Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Freida from Little Chalfont Primary
School and Richard from Wilson's School found one way of starting
at $y = 4x + 7$ and ending at $y = 4x-2$:
Sophie, Evie and Sinthu from Dr Challoner's
High School also started with the same two reflections but then
switched the translations and still ended at $y = 4x-2$:
Keira, Christina and Amy, also from Dr
Challoner's High School, explained why they also started with a
pair of reflections:
Jack from Hertford South Primary drew a table of all the
possibilities and explains: