Explaining, convincing and proving

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

What is the same and what is different about these circle questions? What connections can you make?

Explore the relationships between different paper sizes.

Use the differences to find the solution to this Sudoku.

What do you get when you raise a quadratic to the power of a quadratic?

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

Can you rearrange the cards to make a series of correct mathematical statements?