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: Geometers 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 Geometers Sketchpad. Worksheets to use with Geometers 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 Geometers 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:
- Become familiar with the rigid motions of reflection,
rotation, translation, and dilation.
- Practice use of Geometers Sketchpad using the activity
- Prepare a tentative design concept by choosing your polygon
- Use the first design day to experiment with your design.
- Print your schematic with reflection lines and take note of
translation vectors used and angles of rotation.
- Prepare your schematic using color coding so that all
transformations are clear and provide a legend for your
Directions to teacher/administrator using the lesson?
- Teach rigid motions
- Provide transformation activity sheets to familiarize students
with Geometers Sketchpad and the rigid motions (see
attachments-CJones.cwk in ClarisWorks 5.0)
- Encourage students to have a design plan before they begin
(see attachments-CJones.cwk in ClarisWorks 5.0)
- Encourage students to use the first design day to experiment
with their design
- Encourage students to take careful note of reflection lines,
translation vectors, angles of rotation, and dilation scale
- 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