Problem
Charles has been blindfolded. The other children 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 Charles walked?

What is this problem about?
In this problem we explore 2-dimensional space by means of Charles 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.

Achievement Objectives
Geometry (Level 2)
- describe and interpret position, using the language of direction and distance
- make clockwise and anticlockwise turns

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment, act it out)

Resources
Blindfold
Mosaic shapes
Blackline master of the problem

Specific learning outcomes
The children will be able to:
- describe movements using clockwise and anticlockwise turns
- follow instructions using distance, direction and turn

Teaching sequence

1. Get all the children to stand up and follow your instructions (best done outside).
   - Turn clockwise.
   - Turn anticlockwise.
   - Walk three steps forward and make a half turn clockwise. Walk three steps forward. Where did you end up?
2. Pose problem to the class.
3. As the children work on the problem ask questions about their use of clockwise and anticlockwise turns.
4. Encourage the children to think of more than one way to solve the problem (act it out, draw a picture)
5. Share solutions.
6. Get the children to select another shape (drawn from a "hat") and write instructions for "walking the shape".
7. Get the children to try out their instructions on another pair.

Extension to the problem
Could you get Charles to ‘walk out’ an ‘S’shape?

Solution
Charles will produce a square with sides three paces long.

Extension: To get an ‘S’ shape, tell Charles to walk forward three paces and make a quarter turn anticlockwise. Then walk forward three paces and make another quarter turn anticlockwise. Next Charles should walk three paces forward followed by a quarter turn clockwise. Then Charles should take three paces forward and take another quarter turn clockwise. Finally he’ll need to take three paces forward.