Charlie has been blindfolded. The other students have given him some instructions to follow. They say that he has to walk three steps forward and then make a quarter turn clockwise. They get him to do that three more times in a row.

What shape has Charlie walked?

In this problem we explore 2-dimensional space by means of Charlie's body. It is a chance to experience movement under direction and hence to start to get a feeling for (or to practice) direction, turns and distance in the plane.

### Problem

Charlie has been blindfolded. The other students have given him some instructions to follow. They say that he has to walk three steps forward and then make a quarter turn clockwise. They get him to do that three more times in a row. What shape has Charlie walked?

- Get all the students to stand up and follow your instructions (best done outside).

-*Turn left.*

- Turn right.

- Walk three steps forward and make a half turn left. Walk three steps forward. Where did you end up? - Pose problem to the class.
- Encourage the students to think of more than one way to solve the problem (act it out, draw a picture)
- Share solutions.
- Get the students to write instructions for "walking another shape".
- Get the students to try out their instructions on another pair.

#### Extension to the problem

Could you get Charlie to ‘walk out' a square shape using clockwise and anticlockwise turns?

What other shapes can you instruct Charlie to 'walk out'?

Could you give Charlie instructions to 'walk' the shape of a building in your school?

#### Solution

Charlie will produce a square with sides three paces long.

#### Extension:

The students' instructions would need to include telling Charlie to walk the same number of paces for each side and to make 3 turns either all clockwise or all anticlockwise.

Instructions could be given for Charlie to walk an oblong (rectangle).

Students could 'walk' (round) a chosen building, noting a starting place and counting paces, then give instructions to another student.