2D representations of 3D shapes

problem

Chopped Dice

Age

14 to 16

Challenge level

Can you make a new type of fair die with 14 faces by shaving the corners off a cube?
problem

Bent Out of Shape

Age

14 to 18

Challenge level

An introduction to bond angle geometry.
problem

Take Ten

Age

11 to 14

Challenge level

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
problem

Cutting a Cube

Age

11 to 14

Challenge level

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
problem

Weird Universes

Age

16 to 18

Challenge level

Consider these weird universes and ways in which the stick man can shoot the robot in the back.
problem

New House

Age

7 to 11

Challenge level

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?
problem

28 - Upward and Onward

Age

7 to 11

Challenge level

Can you find ways of joining cubes together so that 28 faces are visible?
problem

Three Cubed

Age

7 to 11

Challenge level

Can you make a 3×3 cube with these shapes made from small cubes?
problem

Picture a Pyramid

Age

7 to 11

Challenge level

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
problem

Arranging Cubes

Age

7 to 11

Challenge level

A task which depends on members of the group working collaboratively to reach a single goal.