Explaining, convincing and proving

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

Work in groups to try to create the best approximations to these physical quantities.

Have a go at being mathematically negative, by negating these statements.

Can you match the charts of these functions to the charts of their integrals?

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

How do these modelling assumption affect the solutions?

In this short challenge, can you use angle properties in a circle to figure out some trig identities?

Can you prove our inequality holds for all values of x and y between 0 and 1?