This challenge is quite tricky, but it is a motivating context in which children can develop a logical, systematic approach.
It would be useful to introduce the problem on an interactive whiteboard so that the whole group can be involved with deciding which mats to turn. Alternatively, cardboard mats coloured differently on each side could be used and pinned to a board. This initial whole group work will familiarise the children with the "rules" of the problem so that they will be confident to find the smallest
number of moves in pairs.
It will be important for them to devise a recording system that they are happy with, and this is something that can be addressed in the introduction, for example by asking whether they would be able to repeat the moves they made. Encourage them to think about odd and even numbers of flips, and when they come to investigate other numbers of tiles, you might expect them to generalise for multiples of three at least.
Elise Levin-Guracar kindly shared this sheet with us which includes a chart for tracking moves. She found it was was helpful to point out to students where they were trying the same thing over and over again, and where they could be trying something new. The last page of the document is a chart by number of dots and the minimum moves to flip. There are also blank moves charts. Thank you, Elise!
How will you keep track of what you have tried?