These two group activities use mathematical reasoning - one is numerical, one geometric.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
What could the units digit of a prime number be?
What does this tell you about one of the prime numbers?
Where must the zero go?