Visualising and representing

Grannie's watch gains 30 minutes every hour, whilst Grandpa's watch loses 30 minutes every hour. What is the correct time when their watches next agree?

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

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?

Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Can you make the numbers around each face of this solid add up to the same total?

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

How does the perimeter change when we fold this isosceles triangle in half?

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?