Cubes and cuboids

problem

Twelve Cubed

Age

14 to 16

Challenge level

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
problem

Inside Out

Age

14 to 16

Challenge level

There are 27 small cubes in a 3 × 3 × 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you can colour every face of all of the smaller cubes?
problem

Cubic Covering

Age

14 to 16

Challenge level

A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?
problem

Summing Squares

Age

14 to 16

Challenge level

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
problem

Cubic Vision

Age

14 to 16

Challenge level

How many cubes can you see?
problem

Painted Purple

Age

14 to 16

Challenge level

Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?
article
Dice, Routes and Pathways

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to think mathematically, especially geometrically.
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Making Maths: Link-A-Cube

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
article
Thinking 3D

How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?
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Paper Folding - Models of the Platonic Solids

A description of how to make the five Platonic solids out of paper.