Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
How far have these students walked by the time the teacher's car
reaches them after their bus broke down?
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?
Mark marked out the points $J$, $K$, $L$ and $M$ on a straight line, so that $JK=13$cm, $KL=11$cm, $LM=14$cm and $MJ=12$cm. What is the distance, in cm, between the two points furthest apart?
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.