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There are lots of answers to this problem, depending on what questions you choose to ask.
Have a go yourself, and if you discover anything interesting,e-mail us to tell us what you've done! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send in a summary of your children's work.
These two group activities use mathematical reasoning - one is numerical, one geometric.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.