Any point in the 1D world can be described by a single number which shows how far along the line you are. As you increase slider a, talk about the first dimension.You can download and open the original Geogebra file here which gives more control than just playing the gif. It’s pretty simple but might be a good way in to 3D coordinates and more generally explaining the concept of dimensions. I feel I would need to construct it to be sure I haven’t got any repeats within these 6. But I’m still not convinced that this means 6 is the answer to the question. I convinced myself there are six ways of doing this. So then it was a case of working out how many ways there are of arranging 4 things in a 2×2 arrangement where rotation is not allowed. Because no two small cubes of the same colour can share a face, the small cubes must be arranged so that they on diagonally opposite corners of the large cube. I came to the realisation that I need only look at the 4 small cubes on the front face because I can deduce where other 4 cubes on the rear face will be. This 3D animation created on Geogebra (file here) may also help if real cubes are not available.Īs John Mason points out in the book, whichever representation is used, it is important to record carefully the “different” cubes so they can be compared. The position of the small cubes actually have to be changed. If we have the physical cubes in the form of multilink cubes we are likely to see that “different” means that one large cube cannot be simply rotated to form another one. Then the question comes what do we mean by “different” large cubes, which is a conversation starter in itself. The first challenge of this task is to interpret what it is asking and construct a mental image of that.
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