Just because a mathematical situation is familiar doesn't mean it has to be dull! Looking at a familiar context through a new lens can generate new insights and understanding. These problems invite you to look again at ideas you may think you know inside-out, and see what new discoveries you can make.
problem
Gibraltar geometry
Age
11 to 14
Challenge level
Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?
problem
Pocket money
Age
11 to 14
Challenge level
Which of these pocket money systems would you rather have?
problem
Farey sequences
Age
11 to 14
Challenge level
There are lots of ideas to explore in these sequences of ordered fractions.
problem
Same answer
Age
11 to 14
Challenge level
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
problem
Mediant madness
Age
14 to 16
Challenge level
Kyle and his teacher disagree about his test score - who is right?
problem
Farey neighbours
Age
16 to 18
Challenge level
Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?
problem
Ford circles
Age
16 to 18
Challenge level
Can you find the link between these beautiful circle patterns and Farey Sequences?
