Describing patterns and sequences

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Find the next number in this pattern: 3, 7, 19, 55 ...

Investigate the successive areas of light blue in these diagrams.

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

July 1st 2001 was on a Sunday. July 1st 2002 was on a Monday. When did July 1st fall on a Monday again?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.