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Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Factor-multiple Chains

Age 7 to 11 Challenge Level:

If you haven't already had a look, it might be worth investigating this spreadsheet which you can put different numbers into to make chains.
For the smallest chain, what number might it be a good idea to start with on the left?
What could you try first to make the largest chain? You could choose to start with a particular number on the right this time.
How will you know which numbers you have already tried?