Geometric Reflections

Target Grade/Subject:

This lesson is targeted towards ninth and tenth grade students in a general high school geometry course. This level contains student pursuing advanced and standard diplomas. Some students in this class will go on to take more mathematics courses, while for others it is their last math course that they will take. Therefore, it is a highly variable population in terms of performance, goals, and motivation.

This group of students relies heavily on teachers for expertise and guidance in the subject area. One main characteristic of this age group is the need to know the purpose and relevance of what they are learning. They will constantly be asking, “Why do I need to learn this? Will I use this later on in life?” and similar questions. Students do not want to spend the time learning a concept if they feel that they will not use it later on in life. The students will not apply the knowledge that they learn – they will just memorize it for the test. Most students this age benefit from learning techniques, tools and methods other than the textbook and lecture. Having them interact and be able to explore reflections hands-on is very beneficial to their learning.

This lesson will engage students in the topic of reflections. They will be using the computer program Geometry Sketchpad to help them discover the characteristics of a reflection and how to determine the reflection image and coordinates. The computer program is very quick and easy to use in exploring different shapes, images, and lines of reflections. Students will receive clear, step-by-step instructions on reflections, but will be able to have some freedom in choosing their shapes, sizes, and coordinate points. Students will be able to understand reflections and its properties and be able to see examples of reflections in everyday life.

Objective:

The students will determine the characteristics of reflections, demonstrate how to sketch the reflection images and be able to state the coordinates of the reflected image; students will demonstrate their understanding of the lesson through a short worksheet.

SOL Geometry 2: The student will use pictorial representations, including computer software and coordinate methods to solve problems involving symmetry and transformation. This will include:

*Using formulas for finding distance, midpoint, and slope

*Investigating and determining whether a figure is symmetric with respect to a line or a point

*Determining whether a figure has been translated, reflected, or rotated

(This lesson only applies to the reflection section of this SOL)

Materials:

Ø Geometry Sketchpad computer program

Ø One computer for each student or pairs of students

Ø Handout on reflections with step-by-step directions

Ø Worksheet to be completed at the end of the lesson

Students should have some previous knowledge about and experience with the computer program.

Lesson Description:

Ø Introduce transformations and discuss the definitions of them. Transformations are different ways of moving geometric figures.

Ø Discuss the terms used with transformations, such as pre-image (the point or figure before transformation), image (point after transformation), and isometry (when the pre-image and image are congruent).

Ø Define reflections (reflecting a point or image over a line of reflection so that a point and its corresponding reflected point are perpendicular bisectors of each other).

Ø Proceed with the handout labeled “Reflections”. (SEE ATTACHED) Go step-by-step and answer any questions.

Ø At the end of the lesson, give the students the worksheet to complete on their own.

Evaluation Procedure:

The objectives are met if the students are able to correctly complete the worksheet on their own. For learning purposes, full understanding is more important than receiving a good grade, thus the student should be allowed to go back and correct what he/she did wrong until everything is correct.