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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.


Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.


Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

The Mathemagician's Seven Spells

Age 7 to 11
Challenge Level

The great spell has to be broken! It has seven parts. Two children, Anna and David, must break it, but you can help...
The Mathemagician stands by his immense cauldron, flames dancing round. He stares hard at the cauldron and then at the two children.
mathemagician and his cauldron
"Tell me the next two numbers in each of these seven minor spells," chanted the Mathemagician, "and the great spell will crumble away! Watch the smoke to see the spells."
Spell the first: sequence: 1, 2, 4, 8, ?, ?
Spell the second: sequence: 6, 13, 20, 27, ?, ?
Spell the third: sequence: 127, 63, 31, 15, ?, ?
Spell the fourth: sequence: 1, 3, 6, 10, 15, ?, ?
Spell the fifth: sequence: 2, 3, 6, 11, 18, ?, ?
Spell the sixth: sequence: 1, 8, 27, 64, ?, ?
Spell the seventh: sequence: 216, 168, 126, 90, 60, 36, ?, ?
Anna and David managed to break the spell, did you?