2D shapes and their properties

problem
Gold yet again

Age

16 to 18

Challenge level

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."
problem
First forward into Logo 4: circles

Age

7 to 16

Challenge level

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?
problem
Circle panes

Age

7 to 11

Challenge level

Look at the mathematics that is all around us - this circular window is a wonderful example.
problem
Roll on

Age

14 to 16

Challenge level

Weekly Problem 5 - 2006
How many times does the inside disc have to roll around the inside of the ring to return to its initial position?
problem
Sticky tape

Age

14 to 16

Challenge level

Work out the radius of a roll of adhesive tape.
problem
Central distance

Age

11 to 14

Challenge level

Weekly Problem 1 - 2006
The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?
problem
Property chart

Age

11 to 14

Challenge level

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
problem
Shapely pairs

Age

11 to 14

Challenge level

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
problem
Mrs Trimmer's string

Age

5 to 7

Challenge level

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?
problem
Board block challenge

Age

7 to 11

Challenge level

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?