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.
Make a list of the square numbers up to $8\times 8$.
Using the interactivity might help you get started. Don't forget you can always change your mind and alter your solution as you go along!