Lesson 6 Decontamination

Episode 2

Reasoning Resources: Worksheet 2
Whole class preparation: the four compass directions
Beginning of recognition of the independence of compass directions from individuals and map.
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Links with physical geography. There is ‘real north’ out there, which is only pictured on the page by a convention. We can cross- check where we are on maps with other knowledge about the compass directions and the sun etc.
You could ask the class to imagine there is a need to use the robots repeatedly, for checking and decontamination etc, so that there are other kinds of robots.That was the cheapest robot available. We will call that a Left-Right robot. There is an alternative called an N-E-S-W robot. What can you tell me about this robot? Possible responses: ‘lt can move north, south, east or west’; ‘It needs to know which way is north before it can start’; ‘It always knows where north is'.

The pupils should be able to explain that the robot will move north or east or south or west a particular distance. They may point out that north was not marked on the map on Worksheet 1. On this particular map N needs to be drawn on a vertical line pointing up the page.

Give out Worksheet 2, one per pair, and ask how it may be useful.

It may be appropriate to clarify which way is east once we know which way north is.In some cases a lively discussion may ensue if you ask the class if they know where north actually is and how they know it is so. Possible responses could involve use of a compass, where the sun rises or is at noon, the church or mosque orientation, or local knowledge of a road going south or north. For real-life maps when you have found north you can orientate the map to it, which is a good way of reading a map.NB it is not possible for this robot to move diagonally, e.g. NE etc.
Pair and small group work
Here pupils can link together ‘absolute’ directions of NSEW and ‘relative’ directions of left and right. The distances involved are the same for both, but changing the directions may require more thought and discussion.

Ease with the compass directions may only be on the page and with robots, but may not be in real life.
Pupils should work out instructions for this new robot, for the same moves they worked on before. The key questions here are:

  • What do you do to work out the homeward journey for this robot?
  • What are the links between this robot and the first robot?
  • Can you turn instructions for a Left-Right robot into instructions for an N-E-S-W robot?
  • Which method of giving directions is easier? Why?
    Typical responses would be:‘The N-E-S-W robot is easier to use’; ‘We know where north is 50 N-E-S-W is easy’; ‘We're looking down on it, so N-E-S-W is best’; ‘l wouldn't say “go east, then south” to get to the chip shop. I'd say “go straight on and then turn right”; ‘If I'm talking to someone | use left and right’
  • Whole class sharing/discussion
    Recognising and representing which moves to add or subtract to produce the inverse of which part of the return move would be approaching vector concepts on a grid. Discuss the links between the two different robots, including the similarities and the differences. A discussion of which is the easiest/best method to use should throw up suggestions that favour both versions. This could lead to an understanding that different methods are going to be more or less appropriate in different situations.
    Extension
    Suggest that a compass robot can reach the two contamination sites in one journey and return to the landing site without retracing its steps. That would need a longer programme of instructions, especially with the need to avoid the lake. Some pupils may then find how to relate the simpler return journey to the separate journeys that allowed the two sites to be visited.

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    Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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