-3 2 7
-4 -2 3
-6 1 4
1 2 3
4 5 6
7 98
GreekPhysical
Skill 9699691
Mystery 24
EgyptianPhysical
Skill
Mystery
101
601 12
1301 15
1201
PhysicalIndian
Skill 888+88+8+8+8Mystery 55
ChinesePhysical
Skill 52
Mystery
Solutions
Final challenge