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You could start by adding diagonal pairs. What do you notice?
What happens if you keep adding? For example, starting at 1, add 4, then 5, then 8 etc. Could you predict the pattern of totals?
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.