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What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

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Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Drilling Many Cubes

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

If you've decided to go onto some written work in the form of a spreadsheet there are plenty of opportunities for thinking hard about the formulae that are required to generate further results.

These formula will often come from firstly visualising, comparing with others how they have visualised, then, trying to jot down ideas either pictorially or numerically.

The activity could then be extended into looking at the results achieved for a number of sizes of cubes, and asking about the patterns that are evident.

As is often the case, by looking at Digital Roots in many instances further patterning can beobserved.

With any patterns that are noticed it is always good to ask WHY such patterns have come about. This can sometimes lead the person to exclaim "Of course !!!"