Look Again

Look again

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.

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?

Pocket Money 

Age 11 to 14 Challenge Level:
Which of these pocket money systems would you rather have?

Farey Sequences 

Age 11 to 14 Challenge Level:
There are lots of ideas to explore in these sequences of ordered fractions.

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?

Mediant Madness 

Age 14 to 16 Challenge Level:
Kyle and his teacher disagree about his test score - who is right?

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?

Ford Circles 

Age 16 to 18 Challenge Level:
Can you find the link between these beautiful circle patterns and Farey Sequences?

Polar Coordinates 

Age 14 to 18
Cartesian Coordinates are not the only way!