This problem solving activity has a geometry focus.
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?
- Follow instructions using distance, direction and turn.
- Explore basic attributes of simple 2D shapes.
- Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment, act it out).
In this problem we explore 2-dimensional space by using Charlie's movements. It is a chance to experience movement and basic shape attributes. Through this, students start to get a feeling for direction, turns and distance in the plane.
- Mosaic shapes (or a digital representative - search for interactive shape tool)
- Blindfold
- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
The 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?
Teaching Sequence
- 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?
- How do you know that the shape you created was a square? Draw attention to the attributes of the shape created (e.g. length/number of sides, number of corners) - Pose problem to the class. Ensure students understand the directional language used in the problem (e.g. clockwise, quarter turn). You could use a game of Simon Says to practise giving and following these directions.
- 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". Use mosaic tiles (or a digital representation) to provide students with a model from which they can create accurate directions.
- Get the students to try out their instructions on another pair.
Extension
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.
Solution to the 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) or other shape. Look for students to transfer their knowledge of the attributes they can see on a physical shape (e.g. the number of sides) to their instructions.
Students could 'walk' (round) a chosen building, noting a starting place and counting paces, then give instructions to another student.