Being curious

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?

Can you fill in the empty boxes in the grid with the right shape and colour?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?