Visualising and representing

problem
Cubestick

Age

16 to 18

Challenge level

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
problem
Stars

Age

11 to 14

Challenge level

Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Isosceles triangles

Age

11 to 14

Challenge level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
problem
Efficient cutting

Age

11 to 14

Challenge level

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
problem
Fred the class robot

Age

7 to 11

Challenge level

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
problem
Classic cube

Age

16 to 18

Challenge level

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?
problem
Slippage

Age

14 to 16

Challenge level

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
problem
3D treasure hunt

Age

14 to 18

Challenge level

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
problem
Something in common

Age

14 to 16

Challenge level

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
problem
Integral polygons

Age

11 to 14

Challenge level

Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?