Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# How Far Does it Move?

## You may also like

### Walk and Ride

### Rolling Around

### N Is a Number

Or search by topic

Age 11 to 14

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Try to approach the problem systematically.

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 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...

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?

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?