You may also like

problem icon

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.

problem icon

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?

problem icon


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

Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

Are the following statements always true, sometimes true or never true?

How do you know?


What about these more complex statements?

You could cut out the cards from this sheet (wordpdf) and arrange them in this grid.

Can you find examples or counter-examples for each one?

For the “sometimes” cards can you explain when they are true? Or rewrite them so that they are always true or never true?