Being curious

There are lots of different methods to find out what the shapes are worth - how many can you find?

Can you find the values at the vertices when you know the values on the edges?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Sequences of multiples keep cropping up...

The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers? 

How did the the rotation robot make these patterns?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

How many winning lines can you make in a three-dimensional version of noughts and crosses?