Explaining, convincing and proving

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Can you decide whether these short statistical statements are always, sometimes or never true?

Sequences of multiples keep cropping up...

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

How did the the rotation robot make these patterns?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

The clues for this Sudoku are the product of the numbers in adjacent squares.

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?