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THE CRYSTAL MAZE

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.

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THE CRYSTAL MAZE

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  1. THE CRYSTAL MAZE

  2. 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...

  3. GREEK EGYPTIAN INDIAN CHINESE

  4. physical skill mystery

  5. 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)

  6. 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... Eg using the first 3 primes 2,3 and 5 Take the first n primes, multiply them together and add one to obtain a new prime. 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 = 9699691

  7. 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 = where Find the area of a triangle with sides of 4, 13 and 15cm

  8. physical skill mystery

  9. 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 Cut out the nets, fold and stick to make 3 pyramids. Then fit all 3 together to make a cube!

  10. The Egyptians liked to keep things simple They only liked to use unit fractions - with one for the numerator. Eg Eg can be written two ways as an Egyptian fraction: 7 Find three ways to write as an Egyptian fraction 60

  11. Egyptians used symbols to represent numbers: Solve this problem, giving your answer in the Egyptian style!

  12. physical skill mystery

  13. 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 -3 2 7 -4 -2 3 -6 1 4

  14. 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

  15. Indian Mathematicians knew how to quickly add up difficult-looking sums like (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 = 55 squares

  16. physical skill mystery

  17. 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

  18. 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

  19. Chinese Mathematicians were intrigued by magic shapes... Magic squares Magic circles Magic triangles Any side adds to the same total Any line of 3 adds to the same total Any diameter or circle adds to the same total 7 7 Use the digits 1 to 9 to make a magic triangle where each side adds to 23 or 3 6 6 5 4 2 1 3 1 5 4 9 8 2 9 8

  20. -3 2 7 -4 -2 3 -6 1 4

  21. 1 2 3 4 5 6 7 8 9

  22. Solutions Indian Greek Physical Physical Skill 9699691 Skill 888+88+8+8+8 Mystery 24 Mystery 55 Egyptian Chinese Physical Physical Skill 52 Skill Mystery Mystery

  23. Final challenge

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