Cubes and cuboids

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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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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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Paper folding - models of the Platonic solids

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

Age

16 to 18

Challenge level

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
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Plane to see

Age

16 to 18

Challenge level

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
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Four points on a cube

Age

16 to 18

Challenge level

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
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How many dice?

Age

11 to 14

Challenge level

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find there are 2 and only 2 different standard dice. Can you prove this ?
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Counting triangles

Age

11 to 14

Challenge level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
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Christmas boxes

Age

11 to 14

Challenge level

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.