Lesson Plan
Translation, Rotation, Reflection

The Google search terms    I used here.


Lesson Plan - includes some online activities    Click on the blue links.


This lesson is designed to introduce students to translations, reflections, and rotations.
Upon completion of this lesson, students will:
* have been introduced to the concepts of translation, reflection, and rotation.
* have practiced translating, reflecting, and rotating two-dimensional objects on the coordinate plane.


In this series, you will study the four geometric transformations—rotations, reflections, translations, and glide reflections—as a mathematician would: learning how they are defined, what they change, what they don't change, and how they are related to each other.


Develop your transformations skills. You will be able change shapes using rotations, reflections, translations or enlargements - and your mouse. This is at Mathsnet. An excellent interactive resource.

Other interactive resources here 

The link above leads to http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm  It is described as 
"Rotations; translations, or slides; and reflections, or flips, are geometric transformations that change an object's position or orientation but not its shape or size. The interactive figures in this four-part example allow a user to manipulate a shape and observe its behavior under a particular transformation or composition of transformations."


An interesting concept " This lesson allows students to explore the concepts of reflections, translations, and rotations while working their way through a snowboarding course. Students will also learn about M. C. Escher and view some of his artwork. Students will ultimately create a geometric design which they can incorporate into a graphic of a jacket." Online activities at PBS Cyberschool.


Translations and Rotations

Reflections and Glide Reflections


Examples of reflections, rotations and translations and explanations of terms.

from primaryschool.com.au - lots of great ideas on tessellations and tangrams too.


This site allows the demonstration of the following



E-zgeometry page - lots of links

A Disney named site called "Thirteen org"
  • Students explore the relationships among geometric transformations (translations, reflections, rotations, and dilations), tessellations (tilings), and congruence and similarity.
  • Students investigate and describe geometry in nature and real-world applications.
  • Students design a tessellation.

eg. Has a great site for making tessellated patterns. Called Kali Interactive.

Not all the links work but some excellent ones worth exploring to see if they fit!


The Seventeen Wallpaper Tilings

Some of the most fascinating tilings are the so-called wallpaper tilings. These tilings are so symmetric that they can be built up by starting with a single tile by following simple sets of rules. But perhaps the most interesting thing about the wallpaper tilings is that there are exactly seventeen of them! Interactive.


An excellent site with great interactive resources at the Math Interactive Site. R - 12! Includes a great section on the topic!


Another interactive site. A great geometry resource. Lots of shapes that can be manipulated. The Archytech organization. Useful as "Students will use a pattern block applet written by Jacobo Bulaevsky to reinforce the idea of rotational symmetry." Point out the rotation tool for the applet. An activity is here.
The starting point for this activity was here.


This one lets you rotate and flip shapes http://www.galaxy.gmu.edu/~devsuper/test8/geojrmain.html Dr. Super! Give problems too.


Some tangram puzzles using interactive materials at http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm 
"Describing figures and visualizing what they look like when they are transformed through rotations or flips or are put together or taken apart in different ways are important aspects of geometry."
Also here http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm 

A "must see" site http://illuminations.nctm.org/imath/index.html See this for other activities.


 Lots of geometry links http://www.gvsu.edu/math/students/geomsites.html 

Varnelles introduction to geometry - an excellent resource.

Geometry sites on the internet - a resource.

An excellent site called  "Introduction to the World of Virtual Manipulatives. Key Sites to Explore" is at http://inet.paterson.k12.nj.us/~pps/math/mathstuff.htm

Educational Sites - Math
Geometry students can use these Java apps to explore transformations such as translations, reflections, etc.

Transformation of a pentagon


  • Topic: Transformations and symmetry
  • Topic: Reflection
  • Topic: Translation
  • Topic: Rotation
  • Topic: Glide
  • Topic: Dilation
  • Topic: Tessellations
  • Topic: Construction and loci

  • From http://mathforum.org/mathtools/cell.html?rc=tool
    Also transformational geometry

    Also called slides, flips, and turns

    May 2004


    August  2005