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'Coordinate Challenge' printed from http://nrich.maths.org/
Why do this problem?
There are two main parts to this problem
. Learners need to identify the symmetries of various capital letters and to practise reading coordinates. It needs to be approached systematically because not all the clues are straightforward.
It would be good to have the problem displayed on an interactive whiteboard or data projector so that you can use the interactivity throughout the lesson. Start by arranging some of the letters on the grid and asking the children a few questions about where they are placed which will remind them about symmetry and coordinates. For example, you could ask "Where is the letter that has two
lines of symmetry?"; "What do all the letters at ... have in common?".
After this learners could work in pairs on the problem so that they are able to talk through their ideas with a partner. They could either use the interactivity at computers or this sheet
which has letters that can be cut out and moved around. Alternatively, the problem could be copied on to squared paper and the letters drawn on in pencil so that they
can be altered easily.
If pupils do not have much experience of dealing with clues and prioritising their order as this problem requires, it might be appropriate to read each clue in turn as a whole group before working on the task in pairs. This way, you can reassure the learners that it doesn't matter if you cannot immediately use a clue to place a letter definitively. You can also demonstrate that having the
letters to move around, or writing them on the grid in pencil, means that the solution can be refined as more information is revealed.
What kind of symmetry does this letter have?
Where could this letter go on the grid? How do you know?
Which letters fit this clue?
Learners could explore and list the symmetries of all the other letters of the alphabet.
Children could start by identifying the symmetries of the letters, listing whether they have vertical or horizontal line symmetry, rotational symmetry or no symmetry at all. They can then refer to their list as they try to place letters on the grid.