Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

Rolling Around

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Sugary Diversion

Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

An ant is crawling in a straight line from one corner of a table to the opposite corner when he bumps into a one centimetre cube of sugar. Instead of crawling round it, or eating his way through it, he climbs straight up and over it before continuing on his intended route. How much does the detour add to the length of his journey?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.