Use the half arrow shape as a starting block to produce your own wallpaper friezes. Put this shape into the grid to make a repeating pattern.
How many different repeating patterns can you make?
There is a great deal of mathematics in everyday objects. Walls of rooms are no exception. Wallpaper friezes exploit reflections, translations and rotations. Producing their own friezes will give students the opportunity to explore all of the basic transformations of the plane.
There are three transformations:
Translations (or shifts)
Rotations (or turns)
Reflections
Use the half arrow shape as a starting block to produce your own wallpaper friezes. Put this shape into the grid to make a repeating pattern.
How many different repeating patterns can you make?
Teaching sequence
You might try to find actual wallpaper friezes that match up with the patterns found in the problem.
There are 7 different wallpaper friezes that can be made using the basic block in the picture. We list them all here.
Note: Possible patterns such as:
have the same symmetry as one of the 7 listed. For instance 8 = 1 and 9 = 5.
Printed from https://nzmaths.co.nz/resource/friezes at 5:37am on the 20th May 2022