[ppt]transformations! translations, reflections, and...

Transformations!Translations, Reflections, and

Rotations (also known as Slides, Flips, and Turns)

Mel BalserEME 4401

November 7, 2007

Free powerpoint template: www.brainybetty.com 2

Sunshine State Standardsand

National 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.


Materials• Computer• SmartBoard and accessories

(markers, eraser, etc)• Internet access• Video Camera• Editing Software (such as

iMovie)


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!

http://youtube.com/watch?v=oUbmtMcNxxE


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.


What is a translation?

M.C. Escher

Butterfly Wing Close-up


What is a translation?• Translate these objects however you

want!Example:


What is a translation?• What are some examples of translations

that you have seen?


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.


What is a reflection?• A reflection can be thought of as flipping

an object over the line of reflection

In waterIn a mirror

In glassIn a shiny surface

http://forums.renderplus.com/wiki/index.php?title=Image:Reflection80.jpg


What is a reflection?• Can you flip these objects over the line

of reflection?

Example:


What is a reflection?• What are some examples of reflections

that you have seen?


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.


What is a rotation?• Rotations are made clockwise or

counterclockwise

Check this out!

http://www.snafu.com/images/Rotation.gif


What is a rotation?• Can you rotate these objects?• Example:


What is a rotation?• What are some examples of rotations

that you have seen?


Let’s make it a bit more interactive…

•Geoboard Practice•Play Golf! Try and Make Par!

•The Less Moves, the Better!

http://nlvm.usu.edu/en/nav/frames_asid_303_g_3_t_3.html

http://www.mathsonline.co.uk/nonmembers/gamesroom/transform/golftrans.html

http://www.mathsonline.co.uk/nonmembers/gamesroom/transform/golftrans.html

http://www.mathsonline.co.uk/nonmembers/gamesroom/transform/postshape.html

http://www.mathsonline.co.uk/nonmembers/gamesroom/transform/postshape.html


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.

[ppt]transformations! translations, reflections, and...

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