2D representations of 3D shapes

problem

Bent Out of Shape

Age

14 to 18

Challenge level

2 out of 3

An introduction to bond angle geometry.
problem

Take Ten

Age

11 to 14

Challenge level

3 out of 3

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

3 out of 3

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

3 out of 3

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

1 out of 3

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

1 out of 3

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

Three Cubed

Age

7 to 11

Challenge level

2 out of 3

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

Picture a Pyramid

Age

7 to 11

Challenge level

2 out of 3

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

2 out of 3

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

Air Nets

Age

7 to 18

Challenge level

1 out of 3

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.