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Gibraltar Geometry
Pocket Money
Farey Sequences
Same Answer
Mediant Madness
Farey Neighbours
Ford Circles
A Second Look
A Second Look
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 students to look again at ideas they may think they know inside-out, and see what new discoveries they can make.
Gibraltar Geometry Age 11 to 14Challenge Level 
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?
Pocket Money Age 11 to 14Challenge Level
Age 11 to 14
Challenge Level
Which of these pocket money systems would you rather have?
Farey Sequences Age 11 to 14Challenge Level
Age 11 to 14
Challenge Level
There are lots of ideas to explore in these sequences of ordered fractions.
Same Answer Age 11 to 14Challenge Level
Age 11 to 14
Challenge Level
Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?
Mediant Madness Age 14 to 16Challenge Level
Age 14 to 16
Challenge Level
Kyle and his teacher disagree about his test score - who is right?
Farey Neighbours Age 16 to 18Challenge Level
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?
Ford Circles Age 16 to 18Challenge Level
Age 16 to 18
Challenge Level
Can you find the link between these beautiful circle patterns and Farey Sequences?