If you have not done so already, sort these wallpaper patterns by any method you like. You might classify them by color, size, shape, use, etc. BE CREATIVE!

__ TRANSFORMATIONS - __The terms you need to know:

To rotate is to turn about a point. When you make a left-hand turn at a corner, we say you are rotating 90 degrees about the corner.**ROTATION:**

When you look in a mirror, your image is reflected back at you. If you imagine that your image actually exists on the other side of the mirror, you get some idea of the mathematical definition of reflection or mirror image. We can reflect figures by folding along the mirror line as you see below.**REFLECTION:**

Translate means to slide. A translation moves a figure a given distance in a given direction. You can think of a translation as sliding an image across a piece of paper.**TRANSLATION:**

This transformation combines translations and reflections. A glide reflection occurs when you slide an image in one direction and then reflect it over a line.**GLIDE REFLECTION:**

We say a pattern has rotational symmetry when we can turn it by some degree about a point and the pattern looks exactly the same.**ROTATIONAL SYMMETRY:**In the same way, we say a pattern has reflective symmetry when we can fold it across a mirror line so that one half lies on top of the other.**REFLECTIVE SYMMETRY:**Translation symmetry occurs only in patterns that cover a plane. If you can move a copy of a pattern a specific distance in a specific direction so that it lies exactly on top of the original pattern, then the pattern is said to have translational symmetry.**TRANSLATION SYMMETRY:**Glide Reflective symmetry, like translational symmetry, only occurs in patterns that cover a plane. When you move a pattern a given distance in a given direction and then reflect it over a mirror line so that it lies exactly on top of the original pattern, that pattern has glide reflective symmetry.**GLIDE REFLECTIVE SYMMETRY:**

The patterns you have already classified have the above types of symmetry. We call patterns like these which can be repeated to cover the entire plane, "wallpaper patterns." Why do you think mathematicians use this term?

Now that you have looked at examples of the four different types of symmetry, return to your collection of patterns and classify them according to their types of symmetry. Create a chart or a Venn Diagram of your own that will help you in classifying your patterns. Do any of your patterns have more than one type of symmetry? Can you create a table of your patterns' symmetries? How can you fit this information into a Venn Diagram? For hints on how to determine what type of symmetry a pattern has, see our hint book

- Pattern 1

- Pattern 2

- Pattern 3

- Pattern 4

- Pattern 5

- Pattern 6

- Pattern 7

- Pattern 8

- Pattern 9

- Pattern 10

- Pattern 11

- Pattern 12

- Pattern 13

- Pattern 14
- Pattern 15
- Pattern 16
- Pattern 17

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