Transformations! Translations, Reflections, and Rotations (also known as Slides, Flips, and Turns)

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Transformations!Translations, Reflections, and
Rotations (also known as Slides, Flips, and
Turns)

• Mel Balser
• EME 4401
• November 7, 2007

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Sunshine State StandardsandNational Educational
Technology Standards

• MA.C.2.2.2 The student visualizes and
  illustrates ways in which shapes can be combined,
  subdivided, and changed - predicts, illustrates,
  and verifies which figures could result from a
  flip, slide, or turn of a given figure.
• Technology productivity tools
• Students use technology tools to enhance
  learning, increase productivity, and promote
  creativity.
• Students use productivity tools to collaborate in
  constructing technology-enhanced models, prepare
  publications, and produce other creative works.

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Materials

• Computer
• SmartBoard and accessories (markers, eraser, etc)
• Internet access
• Video Camera
• Editing Software (such as iMovie)

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What is a transformation?

• A transformation is a change in the position or
  size of an object
• Movements that do not change the size or shape of
  the object moved are called rigid
  transformations
• There are three types of rigid transformations
  Translations, Reflections, and Rotations. These
  are more commonly referred to as Slides, Flips,
  and Turns.
• To learn more about each, check this out!

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What is a translation?

• Take one step in any direction
• You have just translated yourself!
• More commonly known as slides
• A translation "slides" an object a fixed distance
  in a given direction. 
• The original object and its translation (known as
  the image) have the same shape and size, and they
  face in the same direction.

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What is a translation?
Butterfly Wing Close-up
M.C. Escher
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What is a translation?

• Translate these objects however you want!
• Example

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What is a translation?

• What are some examples of translations that you
  have seen?

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What is a reflection?

• Take a look in the mirror.
• You are staring at a reflection of yourself!
• More commonly known as flips
• An object and its reflection have the same shape
  and size, but the figures face in opposite
  directions.
• A reflection can be seen in water, in a mirror,
  in glass, or in a shiny surface. 

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What is a reflection?

• A reflection can be thought of as flipping an
  object over the line of reflection

In water
In a mirror
In a shiny surface
In glass
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What is a reflection?

• Can you flip these objects over the line of
  reflection?
• Example

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What is a reflection?

• What are some examples of reflections that you
  have seen?

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What is a rotation?

• Turn yourself to the right
• You have just rotated yourself!
• Commonly known as turns
• A rotation is a transformation that turns a
  figure about a fixed point called the center of
  rotation. 
• An object and its rotation are the same shape and
  size, but the figures may be turned in different
  directions.

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What is a rotation?

• Rotations are made clockwise or counterclockwise

Check this out!
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What is a rotation?

• Can you rotate these objects?
• Example

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What is a rotation?

• What are some examples of rotations that you have
  seen?

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Lets make it a bit more interactive

• Geoboard Practice
• Play Golf! Try and Make Par!
• The Less Moves, the Better!

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Want to try more?

• Use a video camera to go outside and find
  examples of transformations in nature and around
  the school. Be sure to include slides, flips,
  AND turns in your video. Use iMovie to edit your
  video. Make it good! These will be presented to
  the class and posted on YouTube to help others in
  their quest to learn more about translations,
  reflections, and rotations.