Describing patterns and sequences

problem
Diagonal in a spiral

Age

7 to 11

Challenge level

Investigate the totals you get when adding numbers in threes on the diagonal of this pattern.
problem
Centred squares

Age

7 to 11

Challenge level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
problem
Circles, circles

Age

5 to 11

Challenge level

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?