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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?

N Is a Number

N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

Up and Across

Age 11 to 14 Challenge Level:

Try to approach the problem systematically, keeping one variable fixed and just altering the other one.

As you go along try to understand why the graph takes the shape that it does:
  • by relating it to the rolling polygon and the journey of the red dot
  • by trying to predict what will happen before you set the polygon rolling
Could the dot have been on the centre of a polygon?
Try for each of the polygons.

Could the dot have been on the centre of the base of a polygon?
Try for each of the polygons.

Could the dot have been on the centre of one of the sloping sides of a polygon?
Try for each of the polygons.

Could the dot have been on the centre of a side opposite the base of a polygon?
Try for each of the polygons.

Could the dot have been on a vertex opposite the base of a polygon?
Try for each of the polygons.

Could the dot have been on a vertex on the base of a polygon?
Try for each of the polygons...

Alternatively...
  • try all possible positions of the dot in a triangle,
  • and then in a square,
  • and then in a pentagon,
  • and then in a hexagon...