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The 3 by 3 grid has 4 lines of symmetry. How might this help?

Try shading only one square. What symmetries are possible?
Try shading 2, 3, 4, ... squares. What symmetries are now possible?

How helpful would this table be?

  Lines of symmetry
  0 1 2 3 4
Shaded squares 1        
2          
3          
4          

What other rows or columns could you add to this table?