**Lesson 1: Why Move Things Around?**

__Student Outcomes__

Students are introduced to vocabulary and notation related to rigid motions (e.g., transformation, image, and map).

Students are introduced to transformations of the plane and learn that a rigid motion is a transformation that is distance preserving.

Students use transparencies to imitate a rigid motion that moves or maps one figure to another figure in the plane.

**A video to help you with this concept:**

Composition of Rigid Motions: http://youtu.be/O2XPy3ZLU7Y

**Lesson 2: Definition of Translation and Three Basic Properties**

__Student Outcomes__

Students perform translations of figures along a specific vector. Students label the image of the figure using appropriate notation.

Students learn that a translation maps lines to lines, rays to rays, segments to segments, and angles to angles. Students learn that translations preserve lengths of segments and degrees of angles.

**The following animation of a translation would be helpful to a beginner:**

http://www.harpercollege.edu/~skoswatt/RigidMotions/translation.html

**Lesson 3: Translating Lines**

__Student Outcomes__

Students learn that when lines are translated they are either parallel to the given line, or the lines coincide.

Students learn that translations map parallel lines to parallel lines.

**Watch this video on translation:**

http://learnzillion.com/lessons/2574-explore-translations-by-investigating-their-effects-on-line-segments-and-angles

**Lesson 4: Definition of Reflection and Basic Properties**

__Student Outcomes__

Students know the definition of reflection and perform reflections across a line using a transparency.

Students show that reflections share some of the same fundamental properties with translations (e.g., lines

map to lines, angle and distance preserving motion, etc.). Students know that reflections map parallel lines to

parallel lines.

Students know that for the reflection across a line ๐ฟ, then every point ๐, not on ๐ฟ, ๐ฟ is the bisector of the segment joining ๐ to its reflected image ๐′.

**Watch this video to help you with reflection:**

http://learnzillion.com/lessons/2733-explore-reflections-by-investigating-their-effects-on-line-segments-and-angles

http://www.brightstorm.com/math/geometry/transformations/reflections/

http://www.brightstorm.com/math/geometry/transformations/reflections/

**Lesson 5: Definition of Rotation and Basic Properties**

__Student Outcomes__

Students know how to rotate a figure a given degree around a given center.

Students know that rotations move lines to lines, rays to rays, segments to segments, and angles to angles.

Students know that rotations preserve lengths of segments and degrees of measures angles. Students know

that rotations move parallel lines to parallel lines.

**Watch this video on rotation:**

**Lesson 6: Rotations of 180 Degrees**

__Student Outcomes__

Students learn that a rotation of 180 degrees moves a point on the coordinate plane (๐,๐), to (−๐,−๐).

Students learn that a rotation of 180 degrees around a point, not on the line, produces a line parallel to the given line.

**A video about this lesson:**

http://learnzillion.com/lessons/3517-understand-how-reflections-and-rotations-change-coordinates

Students learn about the sequence of transformations (one move on the plane followed by another) and that a sequence of translations enjoy the same properties as a single translation with respect to lengths of segments and degrees of angles.

Students learn that a translation along a vector followed by another translation along the same vector in the opposite direction can move all points of a plane back to its original position.

http://learnzillion.com/lessons?utf8=%E2%9C%93&query=sequence+of+transformations&commit=search

**Lesson 7: Sequencing Translations**__Student Outcomes__ Students learn about the sequence of transformations (one move on the plane followed by another) and that a sequence of translations enjoy the same properties as a single translation with respect to lengths of segments and degrees of angles.

Students learn that a translation along a vector followed by another translation along the same vector in the opposite direction can move all points of a plane back to its original position.

**A video to watch:**http://learnzillion.com/lessons?utf8=%E2%9C%93&query=sequence+of+transformations&commit=search

**Lesson 8: Sequencing Reflections and Translations**

__Student Outcomes__

Students learn that the reflection is its own inverse transformation.

Students understand that a sequence of a reflection followed by a translation is not equal to a translation followed by a reflection.

**A video to watch:**

**http://www.brightstorm.com/math/geometry/transformations/transformations-and-isometries/**

**Lesson 9: Sequencing Rotations**

Student Outcomes

Students learn that sequences of rotations preserve lengths of segments as well as degrees of measures of angles.

Students describe a sequence of rigid motions that would map a triangle back to its original position after being rotated around two different centers.

**This video will help you:**

**http://youtu.be/O2XPy3ZLU7Y**

Student Outcomes

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