Conjecturing and generalising

problem
Route to infinity

Age

11 to 14

Challenge level

Can you describe this route to infinity? Where will the arrows take you next?
problem
Cunning card trick

Age

11 to 14

Challenge level

Delight your friends with this cunning trick! Can you explain how it works?
$Who \is the \fairest of \them \all ?$

problem
Who is the fairest of them all ?

Age

11 to 14

Challenge level

Explore the effect of combining enlargements.
problem
...on the wall

Age

11 to 14

Challenge level

Explore the effect of reflecting in two intersecting mirror lines.
problem
Mirror, mirror...

Age

11 to 14

Challenge level

Explore the effect of reflecting in two parallel mirror lines.
problem
Move a match

Age

7 to 11

Challenge level

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
problem
Trapezium four

Age

14 to 16

Challenge level

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
problem
Real statistics

Age

7 to 11

Challenge level

Have a look at this table of how children travel to school. How does it compare with children in your class?
problem
Integral sandwich

Age

16 to 18

Challenge level

Generalise this inequality involving integrals.
problem
Maximum scattering

Age

16 to 18

Challenge level

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?