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Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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Reflecting Squarely

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Shady Symmetry

How many different symmetrical shapes can you make by shading triangles or squares?

Robotic Rotations

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Here is an interactivity that allows you to create rotation patterns.
Move the blue dots to create a shape and use the slider to choose an angle of rotation.




Once you've explored the interactivity, take a look at the patterns below and see if you can recreate them. If you like, you can print out the patterns.

        

How did you work out which angle to rotate by each time?




To make this picture, Charlie drew a kite and then told the robot to rotate it through an angle of $144^{\circ}$.
Alison used an angle of $216^{\circ}$ and got exactly the same pattern!

What other angles could they have used?
Can the other patterns be made using more than one angle?



What is the link between the angle and the number of copies of the image in the pattern?