Length/distance

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?

Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

I cut this square into two different shapes. What can you say about the relationship between them?

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Weekly Problem 48 - 2008
An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?