Perimeter

problem
On the edge

Age

11 to 14

Challenge level

If you move the tiles around, can you make squares with different coloured edges?
problem
Warmsnug double glazing

Age

14 to 16

Challenge level

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
problem
Contact

Age

14 to 16

Challenge level

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
problem
Pick's theorem

Age

14 to 16

Challenge level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
problem
Five circuits, seven spins

Age

16 to 18

Challenge level

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.