Reflections

I am standing behind five pupils who are signalling a five-digit number to someone on the opposite side of the playground. What number is actually being signalled?

Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that was impossible, could you explain why ?

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket?

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.