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Charlie created a symmetrical pattern by shading in four squares on a 3 by 3 square grid:
pattern with squares

Alison created a symmetrical pattern by shading in two triangles on a 3 by 3 isometric grid:

pattern with triangles
Choose whether you would like to work on square grids or isometric grids.
 
How many different symmetrical patterns can you make?
  
Here are some questions you might like to consider:
  • How many different patterns can you make if you are only allowed to shade in one... two... three... four cells?
  • How does the number of patterns with 6 cells shaded relate to the number with 3 cells shaded?
  • Can you make patterns with exactly one... two... three... four lines of symmetry?
  • Can you make patterns with rotational symmetry AND lines of symmetry?
  • Can you make patterns with rotational symmetry but NO lines of symmetry?
  • Can you make patterns using more than one colour?