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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:

Take a look at the interactivity below which shows regular polygons "rolling" along the horizontal surface, leaving a trace of the path of the red dot.

A blue dot tracks the height of the red dot whilst a green dot tracks the horizontal distance travelled by the red dot.

The graph records either the horizontal distance travelled by the red dot or the height of the red dot over time.

Experiment by positioning the red dot at the centre of the polygons, at one of the vertices or at the centre of one of the sides of the polygons and explore how this affects the two graphs.

Full Screen Version


Challenge:

Can you now work out what produced the following two graphs?
The rolling polygon had a radius of 45.
Can you work out how many sides it had and where the red dot was placed?
Try to explain how you worked it out.

Horizontal distance/time graph
Height/time graph