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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.
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?
Quadrilaterals
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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 (word, pdf) 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?
NRICH is part of the family of activities in the Millennium Mathematics Project.