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Teacher Notes This is an enjoyable investigation that can be attempted by most ability groups to some degree. You will probably want to use the formulae questions on slides 7 and 8 with the more able groups. A printable worksheet is available at slide 9 that you might find it useful for lower ability students who might want to shade/colour some of the cubes.

ABCD The six outside faces of a 3 centimetre cube are to be completely painted as shown. When dry, the cube is broken up into single centimetre cubes. The four different types are shown an the right and labelled according to the number of painted faces each has. Work out the number of each type of unit cube for this 3 x 3 x 3 cube.

ABCD The six outside faces of a 3 centimetre cube are to be completely painted as shown. When dry, the cube is broken up into single centimetre cubes. The four different types are shown an the right and labelled according to the number of painted faces each has. Work out the number of each type of unit cube for this 3 x 3 x 3 cube. © bigstockphoto.com

Work out the number of unit cube types for other painted cubes shown and record your results in a table. L = side length of cube. LABCD © bigstockphoto.com

Work out formulae for B, C and D in terms of L. LABCD L8 © bigstockphoto.com

Work out formulae for B, C and D in terms of L. LABCD L8 12(L-2)6(L-2) 2 (L-2) 3 © bigstockphoto.com

Worksheet