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.

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

Which of these pocket money systems would you rather have?

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

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

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

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?

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