Symmetry on a Friday

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

(remember - symmetrical means - can I cut it into 2 identical parts?)

How many different symmetrical patterns can you make by having different squares coloured? Use a different 3 by 3 grid each time, don't just add more and more coloured triangles to one grid.

Start by only colouring in one triangle, how many different symmetrical patterns can you make? Remember, you can put the colour in different triangles.

Now colour in two triangles

Now three

Now four

Now five

Now six

Now seven, then eight, then nine.

  

Here are some questions you might like to consider:

• How does the number of patterns with 6 cells shaded relate to the number with 3 cells shaded?
• Can you make more patterns using more than one colour?

Can you complete this table, and do you notice anything?

Number Shaded	Number Patterns Made
0
1
2
3
4
5
6
7
8
9