# Blindfolds

Achievement Objectives
GM1-3: Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
Student Activity

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?

Specific Learning Outcomes
Follow instructions using distance, direction and turn
Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment, act it out)
Description of Mathematics

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.

Required Resource Materials
Activity

### 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?

1. 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?
2. Pose problem to the class.
3. Encourage the students to think of more than one way to solve the problem (act it out, draw a picture)
4. Share solutions.
5. Get the students to write instructions for "walking another shape".
6. 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.

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