Describing patterns and sequences

Which of these pocket money systems would you rather have?

This activity creates an opportunity to explore all kinds of number-related patterns.

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

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

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?