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.

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Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

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Which of these pocket money systems would you rather have?

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There are lots of ideas to explore in these sequences of ordered fractions.

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Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

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Kyle and his teacher disagree about his test score - who is right?

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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?

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Can you find the link between these beautiful circle patterns and Farey Sequences?

Cartesian Coordinates are not the only way!