Being collaborative

Which of these games would you play to give yourself the best possible chance of winning a prize?

Here are two games you can play. Which offers the better chance of winning?

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Where should runners start the 200m race so that they have all run the same distance by the finish?

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?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

How can we make sense of national and global statistics involving very large numbers?

Surprising numerical patterns can be explained using algebra and diagrams...