Investigate the Rigid Motions of Reflection, Rotation, Translation, and Dilation

Investigate the Rigid Motions of Reflection, Rotation, Translation, and Dilation

Course(s)/Subject(s): Middle School Mathematics 8 and Geometry

Grade Level(s): 8 and Geometry

Key Words: Geometric transformation, reflection, rotation, translation, dilation

Developer(s) Name: Cynthia Jones

School: Carl Sandburg Middle School

Attached Files: CJones

Approximate Time Frame: 5-6 class periods

Materials/Equipment Needed: Geometer’s Sketchpad, computer lab

Description of Lesson (includes context): Students will investigate the rigid motions of reflection, rotation, translation, and dilation. This investigation will be accomplished through classroom instruction and exploration using Geometer’s Sketchpad. Worksheets to use with Geometer’s Sketchpad have been included with this lesson plan (see attachments-CJones.cwk in ClarisWorks 5.0). The final activity (also attached) will be a student-created design illustrating all the transformations.


1. What is the objective of this lesson?

VA FCPS POS Standards: MSM Standard 2 Construct, measure, and analyze geometric figures
Geometry Standard II Transformations and Symmetry

VA FCPS POS Benchmarks
: MSM Benchmark 2.3 Students explore geometric figures
Geometry Benchmark Students investigate and apply symmetries, isometries, and dilations through geometric movement

VA FCPS POS Indicators
: MSM Indicator 2.3.1 Students rotate, reflect, translate, and dilate two-dimensional figures
Geometry Indicator Create and compare preimages and images for reflections, translations, glide reflections, rotations, and dilations on plane figures

VA SOL(s) (including Computer/Technology)
: Mathematics SOL 8.9,
Geometry SOL 2, C/T 8.1



2. What will we examine as evidence of students’ knowledge and/or skill?

Product(s): Student-created design including the schematic detailing the transformations used

Performance(s): Teacher observation of student use of Geometer’s Sketchpad and appropriate application of the transformation



3. What exactly will the students and teacher do during the lesson?

Directions to students for proceeding with the lesson:

  1. Become familiar with the rigid motions of reflection, rotation, translation, and dilation.
  2. Practice use of Geometer’s Sketchpad using the activity sheets provided.
  3. Prepare a tentative design concept by choosing your polygon and transformations.
  4. Use the first design day to experiment with your design.
  5. Print your schematic with reflection lines and take note of translation vectors used and angles of rotation.
  6. Prepare your schematic using color coding so that all transformations are clear and provide a legend for your coding.

Directions to teacher/administrator using the lesson?

  1. Teach rigid motions
  2. Provide transformation activity sheets to familiarize students with Geometer’s Sketchpad and the rigid motions (see attachments-CJones.cwk in ClarisWorks 5.0)
  3. Encourage students to have a design plan before they begin (see attachments-CJones.cwk in ClarisWorks 5.0)
  4. Encourage students to use the first design day to experiment with their design
  5. Encourage students to take careful note of reflection lines, translation vectors, angles of rotation, and dilation scale factors
  6. Encourage students to use color coding on their schematic


4. What options in presentation(s) and/or response(s) are suggested in order to provide the opportunity for all students to demonstrate achievement of the benchmark(s) and indicator(s)?

Students may use one polygon instead of two
Degree of design complexity is student choice
Extra time in lab