median
don steward
mathematics teaching 10 ~ 16

Friday, 18 May 2012

painted cube

the 'painted cube' exploration has plenty of potential for developing, testing and justifying general rules

the problem: a cube (made up of n by n by n 'cubelets') is dipped into paint so that only it's outside faces are covered
when broken apart, how many 'cubelets' will have one face, two faces, three faces and no faces painted?









and the task is good for looking at equivalent problems in different dimensions

for example, the 2-D equivalent would be painting around the edges of an n by n square and seeing how many of the 'squarelets' have 0 , 1 and 2 edges painted









students can be invited to say what will happen in
4 - dimensions...

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