Being curious

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Find the sum of this series of surds.

What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

There are many different methods to solve this geometrical problem - how many can you find?

Can you work out the equations of the trig graphs I used to make my pattern?

Do you have enough information to work out the area of the shaded quadrilateral?

Does it make any difference how we write powers of powers? 

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?