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Make a cube out of straws and have a go at this practical challenge.

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Reasoning about the number of matches needed to build squares that share their sides.

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Tangram Paradox

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Drilling Many Cubes

Age 7 to 14 Challenge Level:

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 !!!"