problem Pythagoras Proofs Age 11 to 16 Challenge level Can you make sense of these three proofs of Pythagoras' Theorem?

problem Garden Shed Age 11 to 14 Challenge level Can you minimise the amount of wood needed to build the roof of my garden shed?

problem Kite in a Square Age 14 to 18 Challenge level Can you make sense of the three methods to work out what fraction of the total area is shaded?

problem Generating Triples Age 14 to 16 Challenge level Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

problem Unusual Polygon Age 14 to 16 Challenge level What is the perimeter of this unusually shaped polygon...

problem Folding in Half Age 14 to 16 Challenge level How does the perimeter change when we fold this isosceles triangle in half?

problem Centre Square Age 14 to 16 Challenge level What does Pythagoras' Theorem tell you about the radius of these circles?

problem Tetromino Diagonal Age 14 to 16 Challenge level Can you calculate the length of this diagonal line?

problem Partly Circles Age 14 to 16 Challenge level What is the same and what is different about these circle questions? What connections can you make?

problem Rectangle Dissection Age 11 to 14 Challenge level Weekly Problem 2 - 2009 The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?